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How to Differentiate in Middle School Math - Maneuvering the Middle

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How to Differentiate in Middle School Math - Maneuvering the Middle

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Today on the blog (and podcast), we have Marissa McCarthy! She is an amazing teacher who uses Maneuvering the Middle resources to teach and differentiate for her 6th grade students. She is a whiz at small groups and a wealth of knowledge.

Marissa has just wrapped up her 13th year of teaching math in Ohio. She has earned her masters in gifted education, previously coached her MathCounts Team, and has previously taught 6th through 8th grade, Algebra 1, and Geometry.

LISTEN ON: APPLE PODCAST | SPOTIFY The interview has been edited for succinctness below.
How do you differentiate in your classroom?

My favorite way to differentiate is utilizing small groups, providing enrichment activities (6th graders are still excited to embrace a challenge), using formative data to reassess my students in small groups, and providing student choice.

What are some of the ways you provide student choice?

One of the ways is pretty simple. I give students a choice on how they practice, whether that be paper based or a digital activity. Or I give them a choice when completing a project. For example, if we are doing a statistics project comparing weather, I allow them to pick the locations.

What tips do you have for someone who needs help differentiating?

1. Remember that differentiation gets easier as the year progresses. Use your formative assessments to help you determine how you want to differentiate.

2. There are a couple of units that I pretest because students come in with so much knowledge, so I am able to determine if there are things that I don't need to cover or skills that I can enrich.

3. Do not reinvent the wheel. Use resources that are already written. Pick one way to differentiate per unit if you aren't sure where to start.

To learn more about Maneuvering the Middle resources, click here.

Can you tell me about your small group routine?

Before the pandemic, I divided the class into 5 groups based on student needs. To help with the routine, each group was named a color, so I could just say "I need to meet with the purple group" today. Some other helpful background information: my classes are 58 minutes and I would spend about 15 minutes per group.
The goal of small groups could be any of the following:

1. Introduce new content

2. Practice previously taught skills

3. Reteach after an assessment.

One of the easy ways to differentiate was how much time I spent with my different groups. Some groups received more time and some less time.

When I had a co-teacher and a student teacher, the groups were more supported, but when it was just me it might take 2 class periods to get through all of the groups, but it is totally worth it.

What is everyone else doing when you are working in a small group?

That is a struggle! It can be hard to manage, but the face time I get with my students is important. Students might be working on a paper or digital activity, or a related performance task.
Everyone gets better with practice. If small groups didn't go well the first few times, keep trying!
Let's talk about vertical alignment! How has your background helped prepare you for teaching 6th grade?

I have taught all of the middle school standards plus Algebra 1 and Geometry, so I know where all of the standards are going. For example, in sixth grade, students write algebraic expressions. Because I have taught Algebra, I was able to pull systems of equations problems and talk with students that what they were learning as sixth graders were preparing them for Algebra. Many students were able to write these two variable equations, and a few students figured out how to solve. I was able to do the same thing with GCF and polynomials. Students were excited to see where they were headed in math!

On the flip side, I observed a fifth grade class and learned so much about where my students were coming from. If you get a chance to do this, you should!

[Check out this link to hear more or read more about 4th and 5th grade Math from Brittany Hege of Mix and Math]

What does a typical planning period look like for you?

My planning period looks different every day. Maneuvering the Middle resources have definitely helped streamline things.

Some planning periods are focused on planning for my small groups. I start by asking: what am I trying to accomplish in my small group? Introduce a new concept, remediate, practice a previously taught skill? I might be deciding on the set of problems I want to use for practice with them or I might decide to use the student handout and make it a mini lesson at the small group table instead of the whole group. I sift through the activities and use them for students in the small group or students not in the small group.

I update my Google Slides with the agenda for the day to keep students on track and put materials on schoology for the day. [Note from the editor: this is just a small fraction of what any teacher does in a given planning period.]

What other tips do you have?

For the digital activity exit tickets, I add a question in Google Forms asking for their class period so I can sort them quickly for my gradebook. I also change the settings, so students know which problems they got wrong, but not the correct answer, so they can try again if they didn't get a perfect score.

For the digital activities, I grade one page for accuracy. If a student doesn't master it, I print off that slide and use it in my small group with those students. No need to start over with a brand new set of problems that I have to write or search for.

Thank you, Marissa, for sharing your tips for using Maneuvering the Middle resources to differentiate and help your students!

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Teacher Spotlight: Marissa McCarthy - Tips for Differentiation

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Today on the blog (and podcast), we have Marissa McCarthy! She is an amazing teacher who uses Maneuvering the Middle resources to teach and differentiate for her 6th grade students. She is a whiz at small groups and a wealth of knowledge. Marissa has just wrapped up her 13th year of teaching math in Ohio.

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Talking Math: 100 Questions That Help Promote Mathematical Discourse

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Talking Math: 100 Questions That Help Promote Mathematical Discourse

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Update 2022: For a recent article on how to talk about math, click here.
Think about the questions that you ask in your math classroom. Can they be answered with a simple "yes" or "no," or do they open a door for students to really share their knowledge in a way that highlights their true understanding and uncovers their misunderstandings? Asking better questions can open new doors for students, helping to promote mathematical thinking and encouraging classroom discourse. Such questions help students:

Work together to make sense of mathematics.

Rely more on themselves to determine whether something is mathematically correct.

Learn to reason mathematically.

Evaluate their own processes and engage in productive peer interaction.

Discover and seek help with problems in their comprehension.

Learn to conjecture, invent and solve problems.

Learn to connect mathematics, its ideas and its applications.

Focus on the mathematical skills embedded within activities.

Below are 100 questions from mathematics expert Dr. Gladis Kersaint to help you address these core areas and promote mathematical thinking and discourse in the classroom. Want these questions visible in your classroom? Curriculum Associates has released an infographic that you can print and have at your desk or in your class for quick access! Here's a preview:

For more, please download Dr. Kersaint's new whitepaper:Orchestrating Mathematical Discourse to Enhance Student Learning.
Dr. Gladis Kersaint
Help students work together to make sense of mathematics

1. What strategy did you use?

2. Do you agree?

3. Do you disagree?

4. Would you ask the rest of the class that question?

5. Could you share your method with the class?

6. What part of what he said do you understand?

7. Would someone like to share ___?

8. Can you convince the rest of us that that makes sense?

9. What do others think about what [student] said?

10. Can someone retell or restate [student]'s explanation?

11. Did you work together? In what way?

12. Would anyone like to add to this?

13. Have you discussed this with your group? With others?

14. Did anyone get a different answer?

15. Where would you go for help?

16. Did everybody get a fair chance to talk, to use the manipulatives, or to be recorded?

17. How could you help another student without telling the answer?

18. How would you explain ___ to someone who missed class today?

Refer questions raised by students back to the class.

Help students rely more on themselves to determine whether something is mathematically correct

1. Is this a reasonable answer?

2. Does that make sense?

3. Why do you think that? Why is that true?

4. Can you draw a picture or make a model to show that?

5. How did you reach that conclusion?

6. Does anyone want to revise his or her answer?

7. How were you sure your answer was right?

Help students learn to reason mathematically

1. How did you begin to think about this problem?

2. What is another way you could solve this problem?

3. How could you prove that?

4. Can you explain how your answer is different from or the same as [student]'s?

5. Let's see if we can break it down. What would the parts be?

6. Can you explain this part more specifically?

7. Does that always work?

8. Is that true for all cases?

9. How did you organize your information? Your thinking?

Help students evaluate their own processes and engage in productive peer interaction

1. What do you need to do next?

2. What have you accomplished?

3. What are your strengths and weaknesses?

4. Was your group participation appropriate and helpful?

Help students with problem comprehension

1. What is this problem about? What can you tell me about it?

2. Do you need to define or set limits for the problem?

3. How would you interpret that?

4. Would you please reword that in simpler terms?

5. Is there something that can be eliminated or that is missing?

6. Would you please explain that in your own words?

7. What assumptions do you have to make?

8. What do you know about this part?

9. Which words were most important? Why?

Help students learn to conjecture, invent and solve problems

1. What would happen if ___? What if not?

2. Do you see a pattern?

3. What are some possibilities here?

4. Where could you find the information you need?

5. How would you check your steps or your answer?

6. What did not work?

7. How is your solution method the same as or different from [student]'s?

8. Other than retracing your steps, how can you determine if your answers are appropriate?

9. What decision do you think he or she should make?

10. How did you organize the information? Do you have a record?

11. How could you solve this using (tables, trees, lists, diagrams, etc.)?

12. What have you tried? What steps did you take?

13. How would it look if you used these materials?

14. How would you draw a diagram or make a sketch to solve the problem?

15. Is there another possible answer? If so, explain.

16. How would you research that?

17. Is there anything you've overlooked?

18. How did you think about the problem?

19. What was your estimate or prediction?

20. How confident are you in your answer?

21. What else would you like to know?

22. What do you think comes next?

23. Is the solution reasonable, considering the context?

24. Did you have a system? Explain it.

25. Did you have a strategy? Explain it.

26. Did you have a design? Explain it.

Help students learn to connect mathematics, its ideas and its application

1. What is the relationship of this to that?

2. Have we ever solved a problem like this before?

3. What uses of mathematics did you find in the newspaper last night?

4. What is the same?

5. What is different?

6. Did you use skills or build on concepts that were not necessarily mathematical?

7. Which skills or concepts did you use?

8. What ideas have we explored before that were useful in solving this problem?

9. Is there a pattern?

10. Where else would this strategy be useful?

11. How does this relate to ___?

12. Is there a general rule?

13. Is there a real-life situation where this could be used?

14. How would your method work with other problems?

15. What other problem does this seem to lead to?

Help students persevere

1. Have you tried making a guess?

2. What else have you tried?

3. Would another recording method work as well or better?

4. Is there another way to (draw, explain, say) that?

5. Give me another related problem. Is there an easier problem?

6. How would you explain what you know right now?

Help students focus on the mathematics from activities

1. What was one thing you learned (or two, or more)?

2. Where would this problem fit on our mathematics chart?

3. How many kinds of mathematics were used in this investigation?

4. What were the mathematical ideas in this problem?

5. What is the mathematically different about these two situations?

6. What are the variables in this problem? What stays constant?

Facilitating student engagement in mathematical discourse begins with the decisions teachers make when they plan classroom instruction. In the next and final blog in this series, we will dive into the specific strategies that teachers can use to foster meaningful conversations about what students are thinking, doing and learning.

This blog is part of a three-post series on the importance of mathematical discourse from Curriculum Associates and Dr. Gladis Kersaint, the author of the recently published whitepaper Orchestrating Mathematical Discourse to Enhance Student Learning. Download your free copy .
For more on mathematical discourse and Curriculum Associates, check out:
Dr. Gladis Kersaint is a Professor of Mathematics Education at the University of Connecticut. Stay in-the-know with all things EdTech and innovations in learning by signing up to receive the weekly Smart Update. This post includes mentions of a Getting Smart partner. For a full list of partners, affiliate organizations and all other disclosures please see our Partner page

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Talking Math: 100 Questions That Help Promote Mathematical Discourse

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By Gladis Kersaint - 100 questions from a mathematics expert to help promote mathematical thinking and discourse in the classroom.

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Check out these resources to help students deepen mathematical understanding and develop diverse problem-solving strategies through Mathematical Discourse.

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10 Best Math Tools for Middle School | Common Sense Education

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10 Best Math Tools for Middle School | Common Sense Education

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10 Best Math Tools for Middle School | Common Sense Education

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10 top-rated apps and websites for the middle school math classroom. Explore this 10 Best Math Tools for Middle School Top Picks list of 10 tools curated by Common Sense Education editors to find relevant and engaging edtech solutions for your classroom.

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Differentiated Instructional Strategies for Middle School Math | Houghton Mifflin Harcourt

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Differentiated Instructional Strategies for Middle School Math | Houghton Mifflin Harcourt

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It is no doubt impossible for me to solve the complex, contextual problem of how you should teach your middle school students in a single blog post. You, and you alone, are the only expert on what it takes to teach your students in your school and community. However, teaching-like all jobs-is one where there are always new ideas to explore and fundamentals to practice.

Approaches to How to Teach Middle School Math

Teaching math at the middle school level is very different from the elementary school level. Middle school math teachers are generally not expected to also help students with other subjects, though of course one cannot fully separate math from other disciplines.

At the middle school level, just by virtue of being older, math students are further along in their mathematical development. This means your mathematical conversations can be more rigorous and substantive. But this also means skill gaps can be harder to fill. It is a time of transition, both for the students who are at a difficult age and for the math content itself, which transitions from the intuitive rules of arithmetic to the abstract mind-warp of algebra.

Differentiating Middle School Math Instruction

There are different schools of thought as to what differentiation in middle school math means. Some educators equate differentiation with tiered math centers. Other educators think about differentiation in terms of catering to students' different learning styles. However, we caution against the common myth that learners are segmented into "visual," "auditory," and "kinesthetic." Regardless of the outlook, educators can agree that differentiation is about addressing the diversity of skills that any classroom presents.

Veteran math educators Marian Small and Amy Lin point out a trap that befalls many middle school teachers. It is not realistic for teachers to create a different instructional path for every student. Because this is commonly perceived as the alternative to one-size-fits-all teaching, instruction in secondary mathematics is sometimes not differentiated at all.

At HMH, differentiation is multifaceted. It includes providing students with choice in their learning and a voice in any classroom conversation, along with tiered math centers, digital activities, and tools to teach one concept in multiple ways. Differentiation in middle school is far deeper than making sure images have sounds and movement to go along with them. It means finding entry points for students who feel left out, providing activities with low floors and high ceilings ( and wide walls), and facilitating discourse among every student.

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6 Differentiated Instructional Strategies for Middle School Math

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It is no doubt impossible for me to solve the complex, contextual problem of how you should teach your middle school students in a single blog post. You, and you alone, are the only expert on what it takes to teach your students in your school and community.

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Quick Physical Games for the Math Classroom | Math for Love

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Quick Physical Games for the Math Classroom | Math for Love

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We hold these truths to be self-evident, that kids need to move around, and creating opportunities to move during math class can pay off in spades.

Therefore, we have a collection of some of our favorite math/movement quick activities to share. These are especially good for K-4, though they're adaptable to older and younger grades too. They provide a dose of movement, fun, and mathematical practice in an abbreviated time frame-perfect for station breaks and transitions.

If we're missing any of your favorites, let us know! A PDF with Common Core tagging is available at our Lessons page.

Teacher-led Games

Student-pair Games

Finger Speed-Sums (1-5 minutes)
Students meet in pairs with one hand behind their back. On the count of three, they each put forward some number of fingers. Whoever says the sum first wins. Then the pair breaks up and each person finds a new person to play with. Advanced players can use two hands instead of just one.

Finger Speed-Differences (1-5 minutes)
Same as speed-sums, except whoever find the difference between the two numbers first wins.

Five High Fives (1 - 2 minutes, or longer with the exploration)
Students try to give a high-five to five different classmates. When they've gotten their five high-fives done, they sit down. This game is part mystery: sometimes it will be possible for everyone to get a high-five; sometimes not. The difference (which the teacher knows but the students don't) is that it is only possible if there are an even number of people giving high-fives. Try this game at different times and let students guess whether they think everyone will get a high-five or not. Why does it only work sometimes, not always?If you make it four or six high-fives instead of five, then everyone will be able to get their high-fives every time.

Why we love these games

Getting kids moving is a win-win. Movement refreshes your students while giving them another take on math concepts. These games are super quick and super fun for everyone.

Tips for the classroom

1. Make sure kids never feel ashamed if they don't already know the right answer. You can also tweak competitive games to make them collaborative.

2. You enthusiasm is critical in these games. Figure out your favorites, and expand on them, or get the students to come up with their own variations. If you're into them and having a good time, the kids will have a good time too.

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Quick Physical Games for the Math Classroom

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We hold these truths to be self-evident, that kids need to move around, and creating opportunities to move during math class can pay off in spades. Therefore, we have a collection of some of our favorite math/movement quick activities to share. These are especially good for K-4, though they're adaptable to older and younger grades too.

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18 Math Review Games for Middle School - Idea Galaxy

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18 Math Review Games for Middle School - Idea Galaxy

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Reviewing is an essential part of learning. It's how our brains remember and keep things from slipping away. Sometimes it can be very tempting to have students review by only answering test like questions and then going over them with the class. The downside of this is that it's boring and not memorable. Also, it goes against best practices for teaching and learning. So, I would like to present an alternative way to review that is action packed, fun, and engaging. Of course I'm talking about games! There are so many ways to practice math concepts and skills using review games.

Games can be played as an individual, with or against a partner, with a small group, or with the whole class. Using a variety of activities, or games, can help spice up your classroom and boost your review. Different topics lend themselves to different games types. Some games are competitive and other games aren't. In my class, I try hard to use the components of games that make people like them, but I also make sure that they don't get overly competitive or focused too much on winning.

Games for independent review

Mazes are one page activities with 16-20 problems on them. Students work through the problems to find the correct answers to the problems help them get through a maze. This individual activity usually take 10-20 minutes depending on the topic. Topics work as mazes as long as they are skills based. The problems have to fit in a small box, so not everything fits in a maze. You can make your own maze, or there are lots of them on Teachers Pay Teachers. Also, if you want a free maze delivered to your inbox each month then join our Maze of the Month Club. I don't mean to brag, but it's pretty awesome 🙂

Students love mazes because they're a different way to practice. I use a maze as a bell ringer virtually every day in my math class, and students complain whenever we don't have one! You can learn even more about how to use mazes in the math classroom here.

Sorting pockets are activities where students put little cards into categories. Typically, this works an individual activity, but it could be done with partners. This works best with topics that have natural categories. Some examples that work with sorting pockets are How Many Solutions to a System of Equations?, and Square Roots and Cube Roots. Sorts work great as an anticipatory set or something for fast finishers to do. I make a class set and then have students work with them over the course of a couple of weeks. These are great for review because students have to make judgments about numbers and equations. They physically categorize the cards and can re-use the sort over and over to get more automatic with identifying key concepts.

Matching games get students engaged and review at the same time. In some matching games students match 3 or 4 characteristics to one item. On the other hand, sometimes students are matching a question with an answer. Either way, this gives students the chance to use little manipulatives and to see the information presented in a different way. You can have students do this with a partner or by themselves. If you have more than one matching game you can use this as a center and have students rotate from one matching set to another. These matching games are easy prep, hands-on practice and they get students solid practice.

With Quizizz you can have your students practice math skills on the computer every day. This online quiz program has a variety of topics, is easy to use, and even has funny memes that crack students up. You can use quizizz that are already prepared by other teachers or you can make your own quizizz. I have found many quizizz for just about every topic I have looked for. Students work on the quizizz individually and they can see how they are doing compared to others. You can take the quiz too and see if they can beat you. (My students LOVE competing against the teacher!) We choose a skill and do a quiz every day for that topic for a few weeks to help us review. I like to use "Homework" mode because everyone doesn't have to be on it at the same time. It also has a timer feature that can be turned on or off (personally, I prefer to turn the timer off on most topics). Kids love this program.

XP Math has a lot of different games related to middle grades math. Students play the games like video games. Many of the games are based off of classic video games or game shows like Wheel of Fortune, Metroid, Deal or No Deal, Minecraft, etc. Adding the video game aspect gets kids engaged in practicing many topics from Pre-Algebra, Algebra, and Geometry. Here are a few games I have used with my students:

Games for partners or small groups

I've seen scavenger hunts done different ways in different classrooms. The most important part is that students get up and moving around the room. If you add the component of trying to find a hidden message or a race aspect to the hunt, students can really get into the activity.

The scavenger hunts that I use have 12 questions. I post one question per paper and place them around the room. In partners, students go around the room and answer the questions. Each multiple choice answer has an object assigned to it. Students then get their answers checked after each question. You can put up two different copies of each question so that there are plenty of questions to go around.

Even my most reluctant learners really get into this game.

Maze Battle

A maze battle is a twist on the mazes that we use in our classroom on a regular basis. I have a few maze activities that are designed as battles with three mazes in a row. Then, students compete against a partner to see who can reach the finish line first. When students are battling each other it's important that you have students who work at similar paces working together. Also, my maze battles have two teams, fire and ice. You can have the partners battling against each other as well as all of the players on Team Fire vs all of the players on Team Ice.

I put a timer on the overhead projector that is counting up and students can look up to see when they finished. They get a penalty for not coloring the arrows or for getting one wrong. We just played this activity the other day and they really enjoyed it. I even had a little token prize for the winner 🙂

Who doesn't love Tic Tac Toe games? This is a class favorite. It usually doesn't take very long and can quickly review a basic skill. In my experience students need to know the concept pretty well before playing tic tac toe, or this game can spiral into a simple game of tic tac toe with not a lot of math happening. You can find tic tac toe games on Teachers Pay Teachers, or you could even have your students make a game board that they play with each other. Basically, to make this game into math tic tac toe, students simply take turns answering questions. When they get a questions right, they win the square with their x or o.

Students love to play QR code games. It's one of those games where students don't even realize they have completed a whole bunch of practice. This game consists of task card like problems with two QR Codes, one that tells students the answer and another QR Code that tells them how many points they have earned. If they get the correct answer, they get the points. If they don't get the correct answer they put the card back into the pile and their opponent gets a crack at it. The point values are random so someone can win even if they don't answer their questions as fast as the other person. You can read more tips and tricks for using QR Codes in this blog post.

I have to admit that the first time I saw paper chains I thought they looked silly and like a waste of time. My mind quickly changed, however. I tried one last year to review scientific notation with my students, and I have been hooked since then. Right now my 7th graders are trying to get their paper chain to go around our entire common area in our building. Every time we complete a paper chain activity, we add it to the huge paper chain out in the common area. We are about a quarter of the way around the room. It is a great visual for to show their work. In addition to being a visual representation of students' work, I also like the partner work that goes into putting the paper chain in order before they actually make the chain.

Cootie catchers in the math classroom? Absolutely! While some people call this activity a fortune teller and others call it a cootie catcher, either way it's a simple twist that's a real winner. It can be done as a person versus person game. Or, you can use the cootie catcher as an individual activity. Either way, it's a fun twist to choose different numbers to get to the problems. This adds a little novelty and get some kids more involved than if the same questions were just on a worksheet.

Show Down

Show down is a great small group game to practice any math concept. To play show down, you just need a set of questions or task cards. Have students get into groups of 4 and give each student a whiteboard. The group turns over one question and all students do the work. When everyone is done with the problem, you flip the card over to reveal the answer. Everyone with the right answer gets a point. Also, students can talk about their answers before or after they have seen the answer. This game works as a way to get students talking about math.

Review games for the whole class

We play this game a lot in my classroom throughout the year. I love it for a review game because everyone is engaged and I can work through problems with them in a game environment. Between the competition and the fun graphics, students are more keyed into solving math problems and understanding the explanations .

This is what one of the game boards looks like:

And here's an example of some problems & their answers:

Basically, there's a game board with a whole bunch of characters. A student chooses one of them. Then, a question in shown and all the students work it out on their paper or whiteboard. I use whiteboards a lot, so when students finish they show me their work. This gives me an opportunity to see who gets it and who doesn't. Next, the answer is revealed in the screen and students who got it right get the points. I don't emphasize the points very much, but the kids seem to like counting points.

There are some bonuses and students really like that part because the bonuses can be good or bad. This game is a great way to review. Your students will love it. (You can check out the Knockout games we play in my class here).

Jeopardy

I use Jeopardy games in my class a couple times a year. With Jeopardy the questions are organized into different categories, and I like that aspect of it. I don't play Jeopardy in teams because I have learned throughout the years that one or two students do all the work and the other kids just go along with it. Instead, we all play the same questions and students either work in partners or individually. Then, students keep track of their points. Jeopardy is a classic review game that can help mix things up in the math classroom.

Task cards have so many different uses for the math classroom. I love playing this target game with the class because it is so easy. I display a task card on the projector for the whole class. Students work on it on their whiteboards. We go over the answer and then I choose a student to throw a suction cup ball at the target I have drawn on the board to find out how many points the questions is worth to the class. After a few rounds, we play double or nothing. The students can throw it a second time to try and get double points. All the students who got the answer right get the points that the student who threw the ball landed on.

It's so simple, yet they have so much fun. They really get into it and it gives us a chance to practice sportsmanship skills, as well. You can check out even more ideas for using task cards in the middle school math classroom here. And read more about the target game here.

Kahoot is a whole class, web-based game. You make an account and then you can either find games that others have created or you can make your own games. Students each need their own electronic device and they can play along. They just go to the website and enter the game code. There is definitely an aspect of speed to this game. After each question students see a leader board and can see how they are doing. Most of the students get really excited when it's time to play Kahoot.

SCOOT

Another great use for task cards is the SCOOT game. To play SCOOT, place a task card on each desk and then give students 1 minute or so to finish the card. Then, everyone scoots to the next seat. There's not competition in this game. But it does get the kids moving. There's no time for anyone to just sit there and do nothing. The movement and small time frames encourage everyone to complete the problems.

Also, I have the answers on the back of the task cards so students can check and see how they did. If they got a problem wrong, I ask them to look back and figure out their mistake. Focusing on learning from mistakes is a way to encourage growth mindset and help students own their learning.

Bingo

This classic game shares a lot of the same characteristics with the other whole class games that I have shared here. There's an aspect of luck to Bingo because any card could be a winner. Usually, I have some type of little prize like Jolly Ranchers or cute erasers for the winners. Students appreciate these little tokens and some of them get really excited to win.

Try a one new game to review

Maybe you've played all of these games in your classroom, or maybe you've never played any of them. What I love about these review games is that most of them are low prep. You can find free versions of these games, make your own version, adapt a resource you already have into a game, or find them on Teachers Pay Teachers. These games are some great ways to spice up your review and get away from just doing boring review worksheets.

I challenge you to try one of them and see how your students respond. I promise that more kids will be engaged and review the concepts at the same time. Let us know which game you tried and how it worked out in the comments below. Thanks for reading! Until next time.

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Reviewing is an essential part of learning. It's how our brains remember and keep things from slipping away. Sometimes it can be very tempting to have students review by only answering test like questions and then going over them with the class. The downside of this is that it's boring and not memorable.

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50+ Fun and Interesting Middle School Math Games

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50+ Fun and Interesting Middle School Math Games

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Here at Education Possible, we're all about interactive learning methods. Math is one of those subjects that can be challenging to teach and boring to review. That's why I include math games for middle school into our lessons whenever possible. My kids seem to learn better when they're having fun and there's less pressure.

Games were incredibly easy to find when we were working on elementary math, but now that my kids are in middle school and learning fractions, decimals, and algebra, it's become a bit more challenging. So I decided to search for math games that would work for my older kids.
Here's my huge list, full of some amazing games that will teach and challenge your middle schooler.
Because so many of the middle school math subjects overlap within the games, I've split the list according to the type of game it is. That way if you're looking for a specific style of game, like an online computer game or a board game, you can easily find it.

This post contains affiliate links.
Apps
5 Dice: Order of Operations Game
A fun way for teens to work on their order of operations. I love that it has a whiteboard included for kids to work through the problem visually.
King of Math
Begin as a simple farmer, but work your way up as you solve a wide variety of mathematical problems.
Middle School Algebra
Bounce the monkey up the steps by answering algebra questions correctly.
Middle School Math HD
Work through a variety of middle school math topics with some cavemen.
NumberStax
Middle Schoolers will love working on their algebra skills with this Tetris-style game.
Zap Zap Fractions
Build a spaceship and zap aliens while solving fraction equations.

Board Games
Equalz
A great card game that not only has numeric cards, but also operator cards that you use to get to a target number.
Equate
Build equations in a crossword-style.
Math Dice
A fun way to work on mental math.
Number Rings
Try to ring all of your numbers using math functions.
Numero
Here's a great post showing how a teacher uses Numero with her students.
Rush Hour
The original logic game where you try to get your red car unstuck. Many levels of play.
Sumoku
A crossword-style game that uses tiles.

Card/Dice/Paper Games
31-derful
See if your kids can arrange 25 cards from a deck so that the rows and columns equal a certain number.
Algebra Taboo
Played just like the board game (get partners to guess the word without using key terms), except the cards you create are math related.
Algebra Tic-Tac-Toe
A simple twist on an old game. Students solve algebraic problems to mark off a box.
Bingo - Fraction, Decimal, Percent
Just like the old favorite, but kids have to know their fraction, decimal, and percent equivalents.
Bottle Cap Matching
Students try to match up fractions, decimals, and percents.
Can You Make It?
You'll choose a random 2+ digit number and 6 single digit numbers. The object is to have students build an equation that equals the large number, by using all of the single numbers.
Crossing the River
A game of chance that uses integer addition.
Equation Top-it: Two-Step
Players solve equations to see who wins each round of this game, similar to war.
Equivalent Fraction Memory Game
An interactive way for students to determine which fractions are equivalent.
Exponent Game
Use a deck of playing cards to work on the concept of exponents.
Four-in-a-Row Mental Math Game
This is a Bingo type of game, except the problems are solved in the kid's head. Great way to work on mental math.
Game of Skunk
A fun dice game to work on the concept of probability.
Integer Flash
A two player card game focusing on multiplying integers.
Mathematics Pictionary
Just like the standard game, except the cards you'll play with are all related to math.
Middle School Math Games
This free download includes directions for 10 different games appropriate for middle schoolers. Games like Fraction War, Connect It, and Integer Multiplication War
Order of Operations Dice Game
Students roll the dice, fill in the numbers and complete the equation.
Percent Scramble! - Finding the Percent of a Number
A card game that focuses on percentages.
Playing Uno - Combine Like Terms
Make your own Uno cards so they include mathematical terms instead of individual numbers.
Square Root Car Racing Board Game
Kids race around the track solving square root problems.
Tarsia Puzzle Maker
Use this software to make your own printable tarsia puzzle using math symbols and equations. Kids will put it together by combining like terms.

Computer Games
Age of the Angles
An Angles and Protractor Game.
Alien Powers
Find the exponent before the alien lands.
Cool Math Games
No matter what you're studying in math, they've got a game for it. Plus logic and strategy games.
Death to Decimals
Get rid of the parachuting "decimals" by choosing the correct fraction equivalents.
Dragon Box
See how Susan used this video game with her son to learn algebra.
Math Jeopardy Games
These Jeopardy games cover just about every topic middle schoolers study in math.
Math Playground
Math games to help students build up their skills in decimals, percents, pre-algebra and geometry.
Middle School Math Games
This website contains a bunch of games for your students to play online, covering a wide variety of middle school math subjects. Popular games like Jepoardy and Millionaire.
Rags to Riches
Solve algebra equations to move up in this Millionaire type game.
Traffic Jam
Try to get your red car out of the traffic jam using logic and strategic thinking. Played just like the board game rush hour.

Graph Paper Games
Metric Conversion Game
It's a tic-tac-toe game that requires students to convert numbers to or from meters.
What Fits?
With this fun game, students work on area, spatial reasoning, and reviewing all kinds of math facts.

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Physical Games
Amazing Math Race
Kids team up and race against each other to be the first to complete a set of mathematical challenges.
Grudgeball
A great idea for math review time. You can use any problems for kids to solve in order to shoot the ball.
Human Coordinate Graphing
Get kids moving while solidifying the concept of coordinate graphing.
Probability Carnival
I love the idea of creating a bunch of probability games and turning them into a carnival!

Problem Solving
CSI: Algebra - STEM Project - Unit 3 - Solving Equations
If your kids love to play detective, they'll love this creative way to study algebra. They'll use math skills to solve six thefts.
The Game of Life - Financial Literacy - Real World Math Project
I love using real life examples when teaching my kids. This activity is all about finances in the real world. Students will work on budgeting, bookkeeping, loan payments, etc.

What is your favorite middle school math game?

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50+ Fun and Interesting Middle School Math Games

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Here at Education Possible, we're all about interactive learning methods. Math is one of those subjects that can be challenging to teach and boring to review. That's why I include math games for middle school into our lessons whenever possible. My kids seem to learn better when they're having fun and there's less pressure.

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Top 10 Things Every Middle School Math Teacher Should Have For Their Classroom - Math in the Middle

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Top 10 Things Every Middle School Math Teacher Should Have For Their Classroom - Math in the Middle

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As it is almost time to start preparing classrooms for the coming school year, I thought I would share my top 10 list of things I couldn't live without as a middle school math teacher.
10. Class sets of rulers, protractors, and compasses
We don't use these all that often but they definitely come in handy when we get to geometry, graphing, and pie charts. I don't ask students to supply their own because by the time we get to the units that require these tools, many of the kids have lost theirs.
9. LARGE supply of pre-sharpened pencils
I either get packs of pre-sharpened pencils or regular packs of pencils that I sharpen over the summer. Regardless of whatever system you have for pencils, students are going to show up for class without a pencil or with a pencil that needs to be sharpened at some point throughout the year. It makes my life easier if I can just give them a pencil that's ready to go that they can use for class instead of waiting for them to sharpen one.
8. Pencil-top Erasers
Kids make mistakes all the time. It makes sense to have erasers on hand to give them when they no longer have one on their pencil. I LOVE these ones from oriental trading - they're cute and there are enough to last at least a year. (The kids love the smiley faces on them, too)!
7. Expanding File Folder
(This is one of those things that I never knew I needed but now that I have one I don't know how I survived without it). You are going to have a lot of papers to grade. My old system was to just throw all the papers I had to grade into my bag to take home. Now I have sections in my 13 pocket file folder from Staples for all the different papers I need to grade, and I have sections for each class where I put the graded papers to give back. I am SOOO much more organized with it.
6. Manipulatives
My favorite go-to manipulatives are two-color counters and algebra tiles. The two-color counters are awesome for teaching integer operations and the algebra tiles are great for simplifying algebraic expressions, adding/subtracting/multiplying/factoring polynomials. I also LOVE my 3-d figure manipulatives. I have foam ones (that are fun to throw at the students) and ones with removable nets that are great for teaching surface area. I also have lots of dice, coins, and spinners for my probability units.
5. Looseleaf and/or Scrap Paper
You can never have too much paper! My students are always required to show all work so I go through paper like crazy.
4. Good Grading Pens
I LOOOOVE my papermate flair grading pens. I love all the colors, they don't bleed through papers, and they just write nice. I get a new pack each school year and it is always my favorite summer purchase!
3. Fun, Nerdy, Math Decorations
I like my room to set the tone as a fun place to learn math. I have math comic strips up around the room (Frank and Ernest have a bunch of good ones), cheesy math posters (such as "Life without geometry is pointless"), and my new addition that I am VERY excited about is an algebra alphabet set that I made to hang around my room. It's colorful, fun, and educational!

If you are interested, you can get a set of my Algebra Alphabet Cards at my TpT store.
2. Graph Paper
If you are teaching pre-algebra or algebra your students will be graphing lines so you will need graph paper. Depending on whether you use binders or notebooks, you may want different types of graph paper. If your students use binders for their notes, you can just use regular 3-hole punch graph paper. If you are using notebooks, then I highly recommend these awesome stick-on graphs that I discovered a couple of years ago! Just stick them into your students' notebooks and they have a nice, neat place to take notes on graphing! (I don't remember where I got these ones, but Amazon has a similar set for sale).
1. Mini Whiteboards, Expo Markers, and "Erasers"
Every math teacher needs a good set of mini whiteboards. Have students work out problems on them, showing their work, and then have them hold them up to show you. Such an easy formative assessment! They are great for review games, too. I definitely recommend getting a set that includes a coordinate plane side, as well, so that students can use them for graphing. I have been using these ones from EAI Education for a few years now and love them! They are thin and lightweight and barely take up any room. If you don't want to invest in a good set of mini whiteboards you can always make your own. My first year of teaching I took a piece of cardstock and a printed out coordinate plane and put them in page protectors. I taped them shut, and had my own little makeshift whiteboards. The nice thing about the homemade ones is that since they are in 3 hole punched page protectors, students can each keep one in their binders (if they are using binders) and always have them on hand. I use old rags as erasers for the whiteboards, but paper towels or actual whiteboard erasers work, too.

I hope you found this list helpful. Do you have any must-haves for your middle school math classroom that weren't on my list? Please share! I will send a FREE set of my Algebra alphabet set to the first 2 people to comment (be sure to leave an email address for me to send it to).

Thanks for reading,
Christina

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Top 10 Things Every Middle School Math Teacher Should Have For Their Classroom - Math in the Middle

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As it is almost time to start preparing classrooms for the coming school year, I thought I would share my top 10 list of things I couldn't live without as a middle school math teacher. 10.

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Teacher Resources for High School Geometry - Videos & Lessons | Study.com

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Teacher Resources for High School Geometry - Videos & Lessons | Study.com

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teacher resources for high school geometry - videos & lessons | study.com

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Teacher Resources for High School Geometry - Videos & Lessons | Study.com

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Look through these well-organized geometry lesson plan outlines as you begin developing your in-class teaching strategy. This chapter also provides...

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My Geometry Course | Mr. Shauver – Learner Educator

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My Geometry Course | Mr. Shauver – Learner Educator

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Out-of-the-Box Ideas for Teaching Algebra and Geometry - WeAreTeachers

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Out-of-the-Box Ideas for Teaching Algebra and Geometry - WeAreTeachers

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If you've ever struggled to keep your students' attention during your middle or high school algebra and geometry classes, you know just how important it is to mix it up a bit with creative teaching ideas. Thomas Edison said, "Opportunity is missed by most people because it is dressed in overalls and looks like work." So here is your chance to dress your lessons up in some fancy finery that looks more like a game, a work of art, or a barrel of laughs. The best thing about these out-of-the-box math ideas is that your students will learn the same important skills that they might have overlooked on the pages of their math textbooks.

1. Use engaging videos.

If the popularity of cute cat videos is any indication of the power of video to engage just about everyone, then using YouTube videos in your math class should be a no-brainer. Here's a great example of how a video can make a concept such as slope make sense and come to life.

2. Add an artistic component for a STEAM approach.

Your artistic and visually minded students will appreciate math lessons that allow their creativity to play a colorful role. This Mandala Math template combines art, math, and meditation in a way that will give each student practice measuring, using a compass, calculating radius and circumference, and expressing their individuality.

3. Connect your students with a personal math trainer.

Because every brain is different and each student processes and understands material in his or her own specific way, the idea of a personal math trainer makes a lot of sense. That is exactly what AGA Math has created with its set of digital tools that create a completely customized experience for each learner. The Personal Math Trainer powered by Knewton feature, or one of the other digital features, offer unlimited practice, real-time feedback, and a variety of question types and learning aids to help teach Algebra, Geometry, and Algebra 2. The Personal Math Trainer also automatically grades homework and generates reports so teachers can tailor instruction to meet students' needs.

4. Make it a game!

Competitive game formats can be a great way to help students review their understanding of concepts, formulas, math vocabulary, and more. SuperTeacherTools makes it easy to create "Jeopardy" style games, "Who Wants to Be a Millionaire" multiple-choice games, and "Speed Match" games using your own content. We also like this low-tech dice game that is a great way for pairs of students to practice calculating area.

5. Enter the world of reality TV.

Several high school math bloggers have found great success simulating the "survival of the fittest" competitions similar to reality TV show scenarios. Survivor Algebra from coolmath.com was created by a former mathphobe who has been able to transform his struggling math students with this collaborative game format. Here is another take on the Survival of the Fittest idea where everyone in the class needs to know the material because their survival depends on it!

6. Use real-world examples.

If your students dare to question the purpose of all those figures and formulas, race over to this site, filled with practical math problems for all grades based on real-world examples.

7. Make 'em laugh.

A shot of humor at the beginning of class can go a long way toward keeping your students engaged and learning. Laughter not only reduces stress, it also releases endorphins, the body's natural feel-good chemical. Want your students to feel good about your class? Pull from these algebra and geometry math memes and cartoons to post at the beginning of every lesson.

Why not toss in a cute cat visual every now and then while you're at it!

8. Use word walls.

Chances are that your students were brought up in cozy elementary classrooms surrounded by colorful walls filled with theme-based decorations. We think that these Word Wall visual reminders for your algebra and geometry classroom walls are the perfect, aged-up version of those comforting learning aids from days past.
Want more fun, out of the box ideas for teaching algebra and geometry? Visit HMH Mathematics to learn about their AGA math curriculum.

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Out-of-the-Box Ideas for Teaching Algebra and Geometry - WeAreTeachers

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If you've ever struggled to keep your students' attention during your middle or high school algebra and geometry classes, you know just how important it is to mix it up a bit with creative teaching ideas. Thomas Edison said, "Opportunity is missed by most people because it is dressed in overalls and looks like work."

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Teaching Probability Of Dependent And Independent Events - Math Classroom Ideas

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Teaching Probability Of Dependent And Independent Events - Math Classroom Ideas

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Math.7.SP.C.8a

Common core State Standards

Math: Math

7: Grade 7

SP: Statistics & Probability

C: Investigate chance processes and develop, use, and evaluate probability models

8a:
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., \"rolling double sixes\"), identify the outcomes in the sample space which compose the event.

c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

Download Common Core State Standards (PDF 1.2 MB)

Thought starters

1. How does Ms. Posada prepare students before they begin to write their own events?

2. How do the manipulatives affect student engagement?

3. What elements of the student presentations help to further reinforce student learning?

School Details

Mineral Springs Middle
4559 Ogburn Ave
Winston Salem NC 27105

Data Provided By:

Teachers

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Probability of Dependent and Independent Events

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Math.7.SP.C.8a Common core State Standards Math: Math 7: Grade 7 SP: Statistics & Probability C: Investigate chance processes and develop, use, and evaluate probability models 8a: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. a.

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Overview

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important "processes and proficiencies" with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council's report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy).

Standards

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The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important "processes and proficiencies" with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections.

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Today's guest blogger is Judy Willis. A former neurologist, Judy is now is an elementary and middle school teacher as well as the author of numerous books on the brain and learning. This post is an excerpt from her latest,
Learning to Love Math.

Before children can become interested in math, they have to be comfortable with it. They must perceive their environment as physically and psychologically safe before learning can occur. Students build resilience and coping strategies when they learn how to use their academic strengths to build math skills and strategies. Your intervention helps them strengthen the networks that carry information through their brains' emotional filters to the area where higher-order thinking skills are concentrated, the prefrontal cortex (PFC). With practice, they will be able to use the highest-level analytical networks in the PFC to evaluate incoming information and discover creative solutions to math problems (in addition to problems in all subject areas). To better understand how your students learn, it is important to first learn how to propel information through those filters and begin building math positivity.

STRATEGY: Arrange Family Conferences

No one wants to add to student pressure, especially when you suspect that a student will suffer emotional or even physical abuse if he or she does not meet certain parental expectations in math. Parents with extremely high expectations for their children are usually motivated by a desire to see their children have more than they have themselves. Unfortunately, when children internalize these expectations and don't fulfill them, they can suffer depression, anxiety, physical illnesses (high levels of cortisol associated with chronic stress lowers the immune response), or psychosomatic illnesses, or they may even inflict physical injury on themselves and others.Family conferences can help parents learn some of the scientific evidence linking the effects of stress to academic success. These interventions will also allow you to explain that the first step to math success is a positive attitude toward the subject matter, not just to the grades associated with it.

You can also suggest ways for these parents to be involved in a positive way. Explain that the brain is most receptive to learning about a topic when there is a clear link between that topic and something the child values. Parents can act as "math allies" if they find ways to integrate real-world math into their child's hobbies and interests. For example, they can encourage their children to calculate how long it will be until their special television show begins if it is currently 3:00 and the show starts at 5:30. They can also help their children compare the costs of things they like (e.g., bicycles, toys, computers) in newspaper ads that offer various percentage discounts off different base prices.

STRATEGY: Retest to De-stress

Reassure all students that if they want to achieve high grades, they will have opportunities that will allow them to regain some sense of control, such as retests. Because progress in math is so strongly based on foundational knowledge, students need to achieve mastery in each topic?which forms the basis from which students can extend their neural networks of patterns and concepts?before they move to the next level. Retests provide opportunities to reevaluate answers and make corrections, as necessary. To ensure mastery, I require that students take a retest when they score under 85 percent. My primary goal is to have students learn the appropriate material so they can move forward with an adequate background for success.

Incorporating accountability into retesting allows students to build skills related to self-reliance, goal planning, and independent learning. Parents or colleagues may voice concerns that students might not act responsibly or seriously once they realize that they'll have a second chance. Accountability increases when you require students to provide evidence of corrective action, such as participating in tutoring, doing skill reviews, or finding textual examples that correctly demonstrate how the type of problem is solved. If the original test and retest scores are averaged together, students understand that they remain accountable for that first test grade.Compared with cheating (an unfortunate response to grade pressure that further decreases confidence and self-esteem), the option of taking retests is a more positive approach to low grades. Retesting takes time on your part, but it shows your students that you respect their capacity to be responsible, successful learners.

STRATEGY: Demonstrate the Value of Math

Key to developing students' interest in math is to capture their imaginations. Instead of allowing them to think of math as an isolated subject, show the extended values of math in ways they find inspiring. If you teach elementary school, find opportunities throughout the day to show students the ways they benefit from mathematics and how it is applicable to their areas of interest. For example, students can use math to determine the number of absent students by counting the students present and then "counting back" to subtract.

In upper grades, cross-curricular planning is a way to achieve this goal. Older students, for example, can solve meaningful problems related to the quantity and price of tickets they need to sell in order to cover their expenses for an upcoming field trip. When you increase your students' positive feelings toward mathematics, you unlock their brains' math-blocking filters, promote long-term memory, and foster greater understanding beyond rote memorization.

What are some techniques you've used to build positivity in your students in math or other subjects?

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Today's guest blogger is Judy Willis. A former neurologist, Judy is now is an elementary and middle school teacher as well as the author of numerous books on the brain and learning. This post is an excerpt from her latest, Learning to Love Math.

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We all have them, some good and some bad. We pick them up from friends, family, and even strangers. But we may not recall who we picked them up from or when they began.

Because we've practiced them over and over, these seemingly thoughtless repeated habits or behaviors, the pathways in our brain have become so broad, fast, and efficient in carrying them out that we do them automatically without even thinking. Yet these unconscious habits and behaviors add structure and order to our lives and help us to make sense of the world we live in.

Our classrooms are full of them. We teachers are pros when it comes to employing and modeling good habits and routines that enable us to manage and carry out the many tasks and demands of teaching. And when it comes to teaching mathematics, we model and teach our students how to carry out procedures and algorithms flawlessly. But why is it that these same students often struggle when confronted with a problem to which the immediate answer is unknown?

Experienced vs. Inexperienced Problem Solvers

According to Levasseur and Cuoco (PDF, 80KB), it's the mathematical habits of mind, or modes of thought, that enable us to reason about the world from a quantitative and spatial perspective, and to reason about math content that empowers us to use our mathematical knowledge and skills to make sense of and solve problems. It's these habits that separate the "experienced" from the "inexperienced" problem solver.

Far too many students can be classified as inexperienced problem solvers who don't know what to do when they don't know what to do. These are the students who lack experiences in making sense of and solving problems, and in communicating and using precise, appropriate mathematics and mathematics language. They have never developed the overarching habits of a productive mathematical thinker.

When they're presented with a problem to which they don't know the immediate answer, their bad habits often rise to the occasion. They may begin with no real strategy in mind, they look for key words and terms that can sometimes be misleading, they want a quick answer, they resort to memorization over understanding, or they simply make no effort at all in finding the solution to the problem.

On the other hand, experienced problem solvers know what to do when they don't know what to do! They practice perseverance and automatically employ the mathematical habits of mind of a productive problem solver in their quest for a problem solution. They automatically engage in Polya's four-step problem-solving process to find a solution to the problem.

No one has to remind experienced problem solvers to first make an attempt at understanding the problem and ask clarifying questions that help them interpret and understand the conditions of the problem. They instinctively try to make sense of the mathematical situation at hand and choose a strategy, tools, and/or models, often based upon previous learning experiences or problems they've solved -- experiences that they see as relevant and applicable in solving the problem.

If they try a strategy and it doesn't work, they try a different one - all part of perseverance in problem solving. And like any good problem solver, once they have a solution, they take one last look to determine if their solution is a reasonable solution to the problem.

Practice and Experience

But these habits of mind can't be learned and developed by simply talking about them or memorizing the definition. Students immersed in classroom experiences that let them engage in learning mathematics concepts through problem solving, making and using abstractions, and developing and applying mathematical theories have greater opportunities for developing mathematical habits of mind. Classrooms steeped in the Common Core Standards for Mathematical Practice (MP) provide maximum opportunities for students to learn and develop these habits as they:

Teachers who saturate learning experiences with the Standards for Mathematical Practice offer students a variety of palatable problems. Presenting relevant, interesting, and challenging problems that can be approached and solved with different strategies and tools gives students choices that best fit their learning preferences. This approach is more inviting to them and leads them to reason about, look for, and make use of structure. In turn, it increases their chances of understanding important math concepts and skills, which in turn increases their ability to explain their thinking and reasoning, and to critique the reasoning of others.

You play a vital role in the development of mathematical habits by conveying to your students a mindset that fosters productive struggle and emphasizes the possible value of wrong answers. You set the stage by embracing the importance and value of grappling with problems. The more you engage your students in learning and doing mathematics, the greater the likelihood of their developing the mathematical habits of mind of a productive mathematical thinker -- and becoming experienced problem solvers who know what to do when they don't know what to do.

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We all have them, some good and some bad. We pick them up from friends, family, and even strangers. But we may not recall who we picked them up from or when they began.

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What to Do on Lame Duck School Days | Cult of Pedagogy

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What to Do on Lame Duck School Days | Cult of Pedagogy

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Listen to this post as a Podcast:

The term "lame duck" is most often used to describe a president who is still sitting in office after his or her successor has been elected. Technically this person is still the president, but his or her decision-making power is generally perceived to be minimal.

We have something like that in school: those days when technically we're still in school, but because it's right before vacation, the end of the school year is near, or we're in the middle of standardized testing, those class hours don't have the same instructional potential as your average school day. In some cases, like on standardized test days in certain districts, teachers are explicitly told they CAN'T plan regular instruction. On these Lame Duck days, it's hard to figure out what we can do to still provide valuable learning experiences for our students.

Sometimes instead of days, we have small bursts of Lame Duck time: The leftover 15 minutes after the fire drill, when you know you don't have enough time to actually finish the lesson you were teaching, but you don't want to just let them sit there. We often call the activities we need for these times "sponge activities." Regardless of what you call it or how much you need, we all have those times when students are right in front of us but the regularly scheduled programming just isn't going to work.

What then?

In some schools, they'll still let you show movies. I worked in a place like that, although near the end, we were starting to get pressured to cut that out. And I understand why: As a parent, when ask my kids what they did in school on any given day, and I hear "watched a movie," I'm annoyed. I mean, I can show my kids a movie at home. Surely school can step it up a notch? What's worse, "show a movie" in some classes actually means "Put a movie on, but let students do whatever they want while the movie provides background noise." And when the movie is, say, The Sound of Music, or some other classic I have waited years to experience with my kids, and then they tell me their music teacher puts it on all the time, I feel robbed as a parent.

Okay, that's my rant about showing movies in class. Take it with a grain of salt, because (a) I totally showed movies when I needed a day to grade papers and get caught up, and (b) I'm fully aware that a TON of absolutely amazing movies, video clips, and documentaries are absolutely jam-packed with educational value. So I get that it's not the worst thing you can do, and I know it CAN be done right. This is why I would never support a school banning videos across the board; that kind of blunt policy doesn't respect teachers' ability to make the best instructional choices for students.

HOWEVER...when it comes time to plan for Lame Duck days, we really do have so many more options beyond the showing of videos. So if you've decided you want to do something else, or you've been told you flat-out have to, here's a great list for what to do instead. Some of these ideas come from my own teaching experience, others come from online resources, and a lot of them are from a Facebook Live broadcast I did a few weeks ago, where other teachers contributed their own ideas.

I've broken this list into three sections, based on how much prep you'd need to do to for each one and how much time each one would take.

Some list items contain Amazon Affiliate links; if you purchase from Amazon after going through these links, Cult of Pedagogy receives a small commission at no extra cost to you.

Low-Prep

These activities can be done at a moment's notice, with little to no required materials. They can be used as a 10-minute filler or as the main activity for a whole class period.

1. Clean-up Day: Give students a chance to clean out their binders or lockers and enlist students to help tidy the classroom as well.

2. Learn a Line Dance: Either you teach your students, they teach each other, or you all learn together from YouTube. What's great about line dancing is that anyone can do it, whether they have rhythm or not. Go back a few years to learn the Cupid Shuffle, further back to learn the Macarena or go way back and learn the Hustle.

3. Thank-You Notes: Since this important life skill isn't really a part of any curriculum, a Lame Duck day is a perfect time to have students practice it and show some gratitude to the people who deserve it. Provide them with paper and envelopes and have them write thank-you notes to friends, family members, school staff members, or other students. For best results, show them a few examples of thoughtfully written notes ahead of time.

4. The Compliments Project: This is an incredible activity where students take turns being in the "hot seat" while their classmates write compliments on the board behind them. You have to see this one to appreciate its full impact. Watch here. Although this activity only takes about 5 to 10 minutes per student, which means it would be something you could squeeze into the end of a class period, you should only get it started if you know you'll eventually have time to put every student in the hot seat.

5. Go Outside: Many of the activities listed in this post could also be done outside, or you could just play a classic outdoors game like Red Rover or Red Light, Green Light. Check out this list of games for ideas.

6. Philosophical Chairs Debate: This technique has a lot of different names, like Four Corners, Physical Barometer, and This or That, but the idea is the same: You read some sort of statement to the class, like "Students should be allowed to go barefoot in school." Designate one side of the room as the "Agree" side and the other as the "Disagree" side. Students must physically walk to the side of the room that best represents their opinion. Then have students take turns explaining why they are standing in that spot. (If you want fantastic pre-made questions on a PowerPoint for this, take a look at my This or That icebreaker).

7. Group Story/Progressive Writing: Have every student take out a sheet of paper and have them all write the first sentence (or two, or three) of a story. Then have them pass it to the right and pick up where the last student left off. Keep going until you have a class set of unique stories. One variation of this is to give everyone the exact same sentence to start with, and see how many directions the different stories take.

Medium-Prep

These require you to do a bit of planning ahead of time, but for many, once you've prepared the materials, they can be used over and over again.

1. Improv Skits: Have groups of students compete by performing improv skits. This can be done in so many ways, but two structures you could use are 3-Word Skits, where students are given three words and must come up with a skit that uses all three, and Bag of Titles, where you (or other students) write lots of interesting or odd titles (e.g., "The Lady with 100 Cats") and the performers must come up with a skit that matches the title. Both of these ideas came from the incredible website Drama Notebook. Another great source for improv ideas is this list of games played on the T.V. show Whose Line Is It Anyway? (Screen these yourself first, as they do contain some adult content.)

2. Icebreakers: Get students talking with one of my three favorite classroom icebreakers.

3. Skype: Once you learn about some of the free educational opportunities offered by Skype, you might not want to do anything else in your free class time. One of these is a Mystery Skype, where you connect with another class in an unknown location (only you and the other teacher will know), and students work together to ask a series of yes/no questions until they guess where the other class is. Another is a Virtual Field Trip, where your class Skypes with someone (often a professional in some part of the world, like an ocean exploration with Fabien Cousteau, the grandson of Jacques Cousteau). To learn more, visit the Skype in the Classroom page in the Microsoft Educator Community.

4. Board Games or Card Games: I think we can all agree that no one plays board games or card games as much as they used to, and the simple fun and social learning that can come from them are worth the time and effort. Some of my family's favorites are Pictionary, Spot It!, Dominoes, Scattergories, Scrabble, Quirkle, Uno, or Yahtzee. Or just buy a few basic decks of cards, then check out the Gather Together Games YouTube channel and learn how to play something classic like Gin Rummy, Spades, or Pinochle.

5. Minute to Win it Games: These require some equipment and set-up, but not a whole lot, and they will really break students out of their shells. This list from Happiness is Homemade has 10 fantastic ideas, like "Cookie Face" and "Junk in the Trunk."

6. Mindfulness Practice: Especially during testing season, mindfulness practice can ease stress and give students a skill they can apply in so many other areas of their lives. Two great resources for starting on this journey are the Mindful Schools website, and the book Teach, Breathe, Learn by Meena Srinivasan. Two easy-to-make mindfulness tools are glitter jars and breathing sticks.

7. Kahoot: If you still haven't tried Kahoot, you're in for a treat. This website lets you create interactive, game show-style quizzes that students play as a class on their own devices. You could create a content-based Kahoot, do one just for fun, or even have students create them.

8. STEM Challenges: A hands-on problem that students need to solve with science, technology, engineering or math skills is cognitively challenging, socially engaging, and just a fun break from routine in any class. Here are some fun challenge ideas. (Don't mind that it says "elementary." They would be fun for older kids, too.)

9. Open Mic: This was something I did several times in my middle school classrooms, and it was an incredibly bonding experience. The idea is simple: Invite any student who has some kind of performance talent-whether it's singing, playing an instrument, magic, martial arts, or even creative writing-to take the stage in your classroom and give a short performance. Something truly magical happens when students get to see their peers step outside of the roles they're normally in during class. And if your students are anything like mine were, they will recognize the courage it takes to get up in front of your peers and do this. I can still remember the day when one of my 8th grade girls got up and sang an Alicia Keys song a capella. Beautifully. When she was done the room just exploded with applause. If you have students who are too shy to perform live or whose talent can't be performed in a classroom setting, let them record themselves at home and play the videos in class. One of our great privileges as teachers is helping our students grow into full, well-rounded human beings, and letting them see their own peers in a different light is absolutely one way to do this. (Listen to me talk about this experience on my friend James Sturtevant's Hacking Engagement podcast.)

High-Prep or Long-Term

1. Genius Hour: Just in case you've never heard of Genius Hour, it's a structure for giving students time to explore topics and skills they choose completely on their own. Sometimes they study a foreign language, teach themselves how to code, even start their own businesses. A Genius Hour project usually happens over a period of weeks or even months, in small increments. So if you've already got a Genius Hour program going, these extra bits of time are perfect for continued work on projects. To learn more about Genius Hour, check out my friend A.J. Juliani's webinar and course here.

2. Community Service Project: One great way to make the most of the end of the school year is to have students identify a need in the community, then plan and execute a service project. Check out these 7 ideas for service learning projects from We Are Teachers. Another type of service project could be organizing a school-wide yard sale, with the profits going to charity.

3. Student Video Project: These can take all kinds of forms: end-of-year retrospectives, book trailers, tutorials or welcome videos for incoming students. You could even hold a student film festival where final projects are shown on the last few days of school. This classroom video guide from EdTechTeacher will help get you started.

4. Amazing Race Game: Just like with the Survivor game above, you could coordinate a game based on the show The Amazing Race following a plan like this one.

5. Literature Circles: Amid all these other creative ideas, the humble literature circle may not seem quite so exciting, but never underestimate the value of a small group of students talking about a fantastic book they're all reading. To learn more, see this Getting Started Guide to Literature Circles from ReadWriteThink.

6. BreakoutEDU Activities: BreakoutEDU is kind of hard to explain, but I'll give it a shot: It's a kit that contains several boxes, a few locks, an invisible ink pen and UV light, a USB drive, and a few other pieces of equipment. The deal with the box is that teachers use them to facilitate games, games that feel like a cross between a mystery and a challenge, where clues are left around the room and students have to answer questions in order to find them. In the same way that you can plug questions or content into a platform like Kahoot, you can do the same with BreakoutEDU (they also have a lot of pre-made games available for purchase). Learn more here.

7. Student/Teacher Unconference: Using a chunk of hours or a whole day, teachers and students plan short lessons on things they are interested in outside of school (crafts, yoga, cooking, martial arts, music, dance, technology), then sign up for time slots like an EdCamp. With the schedule in place, students and teachers can then sign up to attend the ones they are interested in. This would definitely take some planning, especially the first time, but it could be so worth it. What is an unconference?

8. TED Talks: Watching these short, powerful presentations has become almost a rite of passage for 21st century humans. Have students watch a few to understand the style, then plan and deliver their own.

Even More Fantastic Ideas:

There's so much more where this came from.
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Listen to this post as a Podcast: The term "lame duck" is most often used to describe a president who is still sitting in office after his or her successor has been elected. Technically this person is still the president, but his or her decision-making power is generally perceived to be minimal.

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Building a Thinking Classroom in Math | Edutopia

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Building a Thinking Classroom in Math | Edutopia

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June used it the next day. It did not go well. A forest of arms immediately shot up, and June moved frantically around the room answering questions. Many students gave up quickly, so June also spent much effort trying to motivate them to keep going. In general, there was some work attempted when June was close by and encouraging the students, but as soon as she left the trying stopped. This continued for the whole period.

The following day I was back with a new problem. The results were as abysmal as they had been on the first day. The same was true the third day. Over the course of three 40-minute classes, we had seen little improvement in the students' efforts to solve the problems, and no improvements in their abilities to do so. So June decided it was time to give up.

I wanted to understand why the results had been so poor, so I stayed to observe June and her students in their normal routines. After three full days of observation, I began to discern a pattern. That the students were lacking in effort was immediately obvious, but what took time for me to realize was that the students were not thinking. More alarming was the realization that June's teaching was predicated on an assumption that the students either could not or would not think.

Once I realized this, I proceeded to visit 40 other mathematics classes in a number of schools. In each class, I saw the same thing-an assumption, implicit in the teaching, that the students either could not or would not think. Under such conditions it was unreasonable to expect that students were going to be able to spontaneously engage in problem solving.

This motivated me to find a way to build, within these same classrooms, a culture of thinking. I wanted to build what I now call a thinking classroom-one that's not only conducive to thinking but also occasions thinking, a space inhabited by thinking individuals as well as individuals thinking collectively, learning together, and constructing knowledge and understanding through activity and discussion.

Over 14 years, and with the help of over 400 K-12 teachers, I've been engaged in a massive design-based research project to identify the variables that determine the degree to which a classroom is a thinking or non-thinking one, and to identify the pedagogies that maximize the effect of each of these variables in building thinking classrooms. From this research emerged a collection of 14 variables and corresponding optimal pedagogies that offer a prescriptive framework for teachers to build a thinking classroom.

1. The type of tasks used: Lessons should begin with good problem solving tasks. In the beginning of the school year, these tasks need to be highly engaging, non-curricular tasks. Later these are gradually replaced with curricular problem solving tasks that then permeate the entirety of the lesson.

2. How tasks are given to students: As much as possible, tasks should be given verbally. If there are data, diagrams, or long expressions in the task, these can be written or projected on a wall, but instructions should still be given verbally.

3. How groups are formed: At the beginning of every class, a visibly random method should be used to create groups of three students who will work together for the duration of the class.

4. Student work space: Groups should stand and work on vertical non-permanent surfaces such as whiteboards, blackboards, or windows. This makes the work visible to the teacher and other groups.

5. Room organization: The classroom should be de-fronted, with desks placed in a random configuration around the room-away from the walls-and the teacher addressing the class from a variety of locations within the room.

6. How questions are answered: Students ask only three types of questions: proximity questions, asked when the teacher is close; "stop thinking" questions-like "Is this right?" or "Will this be on the test?"; and "keep thinking" questions-ones that students ask in order to be able to get back to work. The teacher should answer only the third type of question.

7. How hints and extensions are used: The teacher should maintain student engagement through a judicious and timely use of hints and extensions to maintain a balance between the challenge of the task and the abilities of the students working on it.

8. Student autonomy: Students should interact with other groups frequently, for the purposes of both extending their work and getting help. As much as possible, the teacher should encourage this interaction by directing students toward other groups when they're stuck or need an extension.

9. When and how a teacher levels their classroom: When every group has passed a minimum threshold, the teacher should pull the students together to debrief what they have been doing. This should begin at a level that every student in the room can participate in.

10. Student notes: Students should write thoughtful notes to their future selves. They should have autonomy as to what goes in the notes and how they're formatted. The notes should be based on the work already on the boards done by their own group, another group, or a combination.

11. Practice questions: Students should be assigned four to six questions to check their understanding. They should have freedom to work on these questions in self-selected groups or on their own, and on the vertical non-permanent surfaces or at their desks. The questions should not be marked or checked for completeness-they're for the students' self-evaluation.

12. Formative assessment: Formative assessment should be focused primarily on informing students about where they are and where they're going in their learning. This will require a number of different activities, from observation to check-your-understanding questions to unmarked quizzes where the teacher helps students decode their demonstrated understandings.

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Over more than a decade, the author has developed a 14-point plan for encouraging students to engage deeply with math content.

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Helping Students See How Graphs Work | Edutopia

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Helping Students See How Graphs Work | Edutopia

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That's why I worked with Dan Meyer and the team at Desmos, a free browser-based application, to develop Cannon Man and other interactive activities. Cannon Man links dynamic animations and graphs in a sequenced, interactive learning experience. Students move through a progression of 14 screens, which they can complete at their own pace.

The Cannon Man Learning Experience

Students begin by viewing a video of Cannon Man, who is shot straight up into the air and then falls straight down, with his parachute opening near the end of his trip. After viewing the video, students might notice many different attributes-the path that Cannon Man takes, his height from the ground, his speed before and after his parachute opens. The exercise directs students to focus on two attributes in particular: Cannon Man's height from the ground and his total distance traveled (both up and down).

Next, students manipulate dynamic segments to show how Cannon Man's height and total distance are changing. Then they sketch a graph to represent a relationship between his height and total distance. After sketching the graph, they answer some reflective questions. They repeat this process with Cannon Man's height and total distance represented on different axes. This gives students the opportunity to use graphs to represent relationships between attributes.

To create Cannon Man, I gathered inspiration from different sources, including existing activities on Desmos such as Function Carnival. A number of researchers inspired my work: Jim Kaput's SimCalc MathWorlds software, Patrick Thompson's theory of quantitative reasoning, Kevin Moore's work with breaking conventions, and Ference Marton's variation theory.

Cannon Man gives students real-time feedback on their work, and teachers can collect student responses. And Cannon Man creates several other opportunities:

Make sense of attributes represented in a graph: If students are going to use graphs to represent relationships between attributes, they need to make sense of those attributes. To frame the activity, it's helpful for teachers to provide opportunities for students to discuss different attributes they notice. The Cannon Man video helps to orient students to the situation and the different attributes.

Show how they might measure each attribute: It's not enough for students to become familiar with attributes. It's also important for them to think about how they might measure each attribute. It's not necessary for students to come up with particular measurements. For example, they might wonder how they can measure Cannon Man's total distance traveled, because Cannon man does not move from left to right. Teachers can help students to think about distance as the accumulated journey, both up and down.

Represent how each attribute can change: Graphs represent more than one attribute. It's useful for students to think about how each attribute can change. In Cannon Man, they can use dynamic segments to represent how each attribute can change. Then they can view a computer animation of the dynamic segments.

Use a graph to represent a relationship between changing attributes: Once students have explored individual attributes, they can use a graph to represent a relationship between those attributes. It's useful for students to move beyond a focus on what graphs look like to a focus on what graphs represent. In Cannon Man, they can use a variety of tools to sketch different kinds of graphs. They can receive real-time feedback by viewing a dynamic computer sketch of a graph.

Use a different graph to represent the same relationship: To continue to investigate relationships between attributes, it's helpful for students to represent relationships in different ways. It's typical for students to have opportunities to use different types of representations, such as a table or equation instead of a graph. With Cannon Man, students have opportunities to represent the same relationship with a different graph.

Three Takeaways

How students think about the attributes matters: Give students opportunities to make meaning of the attributes before representing them in a graph. To promote students' thinking about attributes, teachers can ask questions such as: "Can you show me where you see Cannon Man's distance? How might you measure it?"

Focus on both the whole and the parts: Have students represent change in individual attributes first and then change in both attributes. To promote students' thinking about changing attributes, ask questions such as: "How does moving the dynamic segment right and left show that Cannon Man's height is increasing, then decreasing?"

Two graphs are better than one: Have students use more than one graph to show the same relationship. To keep a focus on relationships, teachers can ask questions such as: "How can a single graph show both attributes at the same time?"

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Helping Students See How Graphs Work | Edutopia

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That's why I worked with Dan Meyer and the team at Desmos, a free browser-based application, to develop Cannon Man and other interactive activities. Cannon Man links dynamic animations and graphs in a sequenced, interactive learning experience. Students move through a progression of 14 screens, which they can complete at their own pace.

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Bringing Wonder Into Mathematics | Edutopia

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Bringing Wonder Into Mathematics | Edutopia

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Creatively combining the Notice Wonder strategy with a numberless word problem helps students see themselves as mathematicians.

©Shutterstock.com/Monkey Business Images

Doris Lessing once said, "Any human anywhere will blossom in a hundred unexpected talents and capacities simply by being given the opportunity to do so."

My wife and I experienced what Lessing described through a process with our third-grade girls as they were struggling with a multiplication math standard (3.OA.4). The girls were getting stuck in a couple of areas regarding the standard, and were developing negative feelings about math and about themselves as mathematicians. We felt some urgency to try something new, and the new thing we tried had to be engaging and fun, and provide ways for the girls to again see themselves as mathematicians.

Lesson 1: A Numberless Word Problem

Although the girls weren't interested in learning the standard, I knew that if I found the right problem, I could pique their interest. In the California Mathematics Framework for third grade, I found an example problem with both a female lead character and monkeys-we love monkeys. I had found our problem:

Molly the zookeeper has 24 bananas to feed the monkeys. Each monkey needs to eat 4 bananas. How many monkeys can Molly feed?
Solution: ? × 4 = 24
Students might draw on the remembered product 6 × 4 = 24 to say that the related quotient is 6. Alternatively, they might draw on other known products-for example, if 5 × 4 = 20 is known, then since 20 + 4 = 24, one more group of 4 will give the desired factor (5 + 1 = 6). Or, knowing that 3 × 4 = 12 and 12 + 12 = 24, students might reason that the desired factor is 3 + 3 = 6. Any of these methods (or others) might be supported by a representational drawing that shows the equal groups in the situation.

For the girls to access our problem, I used the Notice Wonder strategy, which asks a student to address these questions: "What do you notice? And what do you wonder?" A teacher will show a scenario or problem to students, and they answer those two questions (either in writing or in their heads). After a little wait time, students share their answers with a partner, allowing them to hear another's thinking and to articulate their own observations.

Before the girls engaged in looking at the problem, I needed a few more supports in place, so I modified a foldable sheet known as a diamond paper. To modify it, I added quadrant numbers and a Notice Wonder prompt in each quadrant. On the other side, I numbered the four quadrants and added four prompts. You can see what I did below.
©Jeremiah Ruesch
Next I used a numberless word problem approach, in which you take a problem and break it down, first showing students a numberless version and then, one at a time, more complex versions. This process gives all learners multiple repetitions to access the content, calls out important details, and helps students formulate the same question the standard is asking them to solve. Here's the breakdown for the problem at hand:

1. Molly is a zookeeper. She has some hungry monkeys.

2. Molly is a zookeeper. She has some hungry monkeys and some bananas.

3. Molly is a zookeeper. She has some hungry monkeys and 24 bananas.

4. Molly is a zookeeper. She has some hungry monkeys and 24 bananas, and each monkey needs 4 bananas.

One of my daughters read the sentence 1 out loud, and they both wrote their Notice Wonder statements about it. After a few moments, they shared with each other. Then my other daughter read the second sentence, and they wrote their next Notice Wonder statements and shared. Soon all four sentences had been shared. I had the girls write a question they wondered about regarding this situation in the diamond at the center of the paper.

Once the girls had written their questions, I asked them to share with each other. Then they turned their diamond papers over. On the other side, they had to either create a new question, put their questions together to form a bigger question, or choose one of their diamond questions. The girls came up with this new question: How many monkeys is Molly not feeding? They then had four ways to work through the question as they answered it through these four prompts:

1. What is the problem asking?

2. Create a visual model of the problem.

3. Solve the problem.

4. Write a complete sentence answering the question.

Lesson 2: Writing an E-book

The girls, like all kids, like to create, so we created an e-book. They helped create a template to use and made a project list to keep track of their tasks:

1. Write all the text for the spaces.

2. Find and correct all spelling and grammar mistakes.

3. Find matching photos for the text, not just fun, funny, or cute pictures.

4. They could only add images to the picture boxes in the template.

When they could read the text from cover to cover without finding any mistakes and were happy with their photo choices, we would publish.

Using the numberless word problem and their Notice Wonder statements, they wrote an e-book, Hungry Monkeys, based on their work from Lesson 1, with characters who have a debate about the way to solve the question. They left it for the reader to resolve the conflict in the story.

As Lessing said, the girls blossomed in a hundred unexpected ways: They went from having little understanding to being capable of writing a scenario that showed an understanding of multiple representations of the problem. They had a lot of fun, were fully engaged, and now see themselves as both mathematicians and authors as a result of working through this process. I feel it's important to share this process so other students will have the opportunity to blossom too.

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Creatively combining the Notice Wonder strategy with a numberless word problem helps students see themselves as mathematicians. ©Shutterstock.com/Monkey Business Images Doris Lessing once said, "Any human anywhere will blossom in a hundred unexpected talents and capacities simply by being given the opportunity to do so."

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Math as a Social Justice Lever | Edutopia

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Math as a Social Justice Lever | Edutopia

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Some suggest going easy on kids who'd rather drop out than study math, yet math remains an essential life tool across racial, gender, and class lines.

In the book Radical Equations, the legendary Robert Moses raises the math bar for the entire country, not just as a required subject, but as a social justice issue. Yet, according to him, innumeracy is as acceptable for society as illiteracy is unacceptable. He writes:

So algebra, once solely in place as the gatekeeper for higher math and the priesthood who gained access to it, now is the gatekeeper for citizenship; and people who don't have it are like the people who couldn't read and write in the industrial age. But because of how access to -- the learning -- algebra was organized in the industrial era, its place in society under the old jurisdiction, it has become not a barrier to college entrance, but a barrier to citizenship.

Algebra 1 as the End of the Road?

Even though Americans generally believe that math is the most important subject in school, students tend to drop out at higher rates when introduced to harder math and sciences. It seems the desire is there, but the skill and understanding are not. While there are a plethora of reasons for students to drop out, math always seems to come up as one of those levers with my former students.

In recent times, Andrew Hacker, Grant Wiggins, and Nicholson Baker have come for algebra's neck, stipulating that advanced algebra need not be required for students. The argument goes, "If the students weren't required to take anything above algebra, they wouldn't drop out as often." I agree to the extent that I would love for all my students to make it through high school without too much hassle. We have to reorganize the idea of completion and college readiness to assure that all students have an equitable chance at college or a career of their choosing.

But then it makes me wonder if we've stepped back far enough from these statements to understand the implications of limiting higher-order math. I wonder if these folks think similarly of English, and whether kids should have to read anything above Romeo and Juliet, and not Macbeth or Othello. Or the script to the Leonardo DiCaprio version of the movie. Or the manual to the DVD or mobile device that once played the movie.

As far as I can see, higher-level literacy isn't that necessary to the average citizen, either. Or do we not place the same restrictions on literacy as we do on math?

Math Access Is a Right

Those who get Algebra 2 will mostly likely be the ones perceived to be going to college, and that usually leads to discriminatory practices about who's going to get the "badge" for math completion. Those in the higher rungs of society will get Algebra 2 plus whatever other math will assure that they can apply to technical careers or other careers of their choosing. Those in the lower rungs (an increasing section, mind you) will be relegated to Algebra 1, and courses like "Using A Calculator To Plot A Graph" or "Statistics for Those Who Weren't Allowed to Take Algebra 2."

I'm adamant about access and the opportunity for all students to get access to the most information possible. Do I think math needs reform? Absolutely. Do I think eliminating Algebra 2 as a bridge toward that is the way to go? Absolutely not. This will take a concerted effort from educators (specifically K-12) to reconsider what needs to get taught across the board. I know the Common Core Learning Standards were supposed to do that, but I'm unconvinced as of now. Equity shows up here as the foundation for ensuring that all students have the opportunity to take math, and have multiple doors open to them because of the math they take.

If someone said, "Let's end compulsory higher-order math tomorrow," and the fallout happens across racial, gender, and class lines, then I could be convinced that this was a step toward reform. Yet, given the state of what our culture thinks about math right now, in all of our school systems, I can't risk the possibility that our lowest-income schools don't have access to the same knowledge that their higher-income-level counterparts do.

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Math as a Social Justice Lever | Edutopia

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Some suggest going easy on kids who'd rather drop out than study math, yet math remains an essential life tool across racial, gender, and class lines. In the book Radical Equations, the legendary Robert Moses raises the math bar for the entire country, not just as a required subject, but as a social justice issue.

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The Power of Visualization in Math | Edutopia

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The Power of Visualization in Math | Edutopia

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When do you know it's time to try something different in your math lesson?

For me, I knew the moment I read this word problem to my fifth-grade summer school students: "On average, the sun's energy density reaching Earth's upper atmosphere is 1,350 watts per square meter. Assume the incident, monochromatic light has a wavelength of 800 nanometers (each photon has an energy of 2.48 × 10⁻¹⁹ joules at this wavelength). How many photons are incident on the Earth's upper atmosphere in one second?"

My students couldn't get past the language, the sizes of the different numbers, or the science concepts addressed in the question. In short, I had effectively shut them down, and I needed a new approach to bring them back to their learning. So I started drawing on the whiteboard and created something with a little whimsy, a cartoon photon asking how much energy a photon has.

Immediately, students started yelling out, "2.48 × 10⁻¹⁹ joules," and they could even cite the text where they had learned the information. I knew I was on to something, so the next thing I drew was a series of boxes with our friend the photon.

If all of the photons in the image below were to hit in one second, how much energy is represented in the drawing?

Students realized that we were just adding up all the individual energy from each photon and then quickly realized that this was multiplication. And then they knew that the question we were trying to answer was just figuring out the number of photons, and since we knew the total energy in one second, we could compute the number of photons by division.

The point being, we reached a place where my students were able to process the learning. The power of the visual representation made all the difference for these students, and being able to sequence through the problem using the visual supports completely changed the interactions they were having with the problem.

If you're like me, you're thinking, "So the visual representations worked with this problem, but what about other types of problems? Surely there isn't a visual model for every problem!"

The power of this moment, the change in the learning environment, and the excitement of my fifth graders as they could not only understand but explain to others what the problem was about convinced me it was worth the effort to pursue visualization and try to answer these questions: Is there a process to unlock visualizations in math? And are there resources already available to help make mathematics visual?

I realized that the first step in unlocking visualization as a scaffold for students was to change the kind of question I was asking myself. A powerful question to start with is: "How might I represent this learning target in a visual way?" This reframing opens a world of possible representations that we might not otherwise have considered. Thinking about many possible visual representations is the first step in creating a good one for students.

The Progressions published in tandem with the Common Core State Standards for mathematics are one resource for finding specific visual models based on grade level and standard. In my fifth-grade example, what I constructed was a sequenced process to develop a tape diagram-a type of visual model that uses rectangles to represent the parts of a ratio. I didn't realize it, but to unlock my thinking I had to commit to finding a way to represent the problem in a visual way. Asking yourself a very simple series of questions leads you down a variety of learning paths, and primes you for the next step in the sequence-finding the right resources to complete your visualization journey.

Posing the question of visualization readies your brain to identify the right tool for the desired learning target and your students. That is, you'll more readily know when you've identified the right tool for the job for your students. There are many, many resources available to help make this process even easier, and I've created a matrix of clickable tools, articles, and resources.

The process to visualize your math instruction is summarized at the top of my Visualizing Math graphic; below that is a mix of visualization strategies and resources you can use tomorrow in your classroom.

Our job as educators is to set a stage that maximizes the amount of learning done by our students, and teaching students mathematics in this visual way provides a powerful pathway for us to do our job well. The process of visualizing mathematics tests your abilities at first, and you'll find that it makes both you and your students learn.

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When do you know it's time to try something different in your math lesson? For me, I knew the moment I read this word problem to my fifth-grade summer school students: "On average, the sun's energy density reaching Earth's upper atmosphere is 1,350 watts per square meter.

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Ready: 100 questions that promote Mathematical Discourse

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Ready: 100 questions that promote Mathematical Discourse

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Ready: 100 questions that promote Mathematical Discourse

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100 Questions to Promote Mathematical Discourse by Ready author Dr. Gladis Kersaint. A free printable with 100 questions to promote mathematical thinking and encourage classroom discourse.

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A MiddleWeb Blog

Class is underway and your students are involved in a STEM lesson. Take a close look at their reactions.

Are they interested? Are they engaged? Right up front, assess how the students in your class are responding so you can make quick adjustments today - and use what you learn to strengthen lesson designs throughout the year.

Several possible "fails" may be sabotaging your students' learning. Check for some common problems using this handy "STEM Lesson Debugger."

Bug Check 1: Is the challenge interesting and relevant?

Kids need to be interested and involved in the STEM challenge. The problem they are solving should be a real problem - not one that involves mythical beings, for example. If possible, your kids could generate their own problem, with the caveat that grade-level math and science would be applied to solve it.

Perhaps they could choose from a list of problems that you see as realistic, doable, and appropriate. You can find information about STEM Problems your students can address on the STEM by Design Book Website.

Bug Check 2: Does the lesson help them make sense of the science and math they're learning?

Kids frequently ask, "Why should I learn this?" Suppose they are using what they are learning to solve a real problem. Suddenly what they are learning has real value.

If they need to understand Newton's Laws of Motion and use specific algorithms to see if they have improved a roller coaster car, then these concepts become practical and important.

Bug Check 3: Does the lesson use an inquiry-based method of teaching and learning?

The best STEM lessons use an inquiry approach. The teacher doesn't tell kids what they're going to be doing or how to do it. STEM lessons are full of active learning - much of it student-directed. Kids should be in charge of research and decisions about solving the problem.

And the problem should have several "right" solutions, or paths they could follow. During the lesson, students actively plan, construct, and test prototypes in search of workable solutions. Get rid of the "sit and get" approach in your STEM classroom.

Bug Check 4: Do your students feel safe about failing along the way?

They feel may feel that failing to come up with a working solution will affect their grade. Perhaps they think that failure is always a bad thing in school or that you will disapprove of them if they don't get it right the first time. Those are definitely ideas you need to debunk.

Help students understand that engineers generally try many times before they find something that works. Getting a perfect solution the first time around is not the idea. Analyzing a solution to see why it failed is often the best learning experience kids can get - certainly better than having someone tell them an answer. Students must feel that their classroom is a safe place.

Bug Check 5: Do students know how to approach problem-solving?

STEM classes teach kids to think like engineers as they tackle and solve problems. Take a look at the Engineering Design Process pictured here. This process is typical of the engineering thought process in STEM lessons. This is not a step-wise or linear approach. Kids can go back and forth between steps, and might use a step more than once (or even skip a step at times).

Science leader Neil DeGrasse Tyson emphasizes the importance of teaching kids how to think and solve problems:

We think of education all too often as, a student walks into a classroom with an empty mind and then you pour stuff into the head, and now they're educated. And at no time are you actually trained how to think, how to analyze, how to process information, how to judge information."

STEM lessons push students to use a process that requires them to think creatively, analyze, infer, and evaluate (among other cognitive skills).

Bug Check 6: Are your students able to work successfully in teams?

In STEM classes students work in productive teams and use constructive teamwork behaviors to solve challenges. That's a tall order in itself, as our students often tend to be competitive rather than collaborative.

And they may prefer working alone rather than making concessions and working out common solutions. Being on a dysfunctional team can cause a student to tune out and withdraw from the challenge.

I've recently revised a Student Teaming Tips handbook, and it's free on my new book website. To get it, scroll to the bottom and download it. Spending some time helping students become productive team members is worth the investment in any class.

Bug Check 7: Do students have time to finish the lesson?

Most STEM lessons cannot be completed in one class period. It may actually take several periods. These are situations where you have to "go slow to go fast." Plan where students can successfully end one part of the lesson and pick up during the next class.

A well-executed STEM lesson will address the science and math objectives students are learning, and perhaps some technology objectives as well. So you are not "off track" when teaching a STEM lesson. You are taking the students deeper into specific concepts and objectives.

Bug Check 8: Do students have opportunities to use and create technology?

STEM identifies technology as any innovation or device created by people to meet a need or want. Students, then, are actually creating technologies when they design prototypes. During their STEM lesson, they may explore the benefits and limitations of different technologies, such as an electrical plants, hydroponic gardens, or genetic engineering.

Students should become more aware of how new technologies are developed and how they affect us. To the extent possible, they should use the newest technologies available to them in STEM work.
Here's a tool you can download
to remind you of the 8 bug checks!
Once you've debugged your lesson, you can fine-tune it

You can make many other adjustments to help STEM lessons go more smoothly. To truly become interested and involved with the lesson, your students need to have confidence that they can be successful. Inspire them with peer role models.

Encourage them to combine materials and ideas in clever and imaginative ways to create solutions. Give them an active and a "safe" environment. And have fun as you lead them through the messy process of creating solutions for real problems.
Anne Jolly's new book, From the Amazon description: "This practical book...has all the answers and tools you need to get started or enhance your current program. Based on the author's popular MiddleWeb blog of the same name, STEM by Design reveals the secrets to successful lessons in which students use science, math, and technology to solve real-world engineering design problems." STEM by Design: Strategies and Activities for Grades 4-8, is published by Routledge/Eye On Education, in partnership with MiddleWeb. Receive a 20% discount with code MWEB1 at the Routledge website.

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A MiddleWeb Blog Class is underway and your students are involved in a STEM lesson. Take a close look at their reactions. Are they interested? Are they engaged? Right up front, assess how the students in your class are responding so you can make quick adjustments today - and use what you learn to strengthen lesson designs throughout the year.

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60 Ways Math Teachers Can Use Google Classroom | Teacher Tech

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60 Ways Math Teachers Can Use Google Classroom | Teacher Tech

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I have been asked by math teachers how they can use Google Classroom. Google Classroom is great for any subject area, especially math! Earlier I had posted on 5 ways Students Can Use Google Docs in Math. This builds on those ideas with a list of 60 ways Google Classroom can be used by Math teachers. Check out my book " Teaching Math with Google Apps" for more ideas and specific examples.

1. Create a blended classroom: Google Classroom is the perfect tool to transform a traditional class into a blended model.

2. Go paperless: There are many ways that Google Classroom can support a paperless classroom. Stop standing at the copy machine and use Google Classroom instead.

3. Distribute handouts: It is easy to attach files that are either in Google Drive or on the computer. Attach handouts to an announcement or assignment to allow students to easily access.

4. Collect homework: The homework collection process can take many instructional minutes. Eliminate this by having students submit their work in Google Classroom.

5. Return work: Passing student work back in Google Classroom is as simple as checking

6. Use equation editor: Attach Google text documents to assignments. Google Docs has an equation editor built in. Directions and questions can include equations made with the equation editor. Students can respond using the equation editor.

7. Digitally collect student work: If student complete their work on paper they can use the Google Classroom app to take a picture of the work and submit. Students can insert a snapshot of their paper work via the webcam into a Google Doc to submit to Google Classroom.

8. Post solutions: Students can check their work by locating solutions attached to the assignment in Google Classroom. Editing the assignment after it is due, documents can be attached to the assignment that allow students to view the solutions.

9. Post problem of the week: Google Classroom makes it easy for student to locate the problem of the week (POW). Attach to an optional assignment. Participating students can submit their work straight to Google Classroom.

10. Link to interactive simulations: Several websites have interactive math simulations that can help students have a better understanding of math concepts. Google Classroom gives the ability to link to websites as part of lesson sets. Rather than relying on students typing in the correct URL into their browser students can simply click on the link in Google Classroom.

11. Post corrections: After reviewing student work and noting common misconceptions an announcement can be posted to Google Classroom to make clarifications for students.

12. Highlight student exemplars: Work submitted to Google Classroom is saved to a folder in Google Drive. An announcement in Google Classroom can attach student exemplars from the assignment folder in Google Drive.

13. Distribute assignments: Rather than writing assignments on the board students can have access to the assignments 24/7 in Google Classroom.

14. Provide support materials: Sometimes students need a refresher on pre requisite skills such as how to find the common denominator. As part of the lesson set in Google Classroom provide links to videos, links to websites or attach documents on pre requisite skills.

15. Provide differentiation: Math students have different ability levels and interests. Use Google Classroom to provide different types of resources for student needs.

16. Stop lecturing: Google Classroom allows the teacher to post videos, documentation or links to instructional websites. Google Classroom supports a flipped teaching model. A lecture is ephemeral, resources in Google Classroom allow students access to instructional resources anytime

17. Stop repeating yourself: Clearly posting announcements or important information to Google Classroom allows the teacher to not have to repeat themselves. Students can find the information easily by accessing the Google Classroom stream.

18. Provide directions: Verbal directions or directions written on the board can be missed by students who are absent or engaged in another task. Providing directions in Google Classroom ensures that students know what they are suppose to be doing.

19. Offer choices: Students have different interests. Offering assignment choices in Google Classroom gives students a feeling of locus of control and greater buy in.

20. Link to playsheets: Playsheets are digital worksheets with game elements. Playsheets provide students with immediate feedback which provides motivation for students and helps them to know they are on the right track. Rote math practice is best done with a playsheet.

21. Model mathematics with Google Draw: Create virtual manipulatives, such as Algebra Tiles, in a Google Drawing. Distributing the drawing as each student receives a copy allows students to model their mathematics.

22. Provide hyperdocs: Hyperdocs are a Google Document that structures student exploration and learning of a topic. Thank you to Lisa Highfill for her work with Hyperdocs.

23. Give quiet students a voice: Students may feel shy about raising their hand in class. Using the comment features in Google Classroom students can post their question to the class stream.

24. Provide faster feedback: Using Google Classroom to collect work gives the teacher quicker access to student work. Feedback can be provided while students are working on their assignment or immediately after submitting. Students receive feedback via email as soon as feedback is provided.

25. Target struggling students: Google Classroom counts how many students have submitted an assignment. Clicking on the number of students who have not submitted provides the teacher with a list of students who may need additional help.

26. Post videos: Videos that introduce concepts, hook students into the lesson or provide support resources can be added to lesson sets to help students better understand concepts.

27. Have student critique the reasoning of others: Common Core standards call for students to critique the reasoning of others. Using the commenting features in Google Documents students can critique the reasoning of peer explanations of math concepts. Share the documents in the Google Classroom folder with classmates to allow for commenting or create a collaborative document in Google Classroom for students to reason mathematical and respond to the reasoning of others.

28. Use spreadsheets: Spreadsheets are a necessary life skill. Almost every manager uses spreadsheets to organize information. Household budgets can be created and tracked through spreadsheets. Google Classroom allows teachers to assign Google Sheets spreadsheet activities that help students strengthen their spreadsheet skills and to apply their algebraic reasoning through formulas.

29. Provide class feedback: After reviewing student work different themes or issues may become evident. Returning work to students allows the teacher to provide a global feedback comment that can help clarify common misconceptions.

30. Provide meaningful feedback: Inserting comments into a students Google Doc can allow the teacher to give very specific feedback in response to student work.

31. Collect videos: Students can create videos through a screencast, using a mobile device or other video creation methods. Having students create videos can allow them to be more creative and demonstrate their understanding of concepts. Students are able to link to YouTube videos they created or attach video files in Google Classroom.

32. Use Google Slides for real world applications: Students can create and attach a presentation in Google Classroom. The presentation can include images, videos and explanations of how a math concept is modeled in the real world.

33. Have students conduct research: Mathematics is in almost everything. Having students research topics and explain the math involved with an issue is a great activity for students. Google Classroom allows students to turn in multiple documents to the same assignment. Students can collect and organize their research in a Google spreadsheet or document. They can calculate mathematically in a spreadsheet and display charts and graphs. They can explain and present their findings in a Google document or presentation. Additionally they can attach a document of their bibliography.

34. Allow students to ask questions: Rather than waiting for class to ask questions students can post their questions while they are working on their homework. Other students can respond providing the potential for students to receive a quick answer.

35. Collect data: Google Forms and Google Sheets allow for data collection. Students can conduct or answer surveys and use the information to make mathematical calculations. A collaborative spreadsheet allows students to insert their data.

36. Play games: Games are motivating and fun. Playing math games allows students to practice while having fun. Game based learning experiences can also be created within Google Classroom. Provide the rules and ongoing game elements through announcements in the stream.

37. Have students explain their thought process: There are many websites and apps that will show students step by step how to complete a math problem. Asking students to show their work is no longer sufficient. Having students use a Google document to explain their thought process helps to see that students truly understand the concepts rather than simply memorizing an algorithm.

38. Collaborative reasoning: Prior to providing students the algorithm for solving a problem, students can use a collaborative Google Document or Slides presentation to reason out possible solutions to a problem. Attach a document in Google Classroom as "Students can edit file."

39. Persevere in problem solving: Google Classroom allows for ongoing interaction with a student on a problem. Start students with a problem in a Google Document and have them submit the first part. The teacher can return the document to the students through Google Classroom. After receiving feedback students can build on their previous answer and resubmit. This process can be repeated to allow students to work on multi-step problems.

40. Annotate images: Using Google Draw or Google Slides students can identify math within an image. Using the drawing tools students can label and create shapes over an image. Drawings and Slides with an image can be attached to an assignment in Google Classroom as "Make a copy for each student."

41. Reason abstractly: Students can use a Google Document and equation editor to express an idea abstractly as well as to explain how they derived the equation.

42. Use appropriate tools strategically: When providing students a math question they can determine which tools they need to use to approach and solve the problem. Students can "Create" a Google spreadsheet or other Google Document straight from Google Classroom. Students can use tools such as Desmos, Geogebra, Daum Equation Editor from Google Drive and integrate into their Google documents they submit to Google Classroom. Templates of rulers and other mathematical tools can be created in Google Slides or Drawings to help students use virtual tools.

43. Look for patterns or structures: Teachers can attach documents in Google Classroom that contain a pattern for students to identify and explain. Students can share documents with each other to collaborate on identifying the patterns and structures. Teachers have access to the documents through Google Classroom as the students work on them. Teachers can guide students in their reasoning.

44. Have students model geometric concepts: Using Google Drawings, Google Slides or inserting a drawing into a Google Document allows students to draw geometric figures. Locating an image to represent the geometric figures, students can draw the shape on top of the image.

45. Connect with experts: Using Google Hangout a class can ask questions of an expert in the field. Providing the link to the hangout in Google Classroom gives students access to participate in the questioning, watch the interview, and to access the archive of the interview later.

46. Collaborate with other teachers: Google Classroom classes are not restricted to a teachers roster. Students can participate in activities that other teachers in the department are doing. Different teachers can provide different resources and activities to divide up the teaching load.

47. Response to intervention: Different Google Classrooms can be created for students to join based on student needs. Students needing additional support or students needing additional challenges can join a Google Classroom class around intervention of a particular topic. Teachers in the math department can work together to support one of the intervention classrooms.

48. Provide peer tutoring: Students in upper grades can tutor and support students in lower grades through the creation of a Google Classroom class for this purpose.

49. Remind students: Posting announcements in Google Classroom can remind students of upcoming tests or project due dates.

50. Celebrate success: Success builds success. Google Classroom allows the teacher to encourage students through comments in the assignment feedback or publicly in the stream.

51. Collect evidence: Students working on digital resources outside of Google documents can take screenshots to document evidence of their participation. Google Classroom allows students to attach the screenshots to an assignment.

52. Create projects: Google Classroom allows the teacher to build a lesson set with multiple elements. Posting project directions and resources to Google Classroom clearly communicates the project to the students, allows them to easily access resources, and provides students with a digital easy to submit the project.

53. Crowdsource information: Create a collaborative Google spreadsheet in Google Classroom that allows students to find and contribute information around a topic. Students can use the crowdsourced information for their assignment or project.

54. Have students find examples in real life: The Google Classroom app allows students to submit a picture they take on their mobile device. Students can find examples in their everyday life of mathematical application. Students can identify these applications and take a picture to submit to Google Classroom.

55. Give digital quizzes: Google Classroom makes it easy to link to digital quizzes.

56. Share presentations: Teachers can attach their Google Slides presentations or PowerPoint presentations to the stream. Students can follow along or access the slides later.

57. Provide templates: Create spreadsheet templates or other Google documents to get students started on an activity. Use Google Classroom to provide the template as "Make a copy for each student."

58. View work in a folder: Grading is easier when student work for an assignment is contained in a single folder in Google Drive. Use the preview function to view each student assignment in the Google Classroom folder.

59. Use spreadsheets for inquiry: Google Sheets can be structured to guide students through mathematical concepts.

60. Teach programming: Using programs such as Scratch or Google Apps Script can allow students to demonstrate their understanding of mathematical concepts. Google Classroom makes it easy to post tutorials and directions for using Scratch or other programming tools as well as a venue to submit programming projects.

See all my Google Classroom posts at alicekeeler.com/google-classroom

Teaching Math with Google Apps
Teaching Math with Google Apps is available on Amazon.

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60 Ways Math Teachers Can Use Google Classroom - Teacher Tech

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I have been asked by math teachers how they can use Google Classroom. Google Classroom is great for any subject area, especially math! Earlier I had posted on 5 ways Students Can Use Google Docs in Math. This builds on those ideas with a list of 60 ways Google Classroom can be used by Math teachers.

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MSP:MiddleSchoolPortal/Teaching Strategies for Middle School Math - Middle School Portal

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MSP:MiddleSchoolPortal/Teaching Strategies for Middle School Math - Middle School Portal

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Welcome to College of Education and Human Ecology

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EHE trains the next generation of teachers, financial advisors, dietitians, exercise scientists, hospitality managers, researchers and more who improve the human experience for all.

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5th Grade Fraction Clothesline | Math Minds

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5th Grade Fraction Clothesline | Math Minds

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Providing instructional and assessment tasks, lesson plans, and other resources for teachers, assessment writers, and curriculum developers since 2011.

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Our summative tasks are divided into three classes - Novice, Apprentice and Expert. This is not a measurement of the difficulty of the content, but indicates the extent to which they require students to autonomously apply their mathematical knowledge: Novice tasks explicitly test particular items of content knowledge, Expert tasks are far less structured and require strategic problem-solving skills in addition to content knowledge. A "balanced diet" of Novice, Apprentice and Expert tasks is needed to properly assess the Mathematical Practices.

Each task includes a scoring rubric, a set of pre-scored sample student work, and the same set of work without the scores. Scoring practice for this type of task can be an effective Professional Development activity.

A selection of test forms using these styles of task is also available.

Choosing Tasks

There are several ways of navigating:

1. Use the menu on the left to browse by grade and topic area, or search for a key phrase.

2. Go to the Standards tab to find tasks linked to a particular content standard or practice.

3. The complete set of tasks is listed below in alphabetic order.

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Our summative tasks are divided into three classes - Novice, Apprentice and Expert. This is not a measurement of the difficulty of the content, but indicates the extent to which they require students to autonomously apply their mathematical knowledge: Novice tasks explicitly test particular items of content knowledge, Expert tasks are far less structured and require strategic problem-solving skills in addition to content knowledge.

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Taking that internship in a remote mountain lab might not have been the best idea. Pulling that lever with the skull symbol just to see what it did probably wasn't so smart either. But now is not the time for regrets because you need to get away from these mutant zombies...fast.

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Creativity 2.0: Great Way to Show Angles

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Creativity 2.0: Great Way to Show Angles

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2018 Copyright. All Rights Reserved. The Sponsored Listings displayed above are served automatically by a third party. Neither the service provider nor the domain owner maintain any relationship with the advertisers. In case of trademark issues please contact the domain owner directly (contact information can be found in whois).

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Developing A Math Team: Online And In Person

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Developing A Math Team: Online And In Person

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If you heard me use the word "colleague" in a conversation a few years ago, I would have been referencing the people I work with face-to-face.

If you heard me use that same word today, the people I'd be referring to would be much different. In addition to my face-to-face coworkers, I would be gushing about my incredible Illustrative Mathematics Elementary Team members, and all the amazing educators I interact with in the #MTBoS ( MathTwitterBlogosphere). While the majority of these interactions are solely online, I have had the extreme pleasure of learning and growing with my Illustrative Mathematics Elementary Team -- both online and in person -- over the course of this school year.

Our journey together began in September through a collaborative project between Illustrative Mathematics, Smarter Balanced, and Teaching Channel. Having always used illustrative tasks in my classroom, I was beyond excited to have the opportunity to collaborate on the mathematics and student learning of the tasks with professionals of diverse educational occupations. The team consisted of the varying perspectives of a county math supervisor, district math specialist, college professor, and classroom teachers, all the while supported by the mathematicians and content specialists from Illustrative Mathematics and Smarter Balanced. Each team member brought interesting and insightful perspectives that challenged my thinking during every conversation we had.

Through numerous video chats and shared online docs, the team first collaborated on the development of an instructional task around the CCSS fraction progression. We used the 5 Practices for Orchestrating Productive Mathematics Discussions for developing a lesson plan for task implementation in two fifth grade classrooms. I taught the lesson, filmed it, then uploaded it to Teaching Channel Teams for the group to watch and leave feedback.

For anyone who has ever been observed by their colleagues, you understand how intimidating this can be. However, it was amazing to feel so safe and comfortable with a group of colleagues I had, at this point, only met online. I am convinced it was our common vision and passion for the teaching and learning of mathematics that created a very special bond between all of us.

Looking closely at student work and listening to the classroom conversations, we collaborated on revising the lesson for Teaching Channel's filming of Alicia Farmer's classroom the following week. The revised lesson was filmed with Alicia's class and afterwards, Alicia, Jennie (Alicia's district math specialist), and I had the opportunity to sit and reflect on the lesson and the collaborative experience as a whole. Our work did not stop there, however. We used these learning experiences to create and deliver professional development on the fraction learning progression and the thoughtful lesson planning of tasks.

Being departmentalized in fifth grade, I use a lot of "I" when talking about the teaching in my classroom. However, through this work, that "I" has often been replaced by "We." I wasn't the only one curious about what the fraction standards looked and sounded like around particular tasks; we were all curious. I wasn't the only one looking at an Illustrative Mathematics task and anticipating student strategies; we anticipated together. I wasn't the only one analyzing student conversations and working on the next moves; we were doing all of this together. It was in fact the "we" that created an indescribably powerful collaborative learning experience, not only for myself, but for my students as well.

I'm excited to say that our work together did not end here. Members of our Elementary Team have continued to work with Illustrative Mathematics throughout the remainder of the school year. We are currently working together to develop and deliver professional development on fraction instruction with teachers from two school districts in New York City. This work has us continuing to meet online and, even better, we have the opportunity to work together, in person, to deliver the professional development!

Perhaps the most unique piece of this experience is my stance as a learner in this work. Our team plans, discusses, revisits, and revises our plans with the learning of the teachers as our focus. However, ironically, I feel as if I am the learner. In every facet of this experience I have learned more about the content I teach, and the importance of collaboration with passionate math educators. I am proud to call all of the wonderful people involved in this work my colleagues.
Kristin is a Nationally Board certified, fifth grade math teacher at Richard A. Shields Elementary School in the Cape Henlopen School District in Lewes, Delaware.

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Developing A Math Team: Online and In Person

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If you heard me use the word "colleague" in a conversation a few years ago, I would have been referencing the people I work with face-to-face. If you heard me use that same word today, the people I'd be referring to would be much different.

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5 great math projects to keep middle school and high school aged students engaged at the end of the year

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5 great math projects to keep middle school and high school aged students engaged at the end of the year

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Picture it: it's the end of the year, state testing is over, you're finished (or close to finishing) the curriculum for the career... so what do you do for those last few weeks of school to keep the students engaged?

That's what one teacher over on the We Are Teachers Helpline brought up this week. Mandy, a high school math teacher, wonders: how do you keep students engaged and excited to learn when there are three weeks remaining between the end of state testing and the last day of school? "I want something more fun than just work, but they need to be learning as well," she told us. Here are some of the top math projects her colleagues around the globe offered.

#1. Pick a career, any career! A great way to engage students is to get them thinking about their own futures. "Do a real-life lesson where they choose their ideal career, then research the average salary for that job in your state. Then make them create a budget based on that salary, including food, utilities, mortgage, and car. After they are all finished, reflect on cost of living and the importance of a budget and responsible spending." - Melissa H.

#2. Package design. "Assign a project based on designing packaging for oddly shaped products, like tennis balls, ping pong balls, and lollipops. Kids figure out the volume, surface area, and design of the box. They should take into account the space available on the store shelf and size of the shipping box. Then, they can complete surveys about colors and designs to figure out audience appeal. Then they pitch their plan. Real world math!" - Raquel A.

#3. Go interdisciplinary. Give a selection of project options to differentiate their work and bring in other disciplines. "At the end of the year, my math students either research famous mathematicians, create a math game and teach others how to play, or write an ABC book of math concepts in verse. The assignment is purposeful, relevant, fun, and provides choice." - Shelley A.

#4. Pay it forward! Partner with a class in the grade below and have a lesson exchange. Group up students and have them pick one skill they learned this year. Then have them plan a lesson wherein they teach the class that skill, including an assessment. This will reinforce their own knowledge of the skill while sharing it with others.

#5. To the Internet! "If you're looking for great STEM ideas, one great site is www.egfi-k12.org for lesson plans and projects. They're excellent and sorted by every grade level!" - Lorraine A. We think the Robot Soccer Challenge for middle school and Conveyor Engineering Activity for high school look pretty cool.

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5 Awesome End-of-Year Projects to Keep Your Math Students Engaged - WeAreTeachers

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Picture it: it's the end of the year, state testing is over, you're finished (or close to finishing) the curriculum for the career... so what do you do for those last few weeks of school to keep the students engaged? ...

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Overview

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important "processes and proficiencies" with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council's report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy).

Standards

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The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important "processes and proficiencies" with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections.

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common core resources /mathematical practice standards /

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common core resources /mathematical practice standards /

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common core resources /mathematical practice standards /

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common core resources /mathematical practice standards /standard 1: make sense of problems & persevere in solving them /

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common core resources /mathematical practice standards /standard 1: make sense of problems & persevere in solving them /

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Connections to Classroom Practices
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution...They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution...Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems...
Liz O'Neill works with her first grade students engaging them in composing and decomposing numbers within twenty. She begins with two warm-up activities engaging students in working with numbers less than 20. Using sentence frames, students shared with their partner what number they saw and how they saw it. A variety of ways were discussed as a whole group after everyone had a chance to share with their partner. Students then played the game "How Many are Hiding?" Student pairs were given a bag with 10 cubes, a paper plate, and the "How Many Are Hiding Recording Sheet". The partner game gives students practice in composing and decomposing numbers within ten. In addition, sentence frames were posted on the board so students could produce academic language using structured student talk and convince their partners with oral justification.
They monitor and evaluate their progress and change course if necessary...Mathematically proficient students check their answers to problems...
Tracy Lewis leads a re-engagement lesson on the language of word problems, helping students to use word clues to identify mathematical operations. In this clip, she creates a "safe place" for students to examine their own errors and think about how to improve their own work. The students ask each other how they arrived at the answers to the problem and discuss different approaches.
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution.... They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
In this clip, Mia Buljan works with her students on a number talk, using a mental math approach to multiplying a two-digit number and a one-digit number. She invites her students to share their approaches to the problem, and probes them with questions to identify rationales for their reasoning.
Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?"
As her 3rd-grade students work on a multiplication/division word problem, Buljan works with students Enmy and Esbin to dig deeper into their ways of making sense of the problem. She encourages Enmy to persevere and Esbin to let her do so, saying "Just let her try and figure it out. No coaching."
Mathematically proficient students can explain correspondences between equations, verbal descriptions...or draw diagrams of important features and relationships... Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem.
Becca Sherman leads a formative assessment on understanding division in story problems. In this clip, her students use original pictorial representations; the Singapore Bar Model is used as another representation to further understanding of the problem and of division. She asks her students, "how could you add to your math picture, to show this idea?"
Mathematically proficient students... make conjectures about the form and meaning of the solution ...
On the first day of the learning segment, Michelle Makinson engages her learners in a math talk focused on unit fractions, combining into wholes, "parts of," and the idea of equivalence, using manipulatives to create and explain a visual representation of a contextualized representation / word problem. Her students then share with their partners, explaining their approach. This clip also relates to standard 3 (construct viable arguments & critique the reasoning of others), standard 5 (use appropriate tools strategically) and standard 6 (attend to precision).
See this video in the context of an entire lesson. They analyze givens, constraints, relationships, and goals... Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Fran Dickinson leads a number talk on an input/output table and graph, asking "What's my rule?" In this clip, he generates an output number after students offer an input number. The students discuss whether or not 0 is a possible input for the table and graph. This clip is also indicative of standard 3 (construct viable arguments and critique the reasoning of others).
Mathematically proficient students can explain correspondences between equations...They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Fran Dickinson leads a lesson on numerical patterning, in which learners are asked to investigate a numeric pattern and to generalize what they see happening as the pattern grows. In this clip, the learners individually review a copy of two students' work on the MARS "Buttons" task and then discuss what they know or a question that they have about the sample work. This clip is also indicative of standard standard 2 (reason abstractly and quantitatively).
Mathematically proficient students start by explaining to themselves the meaning of a problem... Mathematically proficient students can explain correspondences between equations, [and] verbal descriptions...Younger students might rely on using concrete objects or pictures to help conceptualize... They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Fran Dickinson's students sketch and color code their pattern drawing and use tiles to show what is staying the same and what is changing. In this clip, one student explains to another how blue tiles represent the "old tiles," or the tiles from the previous stage. This clip is also indicative of standard 5 (use appropriate tools strategically).
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution...They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt...Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Joe Condon works with his 6th grade students to identify strategies for comparing unit rates. In this clip, his students first think about their strategies on their own, then share in groups.
They monitor and evaluate their progress and change course if necessary...
Jacob Disston leads a lesson on connections between ideas about equations, inequalities, and expressions, helping students to use mathematical vocabulary for a purpose to describe, discuss, and work with these symbol strings. In this clip, he asks his students to group themselves by the common features of the symbol strings, and justify their groupings to the class. This clip is also indicative of standard 3 (construct viable arguments and critique the reasoning of others) and standard 6 (attend to precision).
They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Cecilio Dimas leads a lesson on constructing, communicating, and evaluating student-generated tables while making comparisons between three different financial plans, helping students use multiple representations of mathematical problems: verbal, tabular, graphical, and algebraic generalization. In this clip, Dimas asks his students to examine a table comparing DVD rental plans, and ask themselves, "Does this make mathematical sense? Why or why not?" This clip is also indicative of standard 3 (construct viable arguments and critique the reasoning of others).
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution...They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.
Jake Disston works with his middle school students to deepen their understanding of the connections between different representations of functions-graphs, t-charts, and equations. In this clip, he begins the period by challenging his students to work at their tables to group the cards they have in front of them, creating as many different groupings as they can, and devising language to describe each group. Disston's colleague Jesse Ragent then asks the students to do a "matching game." He passes out sets of tables and equations to the students, and challenges the students to "find a triple"-- an equation, a table, and a graph that all make up a "family, triple, or set."
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals.
Antoinette Villarin begins her lesson on graphing constant rates of change by reviewing the learning goals and mathematical practices, naming Standards for Mathematical Practice 1, 3, 6, and 7. She notes that it is important that her students understand how to build a mathematical argument, and she shares sentence frames and key vocabulary that the students will use as they build their arguments.

Antoinette presents a model of two bottles attached to each other so that fluid can flow between them, and she asks her students to make sense of the problem by describing what they see happening.

Students share that as the amount of fluid in the top container/prism decreases, the amount in the bottom container/prism increases.

This clip also relates to standard 3 (construct viable arguments & critique the reasoning of others), standard 4 (model with mathematics), standard 6 (attend to precision), and standard 7 (look for and make use of structure).
Mathematically proficient students ...analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.
Antoinette Villarin asks her students to engage in a "turn and talk" with a fellow student, with the purpose of describing how they would know how many centimeters of liquid will be in the bottom container, given the number of centimeters in the top container.

In the "turn and talk," Antoinette's students use the vocabulary and sentence frames she provided to make sense of the problem. Antoinette gathers the students back together and asks the pairs to share their findings with the whole group.

Antoinette describes the constraints for the problem. She then asks students to look at a graphical representation of the problem and respond to the prompt "I think this graph represents ..." on their whiteboards.

Her students then share their statements with their partners. After the students share with each other, Antoinette asks pairs to report out on their conversations.

This clip also relates to standard 3 (construct viable arguments & critique the reasoning of others).
Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Antoinette Villarin asks her student pairs to share their discussions with the whole group. She models academic language - constraints, rate of change, initial value, starting situation - that she expects her students to use.

Once a student pair has shared, Antoinette asks the larger group to add on additional details that helped them identify a matched pair of graphs that show the flow of liquid between a given pair of containers.

Antoinette refers back to her anchor chart of the lesson vocabulary and sentence frames that she expects the students to use, and she names and reinforces students' use of academic language.

This clip also relates to standard 6 (attend to precision), and standard 7 (look for and make use of structure).
Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?"
Antoinette Villarin reminds her student pairs that - once they are confident about a match between graphs - they should record their matches and explain their justification, ensuring that both partners in each student pair understand and can explain their reasoning.

Student pairs discuss and record their thinking on their recording sheets. Antoinette circulates among the pairs and engages them in explaining their thinking - for example, reminding them to identify the starting situation to help guide them.

This clip also relates to standard 6 (attend to precision).
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution.... They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.
Patty introduces her lesson by charging students to identify the "big ideas" they should be thinking about when they work with right triangles. Students pair-share their ideas, and Patty notes when they are making reference to available tools and supports, such as anchor charts, around the room. In her commentary, Patty notes that this lesson is intended to develop students' capacity to engage in modeling mathematical situations. Students identify the Pythagorean Theorem, and Patty prompts them to attend to precision and communicate precisely. In a whole-group sharing, she engages all students to add on to, critique, extend, and clarify each other's thinking. Students deepen their capacity to make sense of the problem or situation. Patty presents student work from a previous assessment and asks students to critique the person's strategies and precision, giving advice to each exemplar learner about how to improve their approach. This clip also relates to standard 3 (construct viable arguments & critique the reasoning of others), standard 4 (model with mathematics), and standard 5 (use appropriate tools strategically).
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution.... They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.
Patty's students give advice to their peers about perseverance and strategies they can use to help themselves in an upcoming MARS performance assessment task. She asks "What do you do when you're stuck? What strategies should you try?" Students think, write, then share their strategies with each other. They identify strategies using anchor charts and calculators, drawing pictures, consulting a peer, taking their time, double-checking their work, and ensuring that it makes sense.
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, ... relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt...
Cathy Humphreys leads an extended exploration of a proof of the properties of quadrilaterals, helping students learn to investigate, formulate, conjecture, justify, and ultimately prove mathematical theorems. In this clip, she models how to gather information for the tinkering stage of the investigative process and emphasizes the importance of the process of private individual thinking prior to the group addressing a task. This clip is also indicative of standard 6 (attend to precision).
They monitor and evaluate their progress and change course if necessary. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Mathematically proficient students ...continually ask themselves, "Does this make sense?"
Continuing into the group section of the task, Humphreys' students work in teams of four engage in extended discussion about the properties of kites made by a factory. Their discussion of the properties of quadrilateral shapes proves less complex for some shapes (square, rectangle, rhombus) than for others (non-isosceles trapezoid.) Humphreys circulates around the classroom as the students work, and in her commentary she notes students' use of imprecise or inaccurate language to defend their thinking. This clip is also indicative of standard 3 (construct viable arguments and critique the reasoning of others), standard 6 (attend to precision), and standard 7 (look for and make use of structure).

They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt... They monitor and evaluate their progress and change course if necessary. See this video in the context of an entire lesson. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution... They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.
They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. (Parts A - E)

See how SEL Competencies and Mathematical Practices work together in this classroom.
(Describing an Ideal Classroom, Appendix) They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.
In the closure of the first day of Humphreys' students' exploration, she orients them to the next phase, which will require students to justify and prove their findings about the diagonals of the kites. In this clip, she asks them to "convince yourself, convince a friend, convince a skeptic" with their justifications.
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends...Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
On the second day of Humphreys' exploration of the properties of quadrilaterals, students work through their understandings of congruent triangles, the triangle postulates, parallel lines, transversals, and other geometric properties to apply those to create proofs for the quadrilaterals. Humphreys illustrates how to use selected notation in a proof as students work through the logic and reasoning. This clip is also indicative of standard 3 (construct viable arguments and critique the reasoning of others) and standard 6 (attend to precision).

In small groups, Cathy Humphreys' students discuss and debate proof arguments. At selected times, she pulls the class together to share findings, ideas, or sample justifications. After sharing ideas or arguments with the entire class, students then return to working in their small groups. This clip is also indicative of standard 3 (construct viable arguments and critique the reasoning of others) and standard 6 (attend to precision).

Cathy Humphreys works with her students as they get closer to being able to present their group defenses of the various properties of quadrilaterals. She reminds them about the difference between the properties of a square and a non-square rhombus, and that the groups should keep track of them development of their thinking as they go along. A group of students defines their quadrilateral, then say "Now let's prove it... we need to not just say that it's a rhombus, but prove it." This clip is also indicative of standard 3 (construct viable arguments and critique the reasoning of others) and standard 6 (attend to precision).

Carlos Cabana works with his high school English language learning students on algebraic reasoning and multiple representations around parabolas. In these clips, his students build sketches of parabolas and link them to a T-table. His students have had some exposure to factoring and multiplying, but it's not automatic for any of them yet. They see how to find x and y intercepting with lines at a procedural stage. The students have previously made tables for parabolas and they can find the vertex in the table, and are developing capacity to use the vertex to calculate other parabolic properties.

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Standard 1: Make Sense of Problems & Persevere in Solving Them | Inside Mathematics

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Classroom Observations Teachers who are developing students' capacity to "make sense of problems and persevere in solving them" develop ways of framing mathematical challenges that are clear and explicit, and then check-in repeatedly with students to help them clarify their thinking and their process.

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Terrific Math Lesson Idea: Carousel Activity

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Terrific Math Lesson Idea: Carousel Activity

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We all have them, some good and some bad. We pick them up from friends, family, and even strangers. But we may not recall who we picked them up from or when they began.

Because we've practiced them over and over, these seemingly thoughtless repeated habits or behaviors, the pathways in our brain have become so broad, fast, and efficient in carrying them out that we do them automatically without even thinking. Yet these unconscious habits and behaviors add structure and order to our lives and help us to make sense of the world we live in.

Our classrooms are full of them. We teachers are pros when it comes to employing and modeling good habits and routines that enable us to manage and carry out the many tasks and demands of teaching. And when it comes to teaching mathematics, we model and teach our students how to carry out procedures and algorithms flawlessly. But why is it that these same students often struggle when confronted with a problem to which the immediate answer is unknown?

Experienced vs. Inexperienced Problem Solvers

According to Levasseur and Cuoco (PDF, 80KB), it's the mathematical habits of mind, or modes of thought, that enable us to reason about the world from a quantitative and spatial perspective, and to reason about math content that empowers us to use our mathematical knowledge and skills to make sense of and solve problems. It's these habits that separate the "experienced" from the "inexperienced" problem solver.

Far too many students can be classified as inexperienced problem solvers who don't know what to do when they don't know what to do. These are the students who lack experiences in making sense of and solving problems, and in communicating and using precise, appropriate mathematics and mathematics language. They have never developed the overarching habits of a productive mathematical thinker.

When they're presented with a problem to which they don't know the immediate answer, their bad habits often rise to the occasion. They may begin with no real strategy in mind, they look for key words and terms that can sometimes be misleading, they want a quick answer, they resort to memorization over understanding, or they simply make no effort at all in finding the solution to the problem.

On the other hand, experienced problem solvers know what to do when they don't know what to do! They practice perseverance and automatically employ the mathematical habits of mind of a productive problem solver in their quest for a problem solution. They automatically engage in Polya's four-step problem-solving process to find a solution to the problem.

No one has to remind experienced problem solvers to first make an attempt at understanding the problem and ask clarifying questions that help them interpret and understand the conditions of the problem. They instinctively try to make sense of the mathematical situation at hand and choose a strategy, tools, and/or models, often based upon previous learning experiences or problems they've solved -- experiences that they see as relevant and applicable in solving the problem.

If they try a strategy and it doesn't work, they try a different one - all part of perseverance in problem solving. And like any good problem solver, once they have a solution, they take one last look to determine if their solution is a reasonable solution to the problem.

Practice and Experience

But these habits of mind can't be learned and developed by simply talking about them or memorizing the definition. Students immersed in classroom experiences that let them engage in learning mathematics concepts through problem solving, making and using abstractions, and developing and applying mathematical theories have greater opportunities for developing mathematical habits of mind. Classrooms steeped in the Common Core Standards for Mathematical Practice (MP) provide maximum opportunities for students to learn and develop these habits as they:

Teachers who saturate learning experiences with the Standards for Mathematical Practice offer students a variety of palatable problems. Presenting relevant, interesting, and challenging problems that can be approached and solved with different strategies and tools gives students choices that best fit their learning preferences. This approach is more inviting to them and leads them to reason about, look for, and make use of structure. In turn, it increases their chances of understanding important math concepts and skills, which in turn increases their ability to explain their thinking and reasoning, and to critique the reasoning of others.

You play a vital role in the development of mathematical habits by conveying to your students a mindset that fosters productive struggle and emphasizes the possible value of wrong answers. You set the stage by embracing the importance and value of grappling with problems. The more you engage your students in learning and doing mathematics, the greater the likelihood of their developing the mathematical habits of mind of a productive mathematical thinker -- and becoming experienced problem solvers who know what to do when they don't know what to do.

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We all have them, some good and some bad. We pick them up from friends, family, and even strangers. But we may not recall who we picked them up from or when they began.

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Before the lesson, students work individually on an assessment task that is designed to reveal their current understandings and difficulties. You then review their work, and create questions for students to consider in order to improve their solutions.

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Grade 8 CCSS PrBL Curriculum Map - Google Docs

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Grade 8 CCSS PrBL Curriculum Map - Google Docs

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Math Lesson Plans for Teachers - Mathematical Awareness Month - Lesson Plans - Share My Lesson

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Math Lesson Plans for Teachers - Mathematical Awareness Month - Lesson Plans - Share My Lesson

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Share My Lesson | Free Lesson Plans & Teacher Resources

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Find the right K-12 lesson plans - for free. Share My Lesson offers free lesson plans, teacher resources and classroom activities created by dedicated educators.

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Assessing background knowledge is an often misunderstood idea, and subsequently fumbled as a process.

Background knowledge is a product of the experiences-academic and otherwise-that a student brings to a lesson. These provide both knowledge in terms of content, as well as schema in terms of analogs students can use to make sense of new ideas.

The purpose of assessing background knowledge is not to get everyone on the "same page," but rather to make visible the nature of what a student knows (rather than a list or academic labels like "proficient). This makes it possible to create personalized learning pathways for students as each learner approaches new-or familiar-thinking on their own terms.

From a planning point of view, it can also allow teachers to identify knowledge gaps, prioritize standards, and revise imminent lessons and units in response. As for how this is done? Conversations, concept maps, drawings, writing prompts-traditional assessment forms can work here, but you've got some flexibility because what you're trying to assess may not be entirely academic or urgent.

M ia MacMeekin created the following infographic that offers 27 ways to assess background knowledge. Ideally, we'd like to see a bit more writing-formal and informal, along with some more conversational dialogue that didn't demand debate protocol, but other suggestions, including mindmapping, creating a prototype, and even the "shout all at once" may have a place in your classroom.
27 Ways To Assess Background Knowledge

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Assessing background knowledge is an often misunderstood idea, and subsequently fumbled as a process. Background knowledge is a product of the experiences-academic and otherwise-that a student brings to a lesson. These provide both knowledge in terms of content, as well as schema in terms of analogs students can use to make sense of new ideas.

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Educational Technology and Mobile Learning

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Cultivating an innovative culture inside your classroom and enhancing your students inquiry-based approaches to learning is not an easy task particularly in the light of all the surrounding distraction coming from digital media. It is probably one of the major challenges facing educators and teachers in the 21st century classroom.

However, no matter how big the challenge is there are always ways to come to grips with it. Our colleague Mia MacMeekin from anethicalisland has designed this beautiful graphic where she featured 27 ways teachers can help their students be innovative.

I really love it that Mia formulated her ideas in the form of action verbs prompting students\teachers to act. Check out her graphic below and share with us what you think of it. Enjoy

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Cultivating an innovative culture inside your classroom and enhancing your students inquiry-based approaches to learning is not an easy task particularly in the light of all the surrounding distraction coming from digital media. It is probably one of the major challenges facing educators and teachers in the 21st century classroom.

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How To Address The STEM Education Gender Gap In Schools - (Deeper Learning)

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How To Address The STEM Education Gender Gap In Schools - (Deeper Learning)

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Closing the Gender Gap in STEM Education

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Get tips on closing the STEM education gender gap. By discussing the topic directly with female students, one school is working to close this gap using various strategies.

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Science & Engineering Practices Next Generation Science Standards

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Science & Engineering Practices Next Generation Science Standards

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Educators receive an introduction to the Science & Engineering Practices in the Next Generation Science Standards. In a professional development session, educators are introduced to the practices. They engage in activities designed with the NGSS in mind and reflect on their learning.

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Playing With Math: How Math Circles Bring Learners Together For Fun | MindShift

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Playing With Math: How Math Circles Bring Learners Together For Fun | MindShift

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In the U.S., "most of the kids come to the math circle because they don't like what they see in school and they're looking for something else."

Creating a math circle takes a lot of energy and planning -- from finding dynamic instructors to booking classroom space -- but it can be well worth the effort if no similar enrichment opportunities are available nearby. Parents might consider forming a circle when their children come home from school saying they're bored with the level of mathematics that's being taught, Sylvester said. "If your kid comes back and wants more challenging math, or if they love math or they love puzzles, then start one."

One Sunday last November, the fledgling program was underway at a community center, with around 19 boys and seven girls mulling over a game called Conway's checkers. The visiting instructor that day was Zvezdelina Stankova, a Mills College professor and director of the Berkeley Math Circle. Each student was given a sheet of paper with a grid of squares -- divided in half by a thick line -- and a pile of pennies to serve as checkers. Beginning at one end of the board, and given particular rules for checker-jumping and a theoretically endless supply of coins, Stankova asked: How far could the coins be advanced?

Students experimented with jumping the checkers to the third row on the other side of the line, and then the fourth, and Stankova demonstrated the winning solutions. What about the fifth row? Many kids became so engrossed, chattering among themselves, they didn't want to stop to hear the next part of the lesson. "No touching the coins!" Stankova finally admonished. "It's impossible to reach the fifth row," she said, briefly explaining that the reason had to do with the quadratic equation and the Golden Ratio.

Stankova grew up in Bulgaria, where it was common for children to attend circles in math, physics, chemistry and poetry. "Kids went to the math circle because they loved what was happening in class and they wanted more of it," she said. By contrast, in the U.S., "most of the kids come to the math circle because they don't like what they see in school and they're looking for something else."
A COMFORTABLE PLACE FOR MATH GEEKS
About three years ago, Sylvester wanted to take Andrew to a math circle after hearing of the programs at Berkeley as well as Stanford, but those courses are popular and hard to get into. He and his wife have fostered their son's passion for numbers in various ways, including online courses and a summer camp in mathematics, as well as math competitions. Although UC Santa Cruz was offering a monthly math circle at one point, that course was put on hold when the professor who ran it went on sabbatical.

Last summer, Sylvester decided to start a circle through the X Academy, a nonprofit that he founded to offer enrichment activities, and he reached out to math professor Paul Zeitz, co-founder of the San Francisco Math Circle. Zeitz promptly volunteered to give an introductory math circle session in Santa Cruz and connected him with Stankova and other willing expert instructors.

"I thought I'd be lucky to get five kids in a room on a Sunday afternoon," Sylvester said. To his surprise, 50 students and their parents signed up to attend the free kickoff session by Zeitz. Through an application process, the Santa Cruz Math Circle ended up with around 25 regular attendees for the rest of the fall course; registration cost $75, but scholarships were available.

Sylvester ran the course with help from X Academy board members (including Meister) and other parent volunteers, who assisted with promotion and setup. Meeting the needs of students from fourth through eighth grades in a single class proved too wide of a spread in ability and maturity to manage, so the software engineer brought in an extra instructor and split the students into two tracks; but younger kids such as Andrew who were ready for the math of the upper-level group could move up.

For many attendees, being in a place where they could dive into math and interact with other number-loving geeks was a welcome shift from the standard school environment, where the subject isn't exactly popular. The circle "creates this community where it's safe to come and talk about math," said teacher Nicholas Bugayong of Rolling Hills Middle School in Watsonville, who volunteered to drive four eighth-grade math students, all from Latino families, to the Sunday sessions. Some of these pupils were otherwise unable to make the 17-mile trek -- their parents couldn't bring them -- or to afford the course without X Academy scholarships.

"Other people don't like math and they say it's a waste of time, but I think it's interesting to learn things that you don't learn in school," said Rolling Hills student Monica Alvarez, 13. Listening to the other students as they volunteered different ideas and strategies for tackling challenging problems "helps you to learn other ways to solve a puzzle," she added.

As for Andrew Sylvester, now age 10, the program prompted some more "math highs," such as when he got into thinking about the Conway's checkers conundrum. And the lessons spurred lively discussions. During one pizza break, he stayed behind in the classroom with two other boys who are also profoundly gifted at math. "They were bent over a piece of paper scribbling, in animated conversation," recalled Strauss, whose son was part of the confab.

"I just like learning the math and arguing with my friends about math stuff -- for example, stuff like if one over infinity equals zero," said 10-year-old Olin Ottemann-Strauss.
MATH CIRCLE STARTUP LESSONS
The Santa Cruz Math Circle resumes this spring. A major challenge will be continuing to arrange for high-quality instructors, Tim Sylvester said. While ideal teachers include math professors or scientists or engineers with doctorates in math, not all such experts have the experience or classroom management skills to instruct young pupils in a dynamic way. But Sylvester hopes to eventually join forces with UC Santa Cruz's math circle.

Even if there is no nearby college to collaborate with, anyone interested in launching a math circle program can find helpful, step-by-step resources on the National Association of Math Circles website, including lesson plans from the book, Circle in a Box. Teachers at some Bay Area schools have created their own programs, Sylvester noted, such as Nueva School in Hillsborough.

Sustaining a circle does require adequate financing, which can be an ongoing challenge if registration fees are to remain affordable. The Santa Cruz program recently got a donation from Cisco Systems, where Sylvester used to work, and parents can make contributions to X Academy through its website. The academy has also applied for a seed grant from the Berkeley-based nonprofit Mathematical Sciences Research Institute, which has funded many math circles over the years. But the institute is currently reviewing that grant program and has ended its support of the San Francisco Math Circle.

While many students often question why they need to learn algebra or calculus that they might not use later in life, Sylvester sees the ability to figure out tough math problems as being an essential life skill.

"One of the reasons you learn math is for the thought process and the problem-solving process," he said. "That's why you do it."
Correction: An earlier version of this story misidentified Barbara Meister as Barbara Sylvester. It also stated that Andrew Sylvester's third grade lessons in long division were at a private school, which is incorrect. He was attending a public school.

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Playing With Math: How Math Circles Bring Learners Together For Fun

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In the U.S., "most of the kids come to the math circle because they don't like what they see in school and they're looking for something else." Creating a math circle takes a lot of energy and planning -- from finding dynamic instructors to booking classroom space -- but it can be well worth the effort if no similar enrichment opportunities are available nearby.

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Google's Free Lesson Plans - A Look At Google's Massive Library Of Free Lesson Plans

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Google's Free Lesson Plans - A Look At Google's Massive Library Of Free Lesson Plans

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You probably already use Google daily, either for Web searches, email, or maps. The tech company is increasingly involved in modernizing education, and it has developed several ventures to encourage an interest in science and computer programming. Some of these ventures are contests, and some are designed for use by afterschool or summer programs. But you can access this great content even if you don't officially participate in a program. Many of these activities use art, music, and social awareness to make technical lessons more appealing. Take a look at these activities, and start thinking outside the little Google search box.

With this worldwide contest, Google has thought far beyond the high school gymnasium science fair that we all know. Even if your students won't officially enter, Google has compiled a lot of great resources for middle and high school science students. Find lesson plans to teach students about scientific inquiry and the scientific method. The Idea Springboard can help students find a project that fits their interests and talents. And the Resources page provides links to science news and education sites.

The Made with Code project is designed to show girls that coding is cool. Students can watch inspirational videos from women and girls who are changing their communities with code. The coding projects let students mix music, build an avatar, or even design a yeti. With work like that, the boys might be jealous. They can use the site, too, of course.

Google holds an annual contest for students who want their own Google design to be the logo for a day. The contest is for grades K-12 and is broken into age groups. The contest page also includes classroom activities to teach children how to brainstorm, critique the efforts of other students, and create their best work.

Google's goal with CS First is to foster computer clubs that teach students to code. Google provides the coding activities free online, so students can use them even without a club. Students can create video games, animation, interactive stories, and more. The activities are designed for older elementary and middle school students but could work for slightly older and younger kids as well.

If you want to incorporate Google tools in your classroom but have questions, start here. Find a Google Educator Group near you or one you can connect with remotely. You will meet other teachers interested in technology and innovation who can collaborate with you, offer advice, and inform you of training opportunities. Talking to another teacher can be much more insightful than simply typing your question into - yes - Google.

Still innovating

Google originally got its name from the word googol - an enormous number. And those Google employees seem to have an enormous number of ideas. In the past few years, the company has tried a bunch of education initiatives. Some have stuck. Some haven't. So while you're exploring these options, remember to check in every few months at the Google education site to see what's new.
Editor's note: This article is a revision and combination of several older Edudemic articles, updated and re-analyzed to reflect the latest innovations.

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You probably already use Google daily, either for Web searches, email, or maps. The tech company is increasingly involved in modernizing education, and it has developed several ventures to encourage an interest in science and computer programming.

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Use The UPS Strategy As An Assessment Tool

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Use The UPS Strategy As An Assessment Tool

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Thought starters

1. How does Ms. Mickle assess learning through each part of the U-P-S strategy?

2. How can students use this strategy to assess their own understanding?

3. How could the data gathered from this strategy be used to inform instruction?

School Details

Cedar Hill High School
1 Longhorn Boulevard
Cedar Hill TX 75104

Data Provided By:

Teachers

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Formative Assessment Using the U-P-S Strategy

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Geometry teacher Tereze Mickle uses the U-P-S strategy to assess her students' understanding. Through the U-P-S strategy, students work on understanding, planning, and solving problems before checking their work. Tereze explains how each step of the process gives her information about her students' learning.

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Using Formative Assessment In High School Math Class

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Using Formative Assessment In High School Math Class

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Math.HSG.CO.B.6

Common core State Standards

Math: Math

HSG: High School: Geometry

CO: Congruence

B: Understand congruence in terms of rigid motions

6:
Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

Download Common Core State Standards (PDF 1.2 MB)

|

Math.HSG.CO.B.7

Common core State Standards

Math: Math

HSG: High School: Geometry

CO: Congruence

B: Understand congruence in terms of rigid motions

7:
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

Download Common Core State Standards (PDF 1.2 MB)

|

Math.HSG.CO.B.8

Common core State Standards

Math: Math

HSG: High School: Geometry

CO: Congruence

B: Understand congruence in terms of rigid motions

8:
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Download Common Core State Standards (PDF 1.2 MB)

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Discussion and Supporting Materials

Thought starters

1. Why does Ms. Pforts begin her class by asking students for real-world examples of congruent figures?

2. Why does Ms. Pforts give the students graph paper and shapes in addition to the geometry software?

3. How does Ms. Pforts know when students are ready to work on the extension activity?

School Details

Mount Pleasant High School
2104 South Grand Avenue
Mount Pleasant IA 52641

Data Provided By:

Teachers

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High school math teacher April Pforts uses a formative assessment process during a lesson on congruence. First, she clarifies the intended learning by reviewing the learning goals and activating students' prior knowledge. Next, students work in pairs and use a geometry software program to prove two triangles are congruent.

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Formative Assessment Example: Proportional Relationships Math Lesson

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Formative Assessment Example: Proportional Relationships Math Lesson

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Math.Practice.MP1

Common core State Standards

Math: Math

Practice: Mathematical Practice Standards

MP1: Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, \"Does this make sense?\" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Download Common Core State Standards (PDF 1.2 MB)

|

Math.Practice.MP3

Common core State Standards

Math: Math

Practice: Mathematical Practice Standards

MP3: Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and--if there is a flaw in an argument--explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Download Common Core State Standards (PDF 1.2 MB)

|

Math.7.RP.A.3

Common core State Standards

Math: Math

7: Grade 7

RP: Ratios & Proportional Relationships

A: Analyze proportional relationships and use them to solve real-world and mathematical problems

3:
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Download Common Core State Standards (PDF 1.2 MB)

Thought starters

1. How does Mr. Elsdon clarify the intended learning for the lesson?

2. How does Mr. Elsdon use questioning to guide his students?

3. How do the students assess their own understanding?

Teachers

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Seventh grade math teacher Charles Elsdon uses a formative assessment process during a lesson on proportional relationships. First, he reviews the learning goals and success criteria, as well as rubrics developed the day before. Next, students work in groups to find multiple solution paths for a percent increase/decrease problem.

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Have Students Collaborate To Learn From Mistakes

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Have Students Collaborate To Learn From Mistakes

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Math.A.REI.1

Common core State Standards

Math: Math

A: Algebra

REI: Reasoning with Equations and Inequalities

1:
Explain each step in solving a simple equation as following from the
equality of numbers asserted at the previous step, starting from the
assumption that the original equation has a solution. Construct a
viable argument to justify a solution method.

Download Common Core State Standards (PDF 1.2 MB)

|

Math.Practice.MP2

Common core State Standards

Math: Math

Practice: Mathematical Practice Standards

MP2: Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability todecontextualize--to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability tocontextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

Download Common Core State Standards (PDF 1.2 MB)

|

Math.Practice.MP3

Common core State Standards

Math: Math

Practice: Mathematical Practice Standards

MP3: Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and--if there is a flaw in an argument--explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Download Common Core State Standards (PDF 1.2 MB)

Thought starters

1. What do students learn from collaboratively viewing student work samples?

2. How would you decide to group the students for this activity?

3. Why is it important for the groups to have guiding questions for the activity?

School Details

Turkey Foot Middle School
3230 Turkeyfoot Rd
Edgewood KY 41017

Data Provided By:

Teachers

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Learning from Mistakes: Linear Equations

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A small group of students in Susie Morehead's eighth grade class analyzes student work samples for clarity and accuracy. They discuss the strengths and weaknesses of the work, and use a list of guiding questions to focus their conversation. The students learn how to better approach and organize their own work from this activity.

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The New York State Education Department is no longer supporting the EngageNY.org website and it will no longer be available for use after April 15, 2022. NYSED encourages educators to download any EngageNY content they wish to use in the future.

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The 4-Part Math Lesson | Unpacking an Effective Math Lesson

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The 4-Part Math Lesson | Unpacking an Effective Math Lesson

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Unpacking an Effective Mathematics Lesson

When it comes to teaching mathematics, we often hear about effective strategies that could be useful during a lesson, but there is little talk about what actually constitutes a complete and effective lesson from start to finish.

In the following video ( or jump to the summary below), I break down the 3-part lesson into 4-parts:

(Can't see the video? Click here)

3-Part Math Lesson

In Ontario, John Van De Walle's 3-part math lesson has been promoted from the Ministry of Education to the districts, districts to school administrators, and from administrators to teachers. Despite efforts to provide resources for teachers, often times, guides provide only an outline of the lesson framework or a relatively basic example of what it may look like in the classroom. If a lesson example is provided, I've noticed the topics are geared towards primary or junior grade levels and the actual problem to be solved does not spark curiosity. Some examples of 3 part math lessons can be found here, here and here.

Just like a game of telephone, the message can get distorted as it moves down the line.

Common Interpretations

By the time the "3-part math lesson" message reaches the teacher, what is interpreted could easily look like the following:

1. A 3-part lesson is an effective way to teach math.

2. The 3-parts are named minds on, action, and consolidation or before, during, and after (or similar).

3. Minds on is like a warm-up to the lesson.

4. Action is where students learn the new concept.

5. Consolidation is where we take our new learning and summarize it/practice.

There are some problems, though.

Many teachers walk away without a clear understanding of what this should really look like in the classroom. Some believe they are "essentially" delivering a 3-part math lesson because they already do a warm-up problem, deliver a lesson, and students consolidate their learning (i.e.: do practice problems).

Other teachers are working hard to improve engagement in math class by using 3 Act Math Tasks in the style of Dan Meyer, but are using them only near the end of a unit. I think waiting until all of the learning goals for the unit have been delivered with traditional, context-less problems is a missed opportunity to engage students throughout the learning process.

Because of these misconceptions and others that may surround the use of the 3-part math lesson and missed opportunities when integrating 3 Act Math Tasks, I will deconstruct an effective 4-part lesson structure into finer parts and model what this might look like in a middle years/intermediate math classroom.

The 4-Part Math Lesson

What I find is missing most often from most 3-part math lessons is the inquiry/discovery portion that should be embedded within the action/during phase. This is why I think it is really important that we break down the action/during portion into smaller parts:

Let's jump into each part.

Part 1: Minds On

Like in a 3-part math lesson, we begin with a minds on. This may take 5 minutes some days or could take up to 25 minutes on others. While most are clear that the minds on/before phase is a warm-up, the biggest misconception I encounter is that it is any random problem to start the class off. John Van De Walle 's 3-part math lesson suggested that the minds on promote activating prior knowledge in order to:

... get the students to be cognitively prepared for the lesson problem by having them think about ideas and strategies they have learned and used before. The teacher organizes a revisit to a concept, procedure or strategy related to the lesson's learning goal.
Sketch of a Three-Part Lesson. Ontario College of Teachers. March 2010.

Extending what John Van De Walle suggests, we should also attempt creating a minds on that extends the context used during the previous lesson to help scaffold us slowly towards the new learning goal for that day. If we can also maintain the context from the previous lesson, that is a huge benefit that will help students build their new knowledge on prior knowledge.

In a recent workshop, I used the Stacking Paper 3 Act Math Task and solving problems with proportions algebraically as an example of the learning goal:

For the minds on portion of the current lesson, we could then use something that will still keep the content and context the same:

Part 2: Inquiry

After students have shared out, discussed and debated over solutions, the teacher then introduces the task for that day. Ideally, this task will maintains the same contextual scenario to allow students to easily leverage their prior knowledge while extending the previous learning goal to the new learning goal for that lesson. Making every effort to ensure the tasks offer real world context via a 3 act math task or similar will maximize the effectiveness of this part of the lesson.

The task used for inquiry/discovery is the most important part of a 4-part math lesson. The overall effectiveness of the lesson is closely related to how well this part is planned. A well designed inquiry/discovery task carefully sends your students down a path where they will ultimately "bump into" the learning goal along the way. When possible, use the same contextual situation from one learning goal to the next to allow students to more easily build their new knowledge through connections made to their prior knowledge.

In the 4-Part Math Lesson video, I extend the Stacking Paper 3 Act Math Task to the Stacking Paper Sequel. In the first, students viewed a video of 5 reams of paper stacked on the floor and used information to determine how many reams it would take to reach the ceiling. The next day, during the inquiry/discovery part of the lesson, students see the same 5 reams of paper now stacked on a table with the total height given.

The question now becomes:

How tall is the table?

While students have never had to solve something like this before, they can use their prior knowledge and a bit of problem solving to come to a conclusion.

Here are some examples:

Solution Exemplar #1:

Solution Exemplar #2:

Solution Exemplar #3:

Part 3: Making Connections

After students have shared out, discussed and debated over solutions, the teacher then prompts students to chat with their elbow partner(s) to decide which method they feel is most efficient. When discussing as a class, the teacher should prompt students by asking questions such as:

when the context changes, will using arithmetic/logic always be as easy as it was here? What if we remove all context?

how long does it take to create a table? ...a graph?

is there a way we can create some steps that will allow us to do problems like this more easily?

As a group with the teacher leading as facilitator, connections between student solutions and the algebraic method or procedure related to the intended learning goal can be established.

After the desired learning goal has been established as a group, we then formally introduce the intended learning goal for this lesson:

Learning Goal:
I can determine the equation of a linear relation using algebra when given the slope/rate of change and a point.

We now solve the Stacking Paper Sequel Task using the algebraic method:

Part 4: Consolidation

The consolidation phase is where we begin to remove the context from the problem and move towards the typical types of problems you see in traditional textbooks and on standardized tests. It might seem as though you are moving backwards from great real world problems that pique curiosity and perplex students, but unfortunately, the types of problems students are currently expected to solve in traditional textbooks and on standardized tests are text-heavy and lack any meaningful context or purpose.

Now that students have an understanding of the learning goal and we have made connections from an authentic real world problem to the algebraic representation, students can use this knowledge to solve problems with little or no context.

Here is an example of a problem we could now use to consolidate the learning:

I think it should be noted that the problem above used to be the FIRST problem I would introduce in the "Action" phase of the 3-part math lesson. It was as simple as I could make it; yet, students still struggled with the concept. Now that they have been given a contextual problem and were enabled to "bump into" the learning goal through the inquiry/discovery portion of the lesson, this is not a troublesome topic.

Upon completing these 4-parts of your math lesson, students should now have the understanding and confidence to do the necessary practice to master the intended learning goal.

The Next Day...

I mentioned earlier that building on the same context from each learning goal to the next can provide a huge benefit. In order to continue the deconstruction of this particular lesson, the task I would use for the Inquiry portion of the next lesson would be the Thick Stacks 3 Act Math Task. In this task, students are provided with an image of two stacks of paper on a shorter table and are given the total height of each stack on the table. Students are then to determine:

What is the height of this table?

Through the inquiry process, students can determine the height of the table and we follow through by making connections when it is realized that we have been given two points in disguise. The learning goal for the next day is:

Learning Goal:
I can determine the equation of a linear relation using algebra when given two points on the line.

In my experience, this can be one of the most challenging learning goals for grade 9 academic students until connections are made. This task allows students to make these connections quickly and in a seemingly natural way.

Here are some possible solutions to this task as well was the consolidation (i.e.: problem with no context) I would use for that lesson:

While I will continue experimenting to make learning math more engaging for my students, the 4-part math lesson seems to provide a good balance and offers opportunities for accessing prior knowledge, learning through inquiry/discovery, building new knowledge by making connections to what we already know, and opportunities to practice traditional math problems. One of the other added benefits is the opportunity to benefit from Dan Meyer 3 Act Math-style problems on a regular basis, without having to wait until the end of a unit to engage learners. Engagement should not be on a once a unit or even a once a week schedule; we need to engage our students on a daily basis by offering contextual problems that pique curiosity and excite learners.

Have you tried the 3- or 4-part math lesson?

Would love to hear your experiences, both positive and negative, in the comments section!

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The 4-Part Math Lesson | Unpacking an Effective Math Lesson

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When it comes to teaching mathematics, we often hear about effective strategies that could be useful during a lesson, but there is little talk about what actually constitutes a complete and effective lesson from start to finish. In the following video ( or jump to the summary below), I break down the 3-part lesson into 4-parts: (Can't see the video?

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Engaging All Students in Common Core Math

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Engaging All Students in Common Core Math

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The teachers at Tahlequah High School in Tahlequah, Oklahoma are committed to making sure all of their students receive engaging and rigorous math instruction. After realizing that some of their ninth graders weren't ready to take Algebra 1, they created an Algebra Skills class. In this class, students (many of whom are in Special Education) spend their ninth grade year working on basic algebra skills with math teacher Gary Akin and Special Education inclusion teacher Marjean Dowling. During their 10th grade year, the same students participate in a contextual Algebra 1 class.

Watching an Algebra Skills lesson on solving equations in one variable, it's clear that these students are getting the support they need to be successful. Gary begins the class by giving students two assessment questions to work on on their own. After monitoring what his students are understanding, he then presents a step-by-step method for solving equations.

Students then work independently to solve problems while receiving one-on-one support from their teachers. Both Gary and Marjean patiently work with students as they break down problems into manageable steps. Watching the teachers make sure students understand each step before moving on shows their commitment to making sure all students receive a strong foundation in algebra.

Meanwhile, other ninth graders at Tahlequah High take a geometry class with Chuck Pack. In this lesson, we see students apply their knowledge of similar triangles to measure the height of the school's flagpole. These students are challenged to use their content knowledge to tackle an engaging, real-world problem.

Chuck's students are eager to work together, share their thinking, and learn from each other. Chuck shares how he calls on extroverted students to share their thinking first, knowing that these students are able to handle critiques from their peers. Chuck then develops the same skills with introverted students by working in small groups. Because of this personalized approach, all students are engaged in making and critiquing arguments.

One of the reasons the teachers at Tahlequah High School have been able to create such a comprehensive math program is because they work so well together. Through regular collaboration with colleagues, the teachers receive feedback and support from each other. As they have transitioned to the Common Core State Standards, the math teachers at Tahlequah High have worked together to learn, experiment, and expand their practices.

In this video, Chuck collaborates with his colleague Gabby Vieth to refine his plans for the flagpole lesson. The teachers reflect on how the lesson has gone in the past and make adjustments based on their current set of students. Through their conversation, the teachers also reflect on their experience with the CCSS. It's powerful to hear Chuck note that one of the biggest shifts he's experienced is moving away from direct teaching and into a facilitator role.

Through this video series, we get to see four teachers who are committed to making sure all of their students succeed in high school math. When Chuck explains his mantra, "Teach kids, not math," it's even more clear that the math team at Tahlequah High cares deeply about all students. The dedication and collaborative spirit of these teachers pays off in their students' success.
Lily Jones taught K/1 for seven years in Northern California. She has experience as a curriculum developer, instructional coach, teacher trainer, and is also a contributing writer for Teaching Channel.

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Engaging All Students In Common Core Math

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The teachers at Tahlequah High School in Tahlequah, Oklahoma are committed to making sure all of their students receive engaging and rigorous math instruction. After realizing that some of their ninth graders weren't ready to take Algebra 1, they created an Algebra Skills class.

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These are only organized in the order that I discovered them. Sorting them will be my next task. Yummy Math (real world applications) S...

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Professional Growth Incentive - Certified Staff | Douglas County School District

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Professional Growth Incentive - Certified Staff | Douglas County School District

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Professional Growth Incentive - Certified Staff | Douglas County School District

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Conceptual Understanding in Mathematics | Granted, and...

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Conceptual Understanding in Mathematics | Granted, and...

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Classroom Challenges are lessons that support teachers in formative assessment. There are 100 lessons in total, 20 at each grade from 6 to 8 and 40 for 'Career and College Readiness' at High School Grades 9 and above.

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4 Awesome New Blooms Taxonomy Posters ~ Educational Technology and Mobile Learning

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4 Awesome New Blooms Taxonomy Posters ~ Educational Technology and Mobile Learning

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Educational Technology and Mobile Learning

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For today's post, We are sharing with you some great posters on Blooms Taxonomy. These posters are designed by gratitude go back to iLearn Technology . They come in different shapes and are ideal for use in classroom. You might need to ask iLearn Technology for permission to print and use in them in class. Have a look and share with us what you think of them. Enjoy

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For today's post, We are sharing with you some great posters on Blooms Taxonomy. These posters are designed by gratitude go back to iLearn Technology . They come in different shapes and are ideal for use in classroom. You might need to ask iLearn Technology for permission to print and use in them in class.

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Resources and Downloads for Differentiated Instruction | Edutopia

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Resources and Downloads for Differentiated Instruction | Edutopia

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Tips for downloading: PDF files can be viewed on a wide variety of platforms -- both as a browser plug-in or a stand-alone application -- with Adobe's free Acrobat Reader program. Click here to download the latest version of Adobe Reader.
Click on any title link below to view or download that file.
Lesson Plans & Rubric - Reteach and Enrich

Sample materials used to teach, assess, reteach, and enrich one week's fifth grade math objective: differentiating prime and composite numbers. Watch our video or read the article to learn more about Mesquite's Reteach & Enrich program.
Reteach Examples Enrich Examples
Example of a game played in enrichment class
Websites
Activities used by Mesquite teachers for teaching prime and composite numbers

Tools for Data Assessment

Teachers at Mesquite meet weekly with the student achievement teacher to review the most recent assessment data and plan instruction for each student accordingly.
5th Grade Math Formative Assessment Tracking Sheet
Sample spreadsheet used to track student performance on each objective.
Tracking Sheet for Bottom 25 Percent of 5th Grade Students
Students whose performance falls in the bottom 25 percent of the class are tracked more closely using spreadsheets like this one.

Benchmark = 1 quarter

AIMS is the state standardized test

PL = Performance Level on AIMS

M = Meets

A = Approaches

FFB = Falls Far Below
Class Development Profile Grid
Grid displaying per student performance for each objective on a benchmark test.

MS = Meets Standard

AS = Approaches Standard

FS = Falls Below Standard
Development Profile Fifth Grade Class
Profile report of overall performance for one fifth grade class on a benchmark test.
Development Profile for Fifth Grade
Profile report of overall performance for entire fifth grade on a benchmark test. Codes such as S1C1, S1C2, are weekly performance objectives; M05 is Mesquite, 5th grade.

Culture

Websites & Readings

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Resources and Downloads for Differentiated Instruction | Edutopia

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Tips for downloading: PDF files can be viewed on a wide variety of platforms -- both as a browser plug-in or a stand-alone application -- with Adobe's free Acrobat Reader program. Click here to download the latest version of Adobe Reader. Click on any title link below to view or download that file.

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How to Teach with Technology: Science and Math | Edutopia

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How to Teach with Technology: Science and Math | Edutopia

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We’re sorry, that page was not found. It may have been moved, renamed, or retired. Please try searching the site or browsing recent articles.

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25+ apps that the TED staff swears make their everyday lives easier | TED Blog

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25+ apps that the TED staff swears make their everyday lives easier | TED Blog

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At our small, fast-moving nonprofit company, everyone does a couple of jobs - and productivity apps help us manage roles that shift between coding, writing/designing and running a full-scale conference twice a year. We asked the TED staff what apps they can't live without. And beyond the classics- Instagram, Google Maps, Spotify, Uber, Seamless -we found some great apps that might help you too. (A star denotes that the app is free, or at least has a free version.)

For random life stuff...

*Sunrise
Like your Google Calendar with key improvements, several staffers swear by this app. It offers shortcuts for adding events, and also bakes things like weather reports and Facebook birthday reminders into the mix of your daily calendar. "It's awesome," says IT Manager Francil Richards.

Yoga Studio
Yoga Studio reminds us of the "Surprise Me" feature on the TED app. You pick the kind of yoga class you want (strength, flexibility, relaxation), your level (beginner, intermediate or advanced) and the amount of time you have (20 minutes, 40 minutes or longer) and it creates a class for you. "Whenever I am traveling or too busy to exercise, I sneak in a lesson," says Product Development Manager Jai Punjabi.

For staying organized...

For getting around...

CityMaps2Go Pro
This app downloads offline, zoomable, searchable maps of major cities, so that even if you are roaming around Tokyo and can't read any of the signs, you can still find your way around. "It's good for people like me who travel internationally, but don't like to get data plans," says Thu-Huong Ha, of our editorial team.

*Moves
Moves tracks every step you take, which sounds creepy, but is actually useful. "It quantifies how many miles you've walked, cycled and run," says Patrick D'Arcy, of the TED Fellows team. "It's not about the calories burned for me, but the ability visualize where I've gone on a map. A friend actually introduced me to the app when he came back from Mexico City and he was able to show me the exact routes he took."

For computer and email ease...

*Authy This app disconnects 2-step authentication from text messaging, and does it in a way that's a little more secure, should your phone fall into the wrong hands. "This is especially handy for when I'm in areas with no reception or am international and don't have a texting plan," says Product Development Associate Bedirhan Cinar. "Google offers an identical app, but I like Authy better because you can password protect it so if someone has your phone, they can't easily access your 2 step codes."

But enough about us. What's the app that YOU find most helpful on a day-to-day basis? Share in the comments!

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At our small, fast-moving nonprofit company, everyone does a couple of jobs - and productivity apps help us manage roles that shift between coding, writing/designing and running a full-scale conference twice a year. We asked the TED staff what apps they can't live without.

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Blended Learning: Making it Work in Your Classroom | Edutopia

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Blended Learning: Making it Work in Your Classroom | Edutopia

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P.K. Yonge views blended learning as the combination of digital content and activity with face-to-face content and activity. It looks very different in each class at the school. When a teacher has an activity that works well face-to-face, there isn't any reason to look for a digital replacement. If they can find something digital that is more effective or efficient, then that is implemented.

P.K. Yonge administrators knew it would be a challenge for their teachers, many of whom were averse to learning new technologies, or didn't have the time to think about how to implement it in their classroom. Blended learning requires both the time and a willingness to learn new things. But the benefits of doing the work seem to far outweigh the challenges. Four years later, P.K. Yonge has almost 20 classes that have transitioned into a blended learning model.

Getting started on using the technology or transitioning curriculum can be intimidating for some teachers. Many teachers at P.K. Yonge recommended finding another teacher to buddy up with through the process, and to help support one another.

How It's Done

Planning a Blended Curriculum

In partnership with the University of Florida, P.K. Yonge designed a summer institute that would give teachers the time and resources to think about blended learning. At the institute, teachers had an opportunity to dig into what blended learning was and how to rebuild their course. They also had the support of graduate students from the University of Florida, who helped them to find and build content. In time, teachers learned the tools and technologies on their own. While most schools won't be able to host a summer program to plan and train teachers, the same planning principles can be used in any school.

The institute itself was designed in a blended learning format. Teachers did different kinds of activities, sometimes meeting face to face and sometimes online. This provided the chance to experience blended learning in similar ways as their students.

Target One Grade Level at a Time

P.K. Yonge decided it would make sense to start by systematically targeting one entire grade level, rather than a smattering of teachers and students across the many different grades. They chose the ninth grade as a place to start because it is the start of high school, and they could roll up or down into the other grade levels from there.

Set Goals for Each Class

Interested teachers were asked to fill out a proposal with the ideas they had for transitioning their curriculum. Teachers were asked to think specifically about why they wanted a blended learning environment and what gaps it could address in the classroom.

Some of the needs teachers had were to provide students with differentiated instruction, to find quick and easy ways to do formative assessment, and to give students access to content 24/7.

Teachers were then asked how those gaps could be filled, what units in their curriculum they could possibly see as blended learning units, and to propose a timeline for the project. Finally, teachers were asked to define specific deliverables for their course. All of this helped build the ownership that was necessary for teachers to really want to do this work.

Keep it Face-to-Face or Make it Digital?

One of the key components of blended learning is to identify what is already working well in your classroom, and what might be better suited as digital content. Teachers need to know that by adding digital content, it doesn't mean throwing out all the direct instruction in the classroom. Keep what is working well in a face-to-face mode, and add what could be more effective in a digital format.

Deliverables differed from teacher to teacher depending on the content area. Some teachers overhauled an entire unit of their course, others focused on creating assessments for learning and putting those in place, while others took a more general approach and decided to transition all their handouts into a digital format so they were more accessible.

It is important to start with some deliverables that are manageable, and then keep adding new components over the year, or even next few years.

Plan for Resources and Access

Two crucial things to think about before you start are what kinds of resources your school already has, and what kind of access students will have to the technology necessary for a blended learning course. P.K. Yonge has been committed to providing computers for its students, and has about 800 available on campus. However, while some teachers have 25 computers in their classroom, others only have a few Ipads. The school also extended its library hours, so that students could access it every day before school and until 5:30 pm afterschool.

Resources

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Transitioning to Blended Learning | Edutopia

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P.K. Yonge views blended learning as the combination of digital content and activity with face-to-face content and activity. It looks very different in each class at the school. When a teacher has an activity that works well face-to-face, there isn't any reason to look for a digital replacement.

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Grade 7 and Grade 8 (with worksheets, videos, games & activities)

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Grade 7 and Grade 8 (with worksheets, videos, games & activities)

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Integers

Exponents and Roots

Rational & Irrational Numbers

Absolute Value

Scientific Notation

Percents

Algebra

Linear Functions

(Graphing Lines on the Coordinate Plane)

Linear Inequalities

Geometry

Angles and Transversals

Circles

Area of Composite Figures

Volumes Of Solids

Surface Areas

Congruence and Similarity

Similar Triangles and Polygons

Constructions

Transformation

Probability

Statistics

Miscellaneous Math Games

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

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Grade 7 and Grade 8 (worksheets, solutions, examples, activities, videos, games)

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Integers, Exponents and Roots, Algebra, Rational and Irrational Numbers, Absolute Values, Scientific Notation, Transformation, Percents, Linear Functions, Linear Inequalities, Geometry, Trigonometry, Construction, Probability, and Statistics. examples and step by step solutions, 7th Grade, videos, games, activities and worksheets that are suitable for Grade 7 and Grade 8

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classroom ideas | the radical rational...

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classroom ideas | the radical rational...

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How To Determine A Student's Prior Knowledge | Edudemic

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How To Determine A Student's Prior Knowledge | Edudemic

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Mangahigh | Online Math Resource | Game Based Learning for Students

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Mangahigh - Where every child finds fun in learning. A digital math resource for blended learning. Transform your teaching with game-based learning. Used by thousands of students every day.

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In her TED talk, " Gaming Can Make a Better World," author and researcher Jane McGonigal posits that in game worlds people are "motivated to do something that matters, inspired to collaborate, to cooperate." Video games are interactive and engaging. It's no wonder they are so pervasive with both children and adults!

A recent trend in the business world has been to bring game world elements into the real world. This methodology is referred to as "gamification." According to a Pew Research Center report, gamification is "interactive online design that plays on people's competitive instincts and often incorporates the use of rewards to drive action -- these include virtual rewards such as points, payments, badges, discounts and free gifts; and status indicators such as friend counts, re-tweets, leaderboards, achievement data, progress bars and the ability to level up."

Corporations, such as Samsung, award badges internally to motivate their employees. The Nike+ iPhone application awards achievements to runners. Foursquare and Yelp assign badges as users check-in at locations via the GPS in their smart phones. Mozilla has a long list of companies, nonprofits and schools that use their open badges to integrate gamification. Dr. Kevin Werbach, from the University of Pennsylvania's Wharton School of Business, teaches a massively open online course, or MOOC, on gamification. According to Werbach's course description, "Organizations are applying it (gamification) in areas such as marketing, human resources, productivity enhancement, sustainability, training, health and wellness, innovation, and customer engagement."

Educators have also begun to adopt the reward structures of video games, such as badges for meaningful achievements, into their lesson planning. Integrating gamification into the classroom is best accomplished when teachers begin to think of themselves as not just educators, but also game designers.

Badges

Badges are a method for recognizing and rewarding accomplishments. According to a white paper by Mozilla, badges "support connected learning environments by motivating learning and signaling achievement both within particular communities as well as across communities and institutions." Most students can already identify with a badge system in video games, such as Xbox Achievements and PlayStation Trophies.

The educational social media site Edmodo includes pre-made badges, as well as the availability for teachers to create or upload their own. Mozilla's Open Badges Project also has tools to let teachers create badges.

Badges can be a student-centered, too. For instance, students can design check-in badges for Civil War battle locations or create achievements for career accomplishments of notable authors.

Leveling Up

Video games frequently do not include how-to instructions for players. The first "level" or "mission" is typically a constructivist tutorial. As the game progresses, the player is given more information and increasingly complex tasks. Tutorial levels teach players the rules as they go, then the challenges are increased and scaffolded. "Boss levels" are where all of the learning comes together. It is at this point where gamers feel the intrinsic reward, or flow, from an earned satisfaction.

Games such as World of Warcraft feature avatars that improve as they succeed. In the game world, this is referred to as "leveling-up." Games also feature "leaderboards" to publicly aggregate and publish earned points. In New York City's Quest 2 Learn, students are given the opportunity to level-up. An example might be introducing Edmodo to deliver blended instruction and then scaffolding a how-to post on a wiki the next day. By the end of the week, students would be at the "boss" or mastery level.

Modding

Some games, such as Minecraft, encourage players to modify, or "mod," the virtual world environment. At the 2012 Games for Change Festival, Valve announced the Teach with Portals website, where players are given the tools to modify their own "test chambers," or puzzle rooms. Giving students tools for modding assignments and projects will empower them to take ownership of their learning.

Easter Eggs

"Easter eggs" are hidden objects left by the coders in websites, video games and -- sometimes -- DVDs. Super Mario Bros. was among the first to popularize hidden objects and secret rooms. Hiding Easter egg challenges within PBL units is more engaging that simple extra credit tasks and questions. Uncovered Easter eggs can be acknowledged with badges.

In-Game Economy

Many games feature an "in-game economy." In the Assassin's Creed series, opponents can be looted and pick-pocketed. Money can be found by unlocking hidden treasure chests. That money can be used to improve buildings, upgrade the avatar or purchase maps featuring hidden locations of desirable objects. Mass Effect 3 awards currency known as paragon points. These are points are earned by "being a positive, kind and friendly player, during conversations and stories." Paragons can be used to purchase better weapons, health and armor. An "in-class economy" can award students who progress in a meaningful way, while also integrating math and financial literacy lessons.

Gamification in the Classroom

In video games, players are encouraged to learn as they go. This is the very definition of constructivism. Constructivism makes learning meaningful and satisfying. By adding some simple gamification elements, lessons and activities will become more engaging and fun!

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In her TED talk, " Gaming Can Make a Better World," author and researcher Jane McGonigal posits that in game worlds people are "motivated to do something that matters, inspired to collaborate, to cooperate." Video games are interactive and engaging. It's no wonder they are so pervasive with both children and adults!

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Viewpoint: Why We Need the Common Core Math Standards | MiddleWeb

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Viewpoint: Why We Need the Common Core Math Standards | MiddleWeb

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Kathy Felt teaches 8th grade mathematics and algebra and chairs the math department at Sherrard Junior/Senior High School in Sherrard, IL. She also teaches Elementary and Junior High Math Methods at Western Illinois University-QC. Kathy serves on the Illinois Mathematical Model Curriculum writing team and is a member of the Illinois Educator Leader Cadre.Through the Cadre, she works with the Common Core consortium group PARCC to develop items for CCSS math assessments. We thought Kathy was a good choice to present the pro-Common Core viewpoint, with a focus on mathematics. _______
OMG! The Math Common Core Standards Didn't Go Away!
by Kathy Felt
In education, it seems that a new "this is the best thing ever" reform movement comes along every couple of years. Educators are wise to this. If the current one doesn't excite you, just wait a little while and it will likely be replaced by something else.

Such was the belief of many middle grades educators when they heard about the Common Core State Standards (CCSS) for ELA and Mathematics. But these haven't gone away, and the time has come to implement them in the classroom. So what do we do now?

Why do we need the CCSS?

To date, 45 states, the District of Columbia, four U.S. territories, and the Department of Defense schools have adopted the Common Core State Standards. States signed on to this educational movement because it originated from the states and recognized that the most important way to assure good public schools is to support quality classroom instruction.

I want to zero in on the math standards because that's what I teach and that's where I've been involved in planning for Common Core implementation and assessment.

Significantly, the CCSS authors gave us not only the mathematics content standards, but mathematical practice standards as well. Together, these standards tell us what and how we should be teaching in our classrooms. The developers took what was deemed necessary for success in college and careers beyond high school and "back-mapped" those skills into the standards all the way down through the K-12 mathematics curriculum to primary school.

Our new common assessments, being developed on a parallel track, will offer vital information on our students' progress throughout their education, with the ultimate goal of being ready for college and careers and possessing the mathematical skills and knowledge necessary to support themselves and their families.

How is this different than NCLB?

Under the No Child Left Behind law, the focus in K-12 public education quickly became about raising test scores. And it didn't take long to realize that mathematics education in this country was not working well. NAEP and other data revealed that less than half of the student population in this country was minimally proficient in mathematics, and it became clear things needed to change.

The problem? Mathematics instruction was focused primarily on procedures and computational skills, without much attention given to deep, conceptual understanding - or the application of these skills and concepts to the world in which our students live. Our math curriculum of the past 20 years and more has frequently been characterized as "a mile wide and an inch deep."

The mathematics we were teaching was also boring, mundane, and had little relevance to our students.

Why? Mathematics teachers, perhaps more than other curricular areas, tended to teach as we were taught. Traditionally, our instruction had been based in showing and telling our students how to do the procedures-not allowing our students to productively struggle to gain the deep understandings necessary to thrive in a 21st century world.

Students today are different than in years past. They have access to information 24/7 - often with technology in their pockets. Their world moves faster and constantly stimulates them in ways unheard of in the past. We need to effectively engage them and use applicable technology in the classroom so they will be excited to learn, know when and how to apply their skills, and understand why the mathematics is important in their high-tech world. When students are engaged in their learning, they like math more and experience greater achievement.

How do we make it work?

Changing what we have always done is not easy. Forging into new territory seems risky. Will our students succeed? Will they thrive? Will it work? It will work if we are willing to accept the professional responsibility to alter what we teach and how we teach it. Clearly what we had been doing was not working. If we are honest with ourselves, we know change is necessary and long overdue.

Because the CCSS is firmly rooted in good teaching practice, we need to have the confidence that if we master new practices, our students will achieve much more. We can't do it by isolating ourselves - by going into our math classrooms and closing the door. But we can do it together, by collaborating with our peers.

The creators of the Common Core standards and methods do not imagine that we will do this alone. The power of these standards is that they are uniform throughout our states and we can collaborate not only with our local peers, but with math teachers in other states who are working to achieve the same standards.

Together, we can design and share effective and engaging lessons. We can utilize tools and strategies developed by our colleagues throughout the country, confident that if they help their students gain true mathematical proficiency, they will also work for us. We can all get better together.

How new assessments will help

The way we will assess our students will change under this initiative. New higher-quality tests are being developed by two national assessment consortia. As a member of the Illinois Educator Leader Cadre working with PARCC (the Partnership for Assessment of Readiness for College and Careers), I have seen the higher quality assessment items coming out of this consortium's efforts. I know they will really get at what my students know and understand - not what they are good at guessing at or plugging into a formula. (See this section for teachers at the PARCC site. Also visit the other consortium site, the Smarter Balanced Assessment Consortium.)

The assessments are also directly linked to best teaching practices. The released items not only tell me what is on THE TEST and in the standards, they show what high quality teaching, mathematical knowledge, and student understanding look like in this new environment. They offer all of this in a real world context and make this process applicable to the world in which my students live.

Bottom line: The Common Core is asking for monumental changes in our mathematics classrooms - perhaps the greatest changes of our careers. But, it is the right thing to do. Our students are worth the considerable effort it will take to achieve this.

Resources that can support new practices

There is no shortage of Common Core math resources available for use in the classroom. The difficult part is determining which resources are most beneficial for individual situations.

Let's start with an obvious question: What ARE these new practices we need to adopt? In her Dec-Jan 2013 Educational Leadership article, "Go Figure: Math & the Common Core," noted math teacher/author Marilyn Burns describes what she thinks needs to change, using an example from her own dinner table. And in this 15-minute video at the Teaching Channel, you'll see how two teachers in New York City are shifting their math instruction in synch with the new standards. Also, this collection at Achieve the Core examines the shifts in math teaching practice and includes a variety of print and video resources.

If you prefer a book, I would suggest Common Core Standards For Middle School Mathematics: A Quick-Start Guide by Amitra Schwols and Kathleen Dempsey. It's part of a series from ASCD covering the math standards across the K-12 spectrum. This book ( which I reviewed here) is truly one of the best I have read on this subject. It can and should be viewed as a handbook and a "go-to" reference for every middle school math teacher. It stresses the progression of understanding for the critical mathematical concepts and offers lots of examples of quality lessons.

If electronic resources are more your preference, I offer several of my favorites:

* The Common Core Conversation ( www.commoncoreconversation.com ) My very favorite "go-to" resource. This is a meta-site, which means it has a plethora of resources. On the homepage, scroll down on the left to select Math. You'll find about 100 high quality sites offering reputable classroom resources for Common Core implementation. There's also a link at the top of the site which leads you to state-by-state Common Core resources, including lessons, scopes and sequences, modules, and activities. Explore your state. Explore other states. You will use this daily. It's proof positive that we are all in this together.

* Teaching Channel ( www.teachingchannel.org ) offers powerful videos clearly demonstrating quality teaching and strategies, both general and math-specific, as well as impressive lesson plans.

* National Council of Teachers of Mathematics ( www.nctm.org) which should, arguably, be an important stop for any math teacher.

* Common Core State Initiative ( www.corestandards.org ) offers official information, the standards, and resources.

The Common Core Standards are here to stay. As a mathematics teacher deeply involved in CCSS development and implementation, I'm convinced that is a very good thing.

This national initiative will demand high quality teaching. It offers us a set of rigorous, coherent math standards that will prepare our students for college and careers. It's up to us to step up and show that - given the right professional development and support - we can teach mathematics in deep and engaging ways.

If you have been slow to jump on this bandwagon, come join us now. Armed with these tools, we really will be able to make a difference in the education of our students. They are so worth the effort!

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Viewpoint: Why We Need the Common Core Math Standards

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Kathy Felt teaches 8th grade mathematics and algebra and chairs the math department at Sherrard Junior/Senior High School in Sherrard, IL. She also teaches Elementary and Junior High Math Methods at Western Illinois University-QC.

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Student-Driven Classrooms: Keeping the Faith | MiddleWeb

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Student-Driven Classrooms: Keeping the Faith | MiddleWeb

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Twice a year, our independent school invites the families of boarding and day students to Family Weekend - a busy, enjoyable time when visitors can attend classes as well as various talks, performances, presentations and athletic events. This year the spring weekend came along just as my Humanities 7 course was finishing up their self-designed unit on "judging" and was not quite ready to dive fully into the next (poetry).

This left me somewhat at a loss for what to do during our special weekend class - on precisely one of those days where you want the students (and yourself) to be at their best.

I eventually decided to hold an official poetry unit kickoff. Olivia asked me right before we started if she could read one of her poems. Her beautiful and powerful reading opened the class perfectly. I then told the kids I was about to give them their one writing prompt for the entire unit, and asked them to take out their iPads and write a poem entitled "Poetry Is."

I reassured them they could choose to read their work as "finished" or "unfinished," depending on how they felt, and told them when they asked that the ambiguity in the title was deliberate and they could go in any direction they chose.

As I expected, they came up with stunning, breathtaking work in just five minutes. For just one example, by Isabela:

A silent thought of laughter,
A memory,
Spirals of colors winding through my mind, All written down on fresh,
white, clean,
perfect paper.

Expression,
A wish,
That's what poetry is...

I could hear parents periodically gasping or murmuring as they listened to all 13 students, including the one who always takes the most time to craft her writing and as a result was the most hesitant to read.

I then put the students in random groups (by passing out playing cards) and asked them to define poetry. They all came to consensus remarkably quickly, and it quickly became clear why. Each group, for different reasons and in different words, felt poetry was... undefinable.
Be calm and move forward...
Well. That placed the outcome of my next two planned activities - thinking about what makes poetry good, and then developing a checklist to assess their own upcoming books of original poetry - in serious doubt.

I reasoned, though, that simply continuing on as originally planned (especially with families watching) was my best move in the moment, so I passed out old literary magazines and asked them to work in pairs and select a favorite poem to share.

This they quickly did, with constant murmurs of admiration (and delight from the group that found a poem written by their art teacher when she was a student here), and again, there were sharp intakes of breath from parents as they listened. I asked the students to think about why they had chosen the poems and what made them good. They came up with a short list, and decided that "connections" was the thread running through them.
And then they were silent...
I asked them to think beyond "connections" to what it was about the poems themselves that made them good. Absolute and complete silence. And eight minutes to go, so the "Wow, look at the time. See you Tuesday!" option was out.

I raised my eyebrows and gazed at the ceiling... and decided to ask them to write a bad poem. But before we could start, Emily, bless her forever, raised her hand.

"I don't think you can write a bad poem," she said, and I told her that was a really important concept and asked her to expand on it. "I think that if your poem does what you wanted it to, then it's good whatever anyone else thinks of it," she said.

I looked around at the class. "Reactions?" And as they contributed ideas, a consensus gradually emerged that only the author can judge when a poem feels right - bearing in mind that for some people, any given poem may never truly feel 100% finished.

"So," I told them as the minute hand approached the 9, signaling the end of class, "I'm thinking that to assess your poetry books, I may ask you to write me a paragraph about them and then I'll write back to you and react to what you said. I'll think about it over the weekend, and you can too, and we can talk on Tuesday." They nodded and began to get ready to move on to their next class.

That evening I was talking to one of the seventh grade parents, who is a successful author. He said both he and his wife thought the poetry kickoff was a great approach for kids this age to a subject that is so abstract and complex. I thanked him warmly, with immeasurable relief.

There's the saying, "When the going gets tough, the tough get going." In my case, though, it's more like: "When the going gets tough, trust your students."

Together, we always seem to get there. It might not necessarily be the destination I expected - but it's almost always the place they needed to go all along.
Bill Ivey is Middle School Dean at all-girl Stoneleigh-Burnham School in Greenfield MA, where he also teaches Humanities 7, Social Media, and the Middle and Upper School Rock Bands. Bill is the advisor for MOCA, the middle school student government, and he coordinates and participates in the middle school service program. Bill's other MiddleWeb posts include Hungering for a Better World and Actually, You ARE Special.

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Student-Driven Classrooms: Keeping the Faith

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Twice a year, our independent school invites the families of boarding and day students to Family Weekend - a busy, enjoyable time when visitors can attend classes as well as various talks, performances, presentations and athletic events.

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Digital Student Portfolios: A Whole-School Approach | MiddleWeb

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Digital Student Portfolios: A Whole-School Approach | MiddleWeb

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Matt Renwick is principal of K-5 Howe Elementary School in Wisconsin Rapids, WI. This article is adapted from the Introduction to his new book Digital Student Portfolios: A Whole School Approach to Connected Learning and Continuous Assessment, available from Powerful Learning Press. by Matt Renwick
Genesis Cratsenberg has worked as a speech and language teacher in our school for several years. She sees many students throughout the day. This morning, Genesis is meeting with a kindergarten student named David. He struggles to clearly articulate sounds, specifically digraphs (pairs of letters to describe one specific sound).

Genesis starts the lesson by showing David several picture cards. He is instructed to state the name of each image. He does what seems like his best, but often falls short of sounding out each letter and blend. Genesis tells him what he is doing well, and then, being the good teacher she is, kindly points out areas for improvement.

They repeat this activity, in the hope of finding growth. David often glances up at Genesis between interactions, looking to her for the answer to a question that neither of them is seemingly able to solve.
The anatomy of a portfolio entry
At first glance, this would seem like your typical student-teacher interaction. The teacher teaches, the student responds, the teacher assesses, provides feedback and alters instruction, the student responds again, and the process starts over.

This cycle of learning sometime bears fruit. But far too often, it leaves the student and teacher in a perpetual circle of confusion and frustration. Fortunately for David, Genesis is about to pull something else from her instructional toolbox.

She opens up an app on her iPad that is designed for speech and language teachers. In it, she can record a student's voice, play back their voice for them, and write down notes - all within the same file. They use the same picture card process as before, except now David knows he is actually going to hear himself speak.

He hesitates for a moment, realizing that this time it's for real. When he is ready, he again responds to the image that is presented. Genesis stops the recording, plays it back to David, and asks, "Did you say it just like I did?" Instead of frustration, David displays understanding. He has heard himself speak. There is no confusion; he can hear what he needs to improve.

David's brow furrows, exhibiting a new look of determination as Genesis asks him to try this activity again. This time he slows down his speech, enunciating each sound correctly within the word. Genesis stops the recording and plays it back for him. The smile that comes across David's face is the feedback Genesis needs to know that he feels successful.
Reflection and follow-through
After the session, Genesis reflects on David's progress. She writes a few sentences in his notebook within Evernote, a web-based application that can house text, audio, images, and links. She also includes David's audio, along with any other relevant information. Genesis makes specific comments about his growth in relation to his previous abilities. Much of the feedback is positive in nature. Once ready, she emails this Evernote entry (called a "note"), containing both audio and text, to David's parents.

A day later, David's dad stops by to visit Genesis in her office. Before conversation can even start, he states, "I really like that note you emailed us." Genesis nods and smiles, telling him how happy she is that he found it useful. Dad and Genesis go on to have an in-depth conversation about David's progress. David's father and his teacher are partners in advancing his learning. Everyone is focused on the same thing. There is no confusion about David's progress and current status, where his strengths lie, and where he needs to improve.

Each student in Genesis' caseload has a series of notes in Evernote. They are organized within an Evernote notebook specifically created for that student. At virtually any time and place, Genesis could pull up any one of her students' notes to analyze and share. All she would need is a digital device and a connection, either Internet-based or via cellular reception. Thanks to Evernote, the information Genesis has collected from her work with each student is easily organized and quickly accessible whenever and wherever she prepares for future intervention sessions.

The comprehensive collections of work that teachers like Genesis and their students curate and reflect upon on a regular basis are examples of digital student portfolios. Using highly flexible software, they are receptacles for learning from the past, reflections on our current capacities, and goal-setting resources for the future.
Students create meaningful goals
Genesis is not the only person setting the direction for her students' learning. The students themselves have created personal, meaningful goals for the year. The goals are based on feedback from Genesis, who uses a variety of assessment activities to help the students reflect on their strengths and current reality.

Each student's learning goals are proudly displayed around her office. The message delivered to everyone who enters her room is, "We are all learners here." That includes Genesis. As she works with these digital tools and resources, she realizes that her role of teacher has evolved into one of teacher/learner.

She is constantly listening and observing, alert to clues that her students are responding to the instruction she provides. Together, they have agreed upon goals that are high, attainable, and visible every day. And the progress toward these goals is fully documented in each student's web-based digital portfolio.

This close observation of one teacher's integration of technology into her daily instruction is an example of where we want to be as a staff. Our K-5 school has engaged in this initiative for the last three years. Our target goal: To enhance and even rethink how we help students make progress toward their learning goals.

Our current portfolio system wasn't cutting it. To prepare for Portfolio Night in April seemed to suggest that there was little worth sharing between September and March.

While we knew we wanted to bring iPads and Evernote into our classrooms, we did not intend to introduce technology just for the sake of change. Instead, we considered an entry point - ongoing, formative assessment - to begin to bridge the print and digital world.

Pedagogy is still our school's driver (Fullan, 2014). Technology is treated as an accelerator (Collins, 2001) for change. With this framework in mind, we were able to better manage this shift in how we teach and learn in our school. There were several bumps in the road, but keeping our focus on what was important made the learning process of collecting and organizing student work online more manageable.
Why digital portfolios?
Through digital student portfolios, learners can document current understandings. They can make revisions as their thinking changes and their skill levels grow. Celebrations of their successes can be shared both locally and globally.

The particular software and services used to create these portfolios is a subject of some interest, to be sure, but it is secondary to the "big idea" itself: compiling a dynamic collection of information from many sources, in many forms and with many purposes, all aimed at presenting the most complete story possible of a student's learning experience.

Different forms of media, such as audio, images, and video, in addition to text, can be inserted into this dynamic compilation of information. Digital student portfolios could be considered a map of a student's "journey toward excellence" (Routman, 2013). This documentation also serves as description of a school's own story. We write our own narrative as we work together - students, teachers, and parents - to realize our mission and vision.

Photos: Matt Renwick
Matt Renwick is head principal at Howe Elementary School in Wisconsin Rapids, Wisconsin and author of Digital Student Portfolios. Prior to becoming a principal, Matt served in many other roles as a public educator, including elementary teacher, assistant principal and athletic director. Howe School has earned many accolades for their literacy initiatives and student achievement, including Spotlight School recognition from the Wisconsin Department of Public Instruction. Connect with Matt via Twitter @readbyexample. He blogs at Reading by Example and writes for EDTECH, MiddleWeb, ASCD and other education resources.

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Digital Student Portfolios: A Whole-School Approach

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Matt Renwick is principal of K-5 Howe Elementary School in Wisconsin Rapids, WI. This article is adapted from the Introduction to his new book Digital Student Portfolios: A Whole School Approach to Connected Learning and Continuous Assessment, available from Powerful Learning Press.

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13 Ways to Make Homework More Meaningful and Engaging | MiddleWeb

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13 Ways to Make Homework More Meaningful and Engaging | MiddleWeb

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In the first installment of Rick Wormeli's homework advice, he made the case for take-home assignments that matter for learning and engage student interest. In Part 2, Rick offers some guiding principles that can help teachers create homework challenges that motivate kids and spark deeper learning in and out of school. These articles are adapted and updated from Rick's seminal book about teaching in the middle grades, by Rick Wormeli Day One & Beyond: Practical Matters for New Middle Level Teachers. Rick continues to offer great advice about homework, differentiation, assessment and many other topics in workshops and presentations across North America. Check back in Part 1 for some additional homework resources.
I've been accumulating guiding principles for creating highly motivating homework assignments for many years - from my own teaching and from the distilled wisdom of others. Here are a baker's dozen. Choose the ones most appropriate for students' learning goals and your curriculum.

1. Give students a clear picture of the final product. This doesn't mean everything is structured for them, or that there aren't multiple pathways to the same high quality result. There's room for student personalities to be expressed. Students clearly know what is expected, however. A clear picture sets purpose for doing the assignment. Priming the brain to focus on particular aspects of the learning experience helps the brain process the information for long-term retention. Setting purpose for homework assignments has an impact on learning and the assignment's completion rate, as research by Marzano and others confirms.

2. Incorporate a cause into the assignment. Middle level students are motivated when they feel they are righting a wrong. They are very sensitive to justice and injustice. As a group, they are also very nurturing of those less fortunate than them. Find a community or personal cause for which students can fight fairly and incorporate your content and skills in that good fight- students will be all over the assignment.

3. Give students a real audience. There's an audience for the students' work and it isn't always us, the teachers. For example, when students work on something that uses a lot of technology - whether it's a PowerPoint talk over the internet, a project blog, or Twitter and other social media, it's not the technology that's motivating-it's the fact that there will be an audience other than the teacher. Somebody will see this, they realize. What will they think of it? they ask themselves. So how can you create real audiences for homework?

4. Incorporate people whom students admire in their assignments. Students are motivated when asked to share what they know and feel about these folks. We are a society of heroes, and young adolescents are interested in talking about and becoming heroic figures.

5. Allow choices, as appropriate. Allow students to do the even-numbered or odd-numbered problems, or allow them to choose from three prompts, not just one. Let them choose the word that best describes the political or scientific process. Let them identify their own diet and its effects on young adolescent bodies. Let them choose to work with partners or individually. How about allowing them to choose from several multiple-intelligence based tasks? If they are working in ways that are comfortable, they are more likely to do the work. By making the choice, they have upped their ownership of the task.

6. Incorporate cultural products into the assignment. If students have to use magazines, television shows, foods, sports equipment, and other products they already use, they are likely to do the work. The brain loves to do tasks in contexts with which it is familiar.

7. Allow students to collaborate in determining how homework will be assessed. If they help design the criteria for success, such as when they create the rubric for an assignment, they "own" the assignment. It comes off as something done by them, not to them. They also internalize the expectations-another way for them to have clear targets.

With some assignments we can post well-done versions from previous years (or ones we've created for this purpose) and ask students to analyze the essential characteristics that make these assignments exemplary. Students who analyze such assignments will compare those works with their own and internalize the criteria for success, referencing the criteria while doing the assignment, not just when it's finished.

8. Avoid "fluff" assignments. For example, assigning students to create a life-sized "dummy" of a person found in a novel (or in history, in science, in math, etc.) doesn't further understanding. It's a lot of coloring, cutting, wadding paper, and stapling (or stuffing old clothing with newspaper) for very little return. Make sure there is a clear connection to curriculum, not just something that would look cool when displayed in the classroom. Students will figure out how empty these assignments are very quickly. They'll see homework as serving little or no purpose other than to give them something to do, which sinks motivation like a big chunk of granite.

9. Spruce up your prompts. Don't ask students to repeatedly answer questions or summarize. Try some of these openers instead: Decide between, argue against, Why did ______ argue for, compare, contrast, plan, classify, retell ______ from the point of view of ______, Organize, build, interview, predict, categorize, simplify, deduce, formulate, blend, suppose, invent, imagine, devise, compose, combine, rank, recommend, defend, choose.

10. Have everyone turn in a paper. In her classic, Homework: A New Direction (1992), Neila Connors reminded teachers to have all students turn in a paper, regardless of whether they did the assignment. If a student doesn't have his homework, he writes on the paper the name of the assignment and why he didn't do it.

I've had students add their parents' telephone number so I could call home and share what the student said about his homework. Calling parents usually results in a terrific homework completion record for students-at least for a few weeks. An added dividend is that classmates don't get as many opportunities to see who didn't do their homework-a reputation to avoid.

11. Do not give homework passes. I used to do this; then I realized how much it minimized the importance of homework. It's like saying, "Oh, well, the homework really wasn't that important to your learning. You'll learn just as well without it." Homework should be so productive for students that missing it is like missing the lesson itself.

12. Integrate homework with other subjects. One assignment can count in two classes. Such assignments are usually complex enough to warrant the dual grade and it's a way to work smarter, not harder, for both students and teachers. Teachers can split the pile of papers to grade, then share the grades with each other, and students don't have homework piling up in multiple classes.

There are times when every teacher on the team assigns a half-hour assignment, and so do the elective or encore class teachers. This could mean three to four hours of homework for the student, which is inappropriate for young adolescents.

13. Occasionally, let students identify what homework would be most effective. Sometimes the really creative assignments are the ones that students design themselves. After teaching a lesson, ask your students what it would take to practice the material so well it became clearly understood. Many of the choices will be rigorous and very appropriate.
▶ More resources from Rick Wormeli:
Consider your true goal with homework: learning that moves into long-term memory, right? Cramming is the stuff of partial memories to be parroted for a quiz that week, then dumped in the brain's recycling bin, never to be seen again.
NEXT: In our final excerpt from Day One & Beyond, Rick Wormeli shares his approach to homework assessment - with an clear emphasis on maintaining teacher sanity. ________
This is one reason I always recommend that, as a basic premise, we avoid Monday morning quizzes and weekend or holiday homework assignments. Sure, there will be exceptions when long-term projects come due. But if we are really about teaching so that students learn and not about appearing rigorous and assigning tasks to show that we have taught, then we'll carefully consider all the effects of our homework expectations. Our students will be more productive at school for having healthier lives at home.

Although Rick never mentions the word homework in this article about helping adolescent students improve their "executive function," you will immediately see the connections! At the AMLE website.

Rick Wormeli was among the first National Board Certified teachers in America. His education career spans 35 years - teaching math, science, English, physical education, health, and history and coaching teachers and principals. He is a columnist for AMLE Magazine and a frequent contributor to ASCD's Education Leadership magazine.

His books include Meet Me in the Middle; Day One and Beyond; Fair Isn't Always Equal: Assessment and Grading in the Differentiated Classroom; Differentiation: From Planning to Practice; Metaphors & Analogies: Power Tools for Teaching Any Subject, and Summarization in Any Subject, plus The Collected Writings (So Far) of Rick Wormeli: Crazy Good Stuff I Learned about Teaching Along the Way.

He is currently working on his first young adult fiction novel and a new book on homework practices in the 21 st century.

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13 Ways to Make Homework More Meaningful and Engaging

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In the first installment of Rick Wormeli's homework advice, he made the case for take-home assignments that matter for learning and engage student interest. In Part 2, Rick offers some guiding principles that can help teachers create homework challenges that motivate kids and spark deeper learning in and out of school.

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review- Realizing Rigor in the Mathematics Classroom | MiddleWeb

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review- Realizing Rigor in the Mathematics Classroom | MiddleWeb

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Realizing Rigor in the Mathematics Classroom
By Ted H. Hull, Ruth Harbin Miles, and Don S. Balka
(Corwin, 2014 - Learn more)
Reviewed by Dina Murphy
Math teachers throughout the United States are facing the challenge and requirement of increasing rigor in their classrooms. At first glance, this seems to imply simply increasing the difficulty: Merriam Webster, after all, defines rigor as "harsh inflexibility," and "the quality of being unyielding." Webster Online Dictionary's entry includes a definition that reads "exactness without allowance, deviation, or indulgence."

These definitions would seem to be putting teachers between a rock and a hard place, one way or another. Realizing Rigor in the Mathematics Classroom will help teachers, curriculum coaches, and school leaders avoid obstacles, pitfalls and traps on their way to achieving rigor and elevating learning for their students.

While dictionaries define the term as rigid, inflexible, or unyielding, educators frequently apply rigor or rigorous to assignments that encourage students to think critically, creatively, and more flexibly.- The Glossary of Education Reform

The authors of this book pursue the definition of rigor in the context of mathematics instruction early on in this book, going from definitions like the ones listed above, through the introduction and early use of the term by the National Research Council and others - and on to its eventual inclusion as a mandated aspect of the framework of math instruction by the Common Core State Standards, and beyond.

We are all, in education, being asked to make our instruction more "rigorous." It behooves us, therefore, to understand what it means to provide this rigorous education to our students.

Inductive understanding

Realizing Rigor in the Mathematics Classroom achieves this understanding in an inductive manner, which is ultimately very effective. The authors use example problems - traditional, and reworked - to illustrate the difference between less and greater rigor in applied instruction.

The nuance of this enigmatic requirement, as the authors take pains to make clear, is that the learning behaviors tell the level of rigor. An active classroom, engaged students, teacher as facilitator rather than lecturer... these are the signposts of rigorous instruction.

Because rigor is an elusive aspect, and because it is nothing so simple as new content material or a classroom checklist, this book takes its time in building up to a clear understanding of the concept. The authors themselves point out that "There is no perfect definition of rigor." (p. 19) Given the required outcomes, they achieve two definitions-
one for content:
"Mathematical rigor is the depth of interconnecting concepts and the breadth of supporting skills students are expected to know and understand." (p. 22)
and one for instruction:
"Mathematical rigor is the effective, ongoing interaction between teacher instruction and student reasoning and thinking about concepts, skills, and challenging tasks that results in a conscious, connected, and transferable body of valuable knowledge for every student." (p. 22)

The authors move forward from there, illustrating what is meant. Along the way, the reader benefits from example problems and descriptions of implementing them, illustrative case studies, guides for assessing levels of rigor achieved, and a consistent reassurance that change is not something that will be achieved overnight (or over the summer, as the case may be). To achieve rigor, teachers, coaches and leaders must all engage in a constant effort to put learning in the minds and hands of their students.

Obstacles and ways to overcome them

Part II of the book addresses obstacles to realizing rigor, while Part III explores solutions. An important understanding of this book is that many of the traditional approaches and relationships within schools are in themselves obstacles to achieving rigor.

Formative assessment, rather than summative assessment, will do more to address problems for both individual students and entire classes, and teachers need to work toward using such cues to adapt instruction on an ongoing basis. This holds true for teachers as well, however, which is a distinctive point this book makes.

An interactive assessment program for teachers and leaders is outlined and described, which seeks to be nonjudgmental and outcome based, and to be concerned more with the quality of learning the students are gaining, rather than with rating the teachers or catching them at fault. Indeed, the authors stress that both coaches and leaders need to spend more time in the classroom, interacting with students and supporting the teachers, rather than simply watching and rating.

This changes the relationship, the roles, the rules... and is just the sort of drastic change needed by and with teachers to create truly rigorous learning environments.

Input and Output goals for all roles

Part IV, the penultimate section of the book, very concisely describes parallel Input and Output goals for teachers, coaches, and leaders. This stresses - once again - the importance of all of these roles in achieving rigorous learning in the math classroom. The successful math department will recognize the need for, and work constantly to improve, the participation of all of these roles.

Realizing Rigor in the Mathematics Classroom will help earnest participants in any of those areas - principals, curriculum directors, department heads, instructional coaches and teachers - who are seeking to achieve rigor in their Common Core classroom. Indeed, even in non-Common Core states (I live and work in Texas, where our Texas Essential Knowledge and Skills [TEKS] Standards have just been revamped for mathematics), this book can be an invaluable tool. I fully intend to put quite a few of the practices and approaches I learned from reading this book into practice this year.
Dina Murphy teaches seventh grade Math at West Brazos Junior High in Brazoria, Texas. Despite having planned to teach Social Studies, she enjoys the challenges of helping students learn to share her love of math. Dina and her 7th grade math team partner are happily embracing technology in their classrooms, and have set themselves a high learning curve in order to offer their students a strong math curriculum that also gives them a good base in 21st century communication and work technology.

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review- Realizing Rigor in the Mathematics Classroom

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Realizing Rigor in the Mathematics Classroom By Ted H. Hull, Ruth Harbin Miles, and Don S. Balka (Corwin, 2014 - Learn more) Reviewed by Dina Murphy Math teachers throughout the United States are facing the challenge and requirement of increasing rigor in their classrooms. At first glance, this seems to imply simply increasing the difficulty: Merriam Webster, after all, defines rigor as "harsh inflexibility," and "the quality of being unyielding."

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A MiddleWeb Blog

STEM is a growing young initiative in the K-12 learning arena. Many people are still trying to wrap their heads around it. Teachers are still wondering, "I teach science (or I teach technology, or I teach math), so am I teaching STEM?"

I recently finished co-teaching a STEM/STEAM eCourse with colleague Nancy Flanagan and guest Dr. Susan Pruet. We found that many people are wrestling with questions about what STEM is, how it's different from traditional math and science classes, and how engineering fits in.

Before figuring out what makes something STEM, educators need to understand what STEM is supposed to accomplish. STEM is a way to achieve specific workforce-related goals, although it also focuses on life skills that all students need. I generally start a STEM class for educators by reminding folks exactly why STEM became such a hot topic.

Why the urgency around STEM?

► Our workforce has a growing need for workers with 21st century skills. The current demand for STEM-capable workers is greater than the supply of applicants who are prepared for STEM careers. So, what 21st Century skills do our kids need to be successful in the workforce and in life in the high-tech, post-digital age? The ultimate goal of STEM is to address that question and prepare students with these skills.

► Currently our biggest demand is for workers who understand math and science and can apply what they know. According to The Atlantic, more and more U.S.-based jobs require workers who possess practical expertise in science, technology, engineering and mathematics. Our students need to understand and be able to apply concepts from algebra, geometry, trigonometry, biology, chemistry, physics and other important disciplines. Currently, American kids are falling short.

STEM intentionally gives students experience in integrating and applying rigorous math and science to solve problems. Since STEM can't focus on every science and math objective, a good rule of thumb is to focus on the most important learning goals in each discipline.

In addition to rigorous science and math, I often discuss some other 21st century skills students need to master. This list will likely look familiar.

* Collaboration and teamwork
* Critical thinking and problem solving
* Communication on multiple levels
* Entrepreneurship, resourcefulness, and resilience
* Creativity and innovation
* A sense of civic responsibility

So, in addition to applying science and math, STEM should build specific kinds of life skills and personal qualities. Civil responsibility, for example, is a personal quality that often develops through identifying and solving real-world problems.

Why include engineering?

Another biggie for STEM is the use of a design process for helping kids think through and solve problems that I usually refer to as "engineering challenges" or "STEM challenges."

Why would students need to use an engineering design process? This is considered a non-negotiable in most STEM projects, since this is the type of thinking that engineers and related professionals go through when they create innovative solutions for real world problems. Our students need to graduate with specific thinking skills that can help them approach diverse challenges.

The engineering design process (EDP) provides an organized method for solving complex problems that require some type of innovation. This process involves a set of steps that go from defining a problem to creating and developing a final solution. The "E" in STEM is a key difference between traditional science and math lessons and STEM lessons.

There are several versions of this engineering design process. (Go to Google image search and type in Engineering Design Process). All contain the same basic steps. The higher the grade level, the more steps are typically included.

Once the educators in my class have looked at the impetus behind STEM and what skills workers need in 21st century jobs, they can understand the need to develop students who are ready for STEM careers. That informs our understanding of what makes something STEM.

So what's the acid test for a STEM project?

At this point, I invite my adult learners to brainstorm some ideas. When it comes to student STEM projects, what are some defining characteristics? Here are several we have come up with:

Features integrated and applied math and science

Revolves around an Engineering Design Process

Engages kids in creating, testing, and evaluating prototypes

Builds a mindset of continual improvement and redesign

Involves an inquiry-based teaching approach and hands-on investigation

Involves students in working and solving problems in teams

Provides students with a risk-free atmosphere in which to make mistakes and try again

Those are some significant things that make something STEM.

Try my "Is It STEM?" checklist

One way to examine our programs to see if they meet the STEM test is to make a rubric or checklist incorporating characteristics like those we brainstormed. What follows might be a starter set of questions to examine proposed or existing STEM projects. This is not comprehensive, but the answers to the following queries can generally reveal whether a program is STEM.

STEM Content:

How was math integrated and applied?

How was science integrated and applied?

How was technology integrated (or created)?

How was the Engineering Design Process used?

Students:

How successfully were students able to engage in team problem-solving?

Were they comfortable viewing failure as okay, and as a next step in a search for an answer?

To what extent did students consider multiple right ways to approach and solve the problem?

Did student teams develop and test a prototype for solving the problem?

Teachers:

Do teachers have deep content knowledge in their field?

Do teachers have the pedagogical skill to make that content accessible to students?

Are the teachers skilled at guiding and facilitating learning?

Do teachers have the resources and training they need in STEM?

What makes something STEM?

Classrooms with students engaged and interested in being scientists, mathematicians, and engineers and having the habits of mind and the skill sets to do that. Our programs need to include real and rigorous STEM work. For the sake of our 21st century students, our communities and our national infrastructure, we need to get this right.

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A MiddleWeb Blog STEM is a growing young initiative in the K-12 learning arena. Many people are still trying to wrap their heads around it. Teachers are still wondering, "I teach science (or I teach technology, or I teach math), so am I teaching STEM?"

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Ideas to Help Students Develop Higher-Order Questions

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Ideas to Help Students Develop Higher-Order Questions

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AMLE - Association for Middle Level Education

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As a middle grades teacher, there are certain questions from your students that you see coming: Why are we doing this? Is this for a grade? When is this due? Can we work with a partner? Is it lunch yet?

And then there are the other questions. These questions poke their smiling faces around corners, surprise you, and make you happy that you're a middle level educator. One day as a sixth grade social studies teacher, I had such a joyous occasion.

I had about six students in my classroom eating lunch as they were working on a project about the Middle East. They were moderately productive amidst their lunch trays, notebook paper, and pens, and I had already fielded several of the standard "oh-my-gosh-Mr. Tomlin-this-project-is-like-impossible" questions-when I was faced with a question that only a middle school student could ask.

With a Jell-O cup in one hand, a boy named Jamie got up from his desk and asked most genuinely, "Mr. Tomlin, what's your favorite smell that you're not supposed to smell?"

Now, I don't know why he wanted to know my personal answer to this riddle, and I don't even remember what I answered. But I remember Jamie. I remember my feelings of joy and bewilderment. And I remember that awesome, novel question.

I think back on this story about Jamie and wonder, "How can we help our students ask thought-provoking, robust, and amazing questions every day?" As middle level educators, we feel a great deal of pressure to create lessons that climb the rungs of Bloom's taxonomy ladder: knowledge, comprehension, application, analysis, synthesis, and evaluation. We work hard to ensure that our plans are populated with higher-order, text-dependent questions to challenge students.

We prepare units with essential questions and enduring understandings for students to take away when they're done. We may even attend professional development workshops about how to write (and assess) higher-order thinking questions. Because we are critical practitioners in the art of teaching and learning, all of that effort has its place.

However, as I think about Jamie's question from lunchtime, I wonder how we can do more to develop student inquiry-to help students develop their own higher-order questions, which they can use to approach any learning situation.

There are 9 simple steps that we can take to build a culture of student inquiry in our middle level classrooms now.

1. Model curiosity. Ask big, higher-order novel questions, and do so as a learner. What are you curious about? Bring your own interests and big ideas into the classroom and share them with passion! Relate them to your content, but push back against the content. "Hey, y'all. Have you ever wondered why people wrote letters back home during WWII? What do you think it would have been like to write one-or to receive one and to write back?"

2. Build a culture of inquiry by cultivating relationships through questions. Solid relationships are the foundation upon which we build everything in the middle level. Therefore, with students, your fellow teachers, and staff, build relationships on genuine inquiry. Ask questions about each others' lives, interests, and (yes the dreaded "F" word) feelings that push boundaries and deviate from the script-like Jamie's.

3. Provide rich stimulus to inspire rich questions. Don't settle for tepid non-fiction or fiction-get the good stuff! Find well-written, progressive pieces about cool topics that get students interested, excited, and involved, so they start asking higher-order questions. And appeal to your students' minds through their ears and eyes as well by using provocative music (i.e., The Rite of Spring, Thelonious Monk, DJ Shadow) and art and photography (i.e., Dali, Banksy, Arbus)

4. Give students examples and keywords for novel questions. As they start building and asking, some students will need words to get them started. Here are some great sources for that: http://www.clemson.edu/assessment/assessmentpractices/
referencematerials/documents/Blooms%20Taxonomy%20Action%20Verbs.pdf. Use these words yourself orally and in print. Make them available for families, too, so they can ask novel questions at home.

5. Leave judgment at the classroom door. Honor a student's effort to ask a novel question-and tell him/her, "I like the way you're thinking!" That genuine, immediate praise will embolden him/her to ask more and to ask deeper questions.

6. (At the same time) Push students to give you more. Be bold. When students ask higher-order questions, make them explain those questions, provide the reasons why they asked them, and give additional follow-up questions to add more layers.

7. Document and celebrate novel questions. As soon as a student asks his/her big question, say, "WHOAAA! Gotta write that down!" Then grab that marker, run over to the wall or chart paper like you're literally on fire, and write it down with deliberate fury! And then use those questions later to show students that you value their thinking throughout the year.

8. Make the novel questions part of a project-based learning unit or Genius Hour (see Welcome to the Genius Hour and http://www.geniushour.com/). If we celebrate students' questions and connect them with authentic, self-selected learning goals, they will be even more motivated to ask novel questions. They will see how higher-order thinking questions can turn into something actionable and productive.

9. Question any list that declares absolutes about student inquiry. These 9 simple steps are not meant to be the end of the inquiry about student inquiry, so model the expectation and keep on asking your own higher-order questions about what works in the classroom. True pedagogical artists never rest!

So what's your favorite smell that you're not supposed to smell? What student questions will make you smile, make you push your fence lines, blow your hair back, make you question your notions, and make you ask more questions?

When you help students become great with inquiry, your classroom will be enriched by fields and fields of novel questions. Perhaps reaching every student and creating great schools is more about asking great questions than coming up with easy answers.

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Ideas to Help Students Develop Higher-Order Questions

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As a middle grades teacher, there are certain questions from your students that you see coming: Why are we doing this? Is this for a grade? When is this due? Can we work with a partner? Is it lunch yet? And then there are the other questions.

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Use The UPS Strategy As An Assessment Tool

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Use The UPS Strategy As An Assessment Tool

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Thought starters

1. How does Ms. Mickle assess learning through each part of the U-P-S strategy?

2. How can students use this strategy to assess their own understanding?

3. How could the data gathered from this strategy be used to inform instruction?

School Details

Cedar Hill High School
1 Longhorn Boulevard
Cedar Hill TX 75104

Data Provided By:

Teachers

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Formative Assessment Using the U-P-S Strategy

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Geometry teacher Tereze Mickle uses the U-P-S strategy to assess her students' understanding. Through the U-P-S strategy, students work on understanding, planning, and solving problems before checking their work. Tereze explains how each step of the process gives her information about her students' learning.

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How To Get Students To Work Independently: Hint Cards

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How To Get Students To Work Independently: Hint Cards

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Discussion and Supporting Materials

Thought starters

1. How does Ms. McPhillips decide what hints to use?

2. What are the effects of using hint cards?

3. How does Ms. McPhillips use hint cards to scaffold understanding?

School Details

John F. Deering Middle School
2 Webster Knight Drive
West Warwick RI 02893

Data Provided By:

Teachers

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Middle school math teacher Audra McPhillips explains how she uses hint cards to support her students and encourage independence. Audra explains how she writes probing questions on the hint cards to help scaffold her students' understanding. Audra shares how she has noticed her students benefiting from the extra support of the hint cards.

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Middle School Math Teaching Tip - Using Color

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Middle School Math Teaching Tip - Using Color

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Discussion and Supporting Materials

Thought starters

1. How does using color help students organize their thinking?

2. What kinds of problems are best suited for this strategy?

3. How does color help students' thinking become visible to others?

School Details

John F. Deering Middle School
2 Webster Knight Drive
West Warwick RI 02893

Data Provided By:

Teachers

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Using Color to Support Mathematical Thinking

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Enjoy your first three pieces of content for free. Subscribe for unlimited access. Have questions about subscribing? Click Here to learn more. Enjoy your first three pieces of content for free. Subscribe for unlimited access. Have questions about subscribing? Click Here to learn more. How does using color help students organize their thinking?

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Dipsticks: Efficient Ways to Check for Understanding | Edutopia

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Dipsticks: Efficient Ways to Check for Understanding | Edutopia

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Through alternative formative assessment, teachers can check for student understanding without falling back on the tedious or intimidating pop quiz.

What strategy can double student learning gains? According to 250 empirical studies, the answer is formative assessment, defined by Bill Younglove as "the frequent, interactive checking of student progress and understanding in order to identify learning needs and adjust teaching appropriately."

Unlike summative assessment, which evaluates student learning according to a benchmark, formative assessment monitors student understanding so that kids are always aware of their academic strengths and learning gaps. It also helps teachers improve the effectiveness of their instruction. "When the cook tastes the soup," writes Robert E. Stake, "that's formative; when the guests taste the soup, that's summative." Formative assessment can be administered as an exam. But if the assessment is not a traditional quiz, it falls within the category of alternative assessment.

Alternative formative assessment (AFA) strategies can be as simple (and important) as checking the oil in your car-hence the name "dipsticks." They're especially effective when students are given tactical feedback, immediately followed by time to practice the skill. My favorite techniques are those with simple directions, like The 60 Second Paper, which asks students to describe the most important thing they learned and identify any areas of confusion in one minute.

You can find another 53 ways to check for understanding toward the end of this post and as a downloadable document.

Observation: A Key Practice in Alternative Formative Assessment

A fundamental element of most AFAs is observation. Rebecca Alber writes there is much to learn by taking observational notes as students work in groups. "However," she clarifies, "if it is quiet during this talk time, and they are watching you watch them, they are most likely lost." Elena Aguilar has witnessed " a fantastic first grade Sheltered English teacher " who directed his students to respond to a story by making hand gestures and holding up picture cards: "In this way, the teacher was able to immediately see who was struggling with the concepts and provide corrective feedback."

By methodically watching and recording student performance with a focused observation form, you can learn a lot about students' levels of understanding in just a few moments. For example, math teacher Taryn Pritchard uses an observation sheet to assess students' mastery levels in only 10 seconds. Pre-planning methodical observations allow instructors to efficiently and effectively intervene when it counts most-in the instant students start down the wrong path.

New to Alternative Formative Assessment? Start Slow

The National Capital Language Resource Center recommends the following when introducing alternative assessment for the first time:

Integrate alternative assessments gradually, while still using the traditional assessments.

Walk students through the rubrics and discuss expectations when you introduce assignments.

Learn to score alternative assessments yourself, and then gradually introduce students to self-evaluation.

Teach students how to thoughtfully give each other feedback as you introduce them to peer-response.

A Simple Way to Gain Information From Your Students: Ask Them

When preservice teachers are confused as to why their students perform poorly on an assignment, I gently say, "Did you ask them why?" Having learners articulate why they're stuck can be profoundly useful for identifying where to target support.

According to the American Institute of Nondestructive Testing, the simplest tool to encourage student self-assessment is evaluative prompts:

How much time and effort did you put into this?

What do you think your strengths and weaknesses were in this assignment?

How could you improve your assignment?

What are the most valuable things you learned from this assignment?

Learners can respond to those prompts using Padlet, a virtual corkboard where many computer users can simultaneously post their responses; follow up with a focused whole-class discussion of those answers. The instructor doesn't always have to develop prompts-students can invent and submit one or more potential exam questions and answers on relevant content. Tell them that you'll include the best contributions on a forthcoming quiz.

Portfolios are a more complex form of ongoing self-assessment, one that can feature in student-led conferences. James Mule, principal of St. Amelia Elementary School in New York, describes how children benefit from the student-led conferences that occur at his institution: "With the student in charge and the teacher acting as a facilitator, the authentic assessment gives students practice in self-evaluation and boosts accountability, self-confidence, and self-esteem."

The biggest benefit of integrating AFAs into your practice is that students will internalize the habit of monitoring their understanding and adjusting accordingly.

53 Ways to Check for Understanding

1. Summary Poem Activity

List 10 key words from an assigned text.

Do a free verse poem with the words you highlighted.

Write a summary of the reading based on these words.

2. Invent the Quiz
Write ten higher-order text questions related to the content. Pick two and answer one of them in half a page.

3. The 411
Describe the author's objective.

4. Opinion Chart
List opinions about the content in the left column of a T-chart, and support your opinions in the right column.

5. So What? Journal
Identify the main idea of the lesson. Why is it important?

6. Rate Understanding

7. Clickers (Response System)

8. Teacher Observation Checklist

9. Explaining
Explain the main idea using an analogy.

10. Evaluate
What is the author's main point? What are the arguments for and against this idea?

11. Describe
What are the important characteristics or features of the main concept or idea of the reading?

12. Define
Pick out an important word or phrase that the author of a text introduces. What does it mean?

13. Compare and Contrast
Identify the theory or idea the author is advancing. Then identify an opposite theory. What are the similarities and differences between these ideas?

14. Question Stems

I believe that ________ because _______.

I was most confused by X.

15. Mind Map
Create a mind map that represents a concept using a diagram-making tool (like Gliffy). Provide your teacher/classmates with the link to your mind map.

16. Intrigue Journal
List the five most interesting, controversial, or resonant ideas you found in the readings. Include page numbers and a short rationale (100 words) for your selection.

17. Advertisement
Create an ad, with visuals and text, for the newly learned concept.

18. 5 Words
What five words would you use to describe ______? Explain and justify your choices.

19. Muddy Moment
What frustrates and confuses you about the text? Why?

20. Collage
Create a collage around the lesson's themes. Explain your choices in one paragraph.

21. Letter
Explain _______ in a letter to your best friend.

22. Talk Show Panel
Have a cast of experts debate the finer points of X.

23. Study Guide
What are the main topics, supporting details, important person's contributions, terms, and definitions?

24. Illustration
Draw a picture that illustrates a relationship between terms in the text. Explain in one paragraph your visual representation.

25. KWL Chart
What do you know, what do you want to know, and what have you learned?

26. Sticky Notes Annotation
Use sticky notes to describe key passages that are notable or that you have questions about.

27. 3-2-1

Three things you found out.

Two interesting things.

One question you still have.

28. Outline
Represent the organization of X by outlining it.

29. Anticipation Guide
Establish a purpose for reading and create post-reading reflections and discussion.

30. Simile
What we learned today is like X.

31. The Minute Paper
In one minute, describe the most meaningful thing you've learned.

32. Interview You
You're the guest expert on 60 Minutes. Answer:

1. What are component parts of _______?

2. Why does this topic matter?

33. Double Entry Notebook
Create a two-column table. Use the left column to write down 5-8 important quotations. Use the right column to record reactions to the quotations.

34. Comic Book
Use a comic book creation tool like Bitstrips to represent understanding.

35. Tagxedo
What are key words that express the main ideas? Be ready to discuss and explain.

36. Classroom TED Talk

37. Podcast
Play the part of a content expert and discuss content-related issues on a podcast, using the free Easypodcast.

38. Create a Multimedia Poster with Glogster

39. Twitter Post
Define _______ in under 140 characters.

40. Explain Your Solution
Describe how you solved an academic problem, step by step.

41. Dramatic Interpretation
Dramatize a critical scene from a complex narrative.

42. Ballad
Summarize a narrative that employs a poem or song structure using short stanzas.

43. Pamphlet
Describe the key features of _______ in a visually and textually compelling pamphlet.

44. You've Got Mail
Each student writes a question about a topic on the front of an envelope; the answer is included inside. Questions are then "mailed" around the room. Each learner writes her answer on a slip of scratch paper and confirms its correctness by reading the "official answer" before she places her own response in the envelope. After several series of mailings and a class discussion about the subject, the envelopes are deposited in the teacher's letterbox.

45. Bio Poem
To describe a character or person, write a poem that includes:

(Line 1) First name

(Line 2) 3-4 adjectives that describe the person

(Line 3) Important relationship

(Line 4) 2-3 things, people, or ideas the person loved

(Line 5) Three feelings the person experienced

(Line 6) Three fears the person experienced

(Line 7) Accomplishments

(Line 8) 2-3 things the person wanted to see happen or wanted to experience

(Line 9) His or her residence

(Line 10) Last name

46. Sketch
Visually represent new knowledge.

47. Top Ten List
What are the most important takeaways, written with humor?

48. Color Cards

Red = "Stop, I need help."

Green = "Keep going, I understand."

Yellow = "I'm a little confused."

49. Quickwrite
Without stopping, write what most confuses you.

50. Conference
A short, focused discussion between the teacher and student.

51. Debrief
Reflect immediately after an activity.

52. Exit Slip
Have students reflect on lessons learned during class.

53. Misconception Check
Given a common misconception about a topic, students explain why they agree or disagree with it.

Other Assessment Resources

In Edutopia's " The Power of Comprehensive Assessment," Bob Lenz describes how to create a balanced assessment system.

The Assessment and Rubrics page of Kathy Schrock's Guide to Everything website hosts many excellent assessment rubrics.

More Rubrics for Assessment are provided by the University of Wisconsin-Stout.

Jon Mueller's Authentic Tasks and Rubrics is a must see-resource in his Authentic Assessment Toolbox website.

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Dipsticks: Efficient Ways to Check for Understanding

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Through alternative formative assessment, teachers can check for student understanding without falling back on the tedious or intimidating pop quiz. What strategy can double student learning gains? According to 250 empirical studies, the answer is formative assessment, defined by Bill Younglove as "the frequent, interactive checking of student progress and understanding in order to identify learning needs and adjust teaching appropriately."

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Math Tech Tips: New feature in celebration of g(Math)'s 50,000th current user: Statistical Displays

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Math Tech Tips: New feature in celebration of g(Math)'s 50,000th current user: Statistical Displays

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I am continually blown away by the rise of current users of g(Math). Today g(Math) passed 50,000 current users!

To celebrate I am launching another aspect of g(Math) that has been missing from Docs and Sheets, statistical displays.

You can now select a table in your Doc and create statistical displays from the data. Currently, there are three options:

If you have a specific type of display you would like to see, please ask!

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New feature in celebration of g(Math)'s 50,000th current user: Statistical Displays

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I am continually blown away by the rise of current users of g(Math). Today g(Math) passed 50,000 current users! To celebrate I am launching another aspect of g(Math) that has been missing from Docs and Sheets, statistical displays. You can now select a table in your Doc and create statistical displays from the data.

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Celebrate Pi Day: Seven Classroom Resources for Pi Learning | Edutopia

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Celebrate Pi Day: Seven Classroom Resources for Pi Learning | Edutopia

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Pi Day is coming on March 14, and the annual celebration offers a great opportunity for students to explore pi and math-related concepts. There are plenty of great teaching resources online to help your class celebrate Pi Day, so we thought we'd help you sort through them all.

Here are a few of our favorites from around the web, starting with an interesting music-related pi lesson, "What Pi Sounds Like," which was produced by musician Michael Blake. This video is a fun resource that can help students of all ages get excited about pi. Happy Pi Day!

San Francisco Exploratorium Pi Day Activities: Without the Exploratorium, official Pi Day celebrations might never have happened. In 1988, Exploratorium physicist Larry Shaw started the tradition, and it was recognized by Congress in 2009. The Exploratorium highlights some great hands-on activities, with links to useful pi-related resources.

Learning Resources From PiDay.org: PiDay.org is a wonderful source for interesting activities, news items, and videos related to pi. Be sure to check out the site's listing of Pi Day videos, as well as the outside links.

Happy Pi Day, TeachPi.org: TeachPi hosts a trove of Pi Day resources, featuring fun classroom activities, Pi Day-inspired music, and other fun learning ideas. There's plenty here to keep students engaged and learning on March 14. Check out the activities section for a bunch of great learning ideas.

Scholastic Pi Day Teaching Ideas: Scholastic produced this list of plans for three grade spans: preschool-grade 1, grades 2-3, and grades 4-6. The page features interesting information about the history of pi, ideas for activities, and a link to a web application for exploring the music of pi. Another great Scholastic resource is "Writing With Pi."

PBS LearningMedia Pi-Related Resources: PBS LearningMedia features a great collection of geometry lessons related to pi. These aren't specifically for Pi Day, but they're especially relevant on March 14. Plus, for more math and pi-themed lessons, OER Commons has curated more than 100 resources from a variety of sources.

TeachersFirst's Pi Day Resources: TeachersFirst offers this great roundup of pi-themed lessons and resources from around the web, focused primarily on high school. Included in the collection are some general math resources, like Simpsons Math.

Pi-Related Resources, Joy of Pi: Author David Blatner is a pi fanatic, and his website Joy of Pi features tons of useful and interesting information. Included on the resources page are links to sites on the history of pi, how to calculate pi, and mysteries about the number.

Quick Reads on Pi

From its history to its occurrence in everyday life, pi is an endlessly fascinating subject. Here's a short list of interesting, insightful, and just plain entertaining reads on the subject.

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7 Classroom Resources for Pi Day | Edutopia

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Pi Day is coming on March 14, and the annual celebration offers a great opportunity for students to explore pi and math-related concepts. There are plenty of great teaching resources online to help your class celebrate Pi Day, so we thought we'd help you sort through them all.

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Videos about numbers and mathematics. Videos by Brady Haran since 2011. Our thanks to Jane Street. Thanks also to SLMath, the Simons Foundation, and our Patreon supporters.

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6 Principles Of Genius Hour In The Classroom

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6 Principles Of Genius Hour In The Classroom

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by Terry Heick
Update: We did a t-shirt campaign of this graphic last year. It's our old logo and needs updating, but for now is still available if you wanted a t-shirt with a kind of learning model on it. You know. If you're into that sort of thing. You can find it here.
Genius Hour in the classroomis an approach to learning built around student curiosity, self-directed learning, and passion-based work.

In traditional learning, teachers map out academic standards, and plan units and lessons based around those standards. In Genius Hour, students are in control, choosing what they study, how they study it, and what they do, produce, or create as a result. As a learning model, it promotes inquiry, research, creativity, and self-directed learning.
What's The Difference?
Genius Hour is most notably associated with Google, where employees are able to spend up to 20% of their time working on projects they're interested in and passionate about. The study and work is motivated intrinsically, not extrinsically. The big idea for Google is that employees motivated by curiosity and passion will be happier, more creative, and more productive, which will benefit the company in terms of both morale, "off-Genius" productivity, and "on-Genius" performance.

Genius Hour provides students freedom to design their own learning during a set period of time during school. It allows students to explore their own curiosity through a self-manifested sense of purpose and study while within the support system of the classroom.
Genius Hour In The Classroom: 6 Principles Of Genius Hour Sense of Purpose
A key distinction compared to more open, self-directed learning and user-generated learning experiences is that within a "Genius Hour" framework, this student-centered approach is only used a portion of the schedule, providing students a choice in what they learn and how they learn it during a set period of time within a school day.
Design
Students must find their own sense of purpose in what they study, make sense of, and create. The context and motivation are no longer entirely academic, which forces both the student and teachers to make adjustments.
Inquiry & Navigation
Without teachers "packaging" content that frames and scaffold content, students are left to design their own learning experiences.
Create
Through surveying possibility, navigation of unfiltered content, gathering information, and narrowed research, students make sense of ideas important to them. This navigation and survey of possibility then leads to more narrow inquiry and research. In this way, inquiry-based learning has significant overlap with Genius Hour. (See also, 20 Questions To Guide Inquiry-Based Learning.)
Socialization
Whether students "make," publish, design, act, or do, "creating" is core to Genius Hour. There is always a visible product or function of the learning.
80/20 Rule
Students connect with teachers to plan, peers to produce, and experts and community members to establish a sense of purpose for their work.
6 Principles Of Genius Hour In The Classroom
The 80/20 rule is important, as it provides the only structure of most Genius Hour learning. Whether it's an "hour," one day per week, or something else, it provides a kind of schedule while contrasting usefully with traditional academic "training."

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6 Principles Of Genius Hour In The Classroom

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by Terry Heick Update: We did a t-shirt campaign of this graphic last year. It's our old logo and needs updating, but for now is still available if you wanted a t-shirt with a kind of learning model on it. You know. If you're into that sort of thing.

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10 Characteristics Of A Highly Effective Learning Environment

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10 Characteristics Of A Highly Effective Learning Environment

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by Terry Heick
For in-person professional development from TeachThought on how to create an effective learning environment in your classroom or school, contact us today.
Wherever we are, we'd all like to think our classrooms are "intellectually active" places. Progressive learning(like our 21st Century Model, for example) environments. Highly effective and conducive to student-centered learning. But what does that mean?

The reality is, there is no single answer because teaching and learning are awkward to consider as single events or individual "things." This is all a bunch of rhetoric until we put on our white coats and study it under a microscope, at which point abstractions like curiosity, authenticity, self-knowledge, and affection will be hard to pin down.

So we put together one take on the characteristics of a highly effective classroom. They can act as a kind of criteria to measure your own against-see if you notice a pattern.
10 Characteristics Of A Highly Effective Learning Environment 1. The students ask the questions-good questions This is not a feel-good implication, but really crucial for the whole learning process to work.
The role of curiosity has been studied (and perhaps under-studied and under-appreciated), but suffice to say that if a learner enters any learning activity with little to no natural curiosity, prospects for meaningful interaction with texts, media, and specific tasks are bleak. (Interested in how to kill learner curiosity in 12 easy steps?)
2. Questions are valued over answers 3. Ideas come from a divergent sources
Many teachers force students (proverbial gun to head) to ask questions at the outset of units or lessons, often to no avail. Cliché questions that reflect little understanding of the content can discourage teachers from "allowing" them. But the fact remains-if students can't ask great questions-even as young as elementary school-something, somewhere is unplugged.
4. A variety of learning models are used 5. Classroom learning "empties" into a connected community
Questions are more important than answers. So it makes sense that if good questions should lead the learning, there would be value placed on these questions. And that means adding currency whenever possible-grades (questions as assessment!), credit (give them points-they love points), creative curation (writing as a kind of graffiti on large post-it pages on the classroom walls), or simply praise and honest respect. See if you don't notice a change.

Ideas for lessons, reading, tests, and projects-the fiber of formal learning-should come from a variety of sources. If they all come from narrow slivers of resources, you're at risk of being pulled way off in one direction (that may or may not be good). An alternative? Consider sources like professional and cultural mentors, the community, content experts outside of education, and even the students themselves. Huge shift in credibility.
6. Learning is personalized by a variety of criteria
And when these sources disagree with one another, use that as an endlessly "teachable moment," because that's what the real world is like.
7. Assessment is persistent, authentic, transparent, and never punitive
Inquiry-based learning, project-based learning, direct instruction, peer-to-peer learning, school-to-school, eLearning, Mobile learning, the flipped classroom, and on and on-the possibilities are endless. Chances are, none are incredible enough to suit every bit of content, curriculum, and learner diversity in your classroom. A characteristic of a highly-effective classroom, then, is diversity here, which also has the side-effect of improving your long-term capacity as an educator.
8. Criteria for success is balanced and transparent. 9. Learning habits are constantly modeled
In a highly-effective learning environment, learning doesn't need to be radically repackaged to make sense in the "real world," but starts and ends there.
10. There are constant opportunities for practice
As great as it sounds for learners to reflect on Shakespeare to better understand their Uncle Eddie-and they might-depending on that kind of radical transfer to happen entirely in the minds of the learners by design may not be the best idea. Plan on this kind of transfer from the beginning.
Image attribution flicker user flickeringbrad and josekevo; 10 Characteristics Of A Highly Effective Learning Environment 10 Characteristics Of A Highly Effective Learning Environment For in-person professional development from TeachThought on how to create an effective learning environment in your classroom or school, contact us today.
It has to leave the classroom because they do.

Personalized learning is likely the future, but for now the onus for routing students is almost entirely on the shoulders of the classroom teacher. This makes personalization-and even consistent differentiation-a challenge. One response is to personalize learning-to whatever extent you plan for-by a variety of criteria-not just assessment results or reading level, but interest, readiness-for-content, and others as well.

Then, as you adjust pace, entry points, and rigor accordingly, you'll have a better chance of having uncovered what the learners truly "need".
10 Characteristics Of A Highly Effective Learning Environment 1. The students ask the questions-good questions This is not a feel-good implication, but really crucial for the whole learning process to work.
Assessment is just an (often ham-fisted) attempt to get at what a learner understands. The more infrequent, clinical, murky, or threatening it is, the more you're going to separate the "good students" from the "good thinkers." And the "clinical" idea has less to do with the format of the test, and more to do with the tone and emotion of the classroom in general. Why are students being tested? What's in it for them, and their future opportunities to improve?
2. Questions are valued over answers 3. Ideas come from a divergent sources
And feedback is quick even when the "grading" may not be.
4. A variety of learning models are used 5. Classroom learning "empties" into a connected community
Students should not have to guess what "success" in a highly-effective classroom looks like. It should also not be entirely weighted on "participation," assessment results, attitude, or other individual factors, but rather meaningfully melted into a cohesive framework that makes sense-not to you, your colleagues, or the expert book on your shelf, but the students themselves.

Cognitive, meta-cognitive, and behavioral "good stuff" is constantly modeled. Curiosity, persistence, flexibility, priority, creativity, collaboration, revision, and even the classic Habits of Mind are all great places to start. So often what students learn from those around them is less directly didactic, and more indirect and observational.
6. Learning is personalized by a variety of criteria
Monkey see, monkey do.
7. Assessment is persistent, authentic, transparent, and never punitive
Old thinking is revisited. Old errors are reflected on. Complex ideas are re-approached from new angles. Divergent concepts are contrasted. Bloom's taxonomy is constantly traveled up and down, from the simple to the complex in an effort to maximize a student's opportunities to learn-and demonstrate understanding-of content.
8. Criteria for success is balanced and transparent. 9. Learning habits are constantly modeled
For professional development around this idea or others you read about on TeachThought, contact us.
10. There are constant opportunities for practice
by Terry Heick
Image attribution flicker user flickeringbrad and josekevo; 10 Characteristics Of A Highly Effective Learning Environment
Wherever we are, we'd all like to think our classrooms are "intellectually active" places. Progressive learning(like our 21st Century Model, for example) environments. Highly effective and conducive to student-centered learning. But what does that mean?

The reality is, there is no single answer because teaching and learning are awkward to consider as single events or individual "things." This is all a bunch of rhetoric until we put on our white coats and study it under a microscope, at which point abstractions like curiosity, authenticity, self-knowledge, and affection will be hard to pin down.

So we put together one take on the characteristics of a highly effective classroom. They can act as a kind of criteria to measure your own against-see if you notice a pattern.

The role of curiosity has been studied (and perhaps under-studied and under-appreciated), but suffice to say that if a learner enters any learning activity with little to no natural curiosity, prospects for meaningful interaction with texts, media, and specific tasks are bleak. (Interested in how to kill learner curiosity in 12 easy steps?)

Many teachers force students (proverbial gun to head) to ask questions at the outset of units or lessons, often to no avail. Cliché questions that reflect little understanding of the content can discourage teachers from "allowing" them. But the fact remains-if students can't ask great questions-even as young as elementary school-something, somewhere is unplugged.

Questions are more important than answers. So it makes sense that if good questions should lead the learning, there would be value placed on these questions. And that means adding currency whenever possible-grades (questions as assessment!), credit (give them points-they love points), creative curation (writing as a kind of graffiti on large post-it pages on the classroom walls), or simply praise and honest respect. See if you don't notice a change.

Ideas for lessons, reading, tests, and projects-the fiber of formal learning-should come from a variety of sources. If they all come from narrow slivers of resources, you're at risk of being pulled way off in one direction (that may or may not be good). An alternative? Consider sources like professional and cultural mentors, the community, content experts outside of education, and even the students themselves. Huge shift in credibility.

And when these sources disagree with one another, use that as an endlessly "teachable moment," because that's what the real world is like.

Inquiry-based learning, project-based learning, direct instruction, peer-to-peer learning, school-to-school, eLearning, Mobile learning, the flipped classroom, and on and on-the possibilities are endless. Chances are, none are incredible enough to suit every bit of content, curriculum, and learner diversity in your classroom. A characteristic of a highly-effective classroom, then, is diversity here, which also has the side-effect of improving your long-term capacity as an educator.

In a highly-effective learning environment, learning doesn't need to be radically repackaged to make sense in the "real world," but starts and ends there.

As great as it sounds for learners to reflect on Shakespeare to better understand their Uncle Eddie-and they might-depending on that kind of radical transfer to happen entirely in the minds of the learners by design may not be the best idea. Plan on this kind of transfer from the beginning.

It has to leave the classroom because they do.

Personalized learning is likely the future, but for now the onus for routing students is almost entirely on the shoulders of the classroom teacher. This makes personalization-and even consistent differentiation-a challenge. One response is to personalize learning-to whatever extent you plan for-by a variety of criteria-not just assessment results or reading level, but interest, readiness-for-content, and others as well.

Then, as you adjust pace, entry points, and rigor accordingly, you'll have a better chance of having uncovered what the learners truly "need".

Assessment is just an (often ham-fisted) attempt to get at what a learner understands. The more infrequent, clinical, murky, or threatening it is, the more you're going to separate the "good students" from the "good thinkers." And the "clinical" idea has less to do with the format of the test, and more to do with the tone and emotion of the classroom in general. Why are students being tested? What's in it for them, and their future opportunities to improve?

And feedback is quick even when the "grading" may not be.

Students should not have to guess what "success" in a highly-effective classroom looks like. It should also not be entirely weighted on "participation," assessment results, attitude, or other individual factors, but rather meaningfully melted into a cohesive framework that makes sense-not to you, your colleagues, or the expert book on your shelf, but the students themselves.

Cognitive, meta-cognitive, and behavioral "good stuff" is constantly modeled. Curiosity, persistence, flexibility, priority, creativity, collaboration, revision, and even the classic Habits of Mind are all great places to start. So often what students learn from those around them is less directly didactic, and more indirect and observational.

Monkey see, monkey do.

Old thinking is revisited. Old errors are reflected on. Complex ideas are re-approached from new angles. Divergent concepts are contrasted. Bloom's taxonomy is constantly traveled up and down, from the simple to the complex in an effort to maximize a student's opportunities to learn-and demonstrate understanding-of content.

For professional development around this idea or others you read about on TeachThought, contact us.

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10 Characteristics Of A Highly Effective Learning Environment

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by Terry Heick For in-person professional development from TeachThought on how to create an effective learning environment in your classroom or school, contact us today. Wherever we are, we'd all like to think our classrooms are "intellectually active" places. Progressive learning(like our 21st Century Model , for example) environments.

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Assessing Group Work - Teaching Excellence & Educational Innovation - Carnegie Mellon University

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Assessing Group Work - Teaching Excellence & Educational Innovation - Carnegie Mellon University

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All of the basic principles of assessment that apply to individual students' work apply to group work as well. Assessing group work has additional aspects to consider, however. First, depending on the objectives of the assignment, both process- and product-related skills must be assessed. Second, group performance must be translated into individual grades, which raises issues of fairness and equity. Complicating both these issues is the fact that neither group processes nor individual contributions are necessarily apparent in the final product. Thus, instructors need to find ways of obtaining this information.

The general principles described in the next few sections can be adapted to the context of specific courses.

Assess process, not just product.

If both product and process are important to you, both should be reflected in students' grades - although the weight you accord each will depend on your learning objectives for the course and for the assignment. Ideally, your grading criteria should be communicated to students in a rubric. This is especially important if you are emphasizing skills that students are not used to being evaluated on, such as the ability to cooperate or meet deadlines.

Ask students to assess their own contribution to the team.

Have students evaluate their own teamwork skills and their contributions to the group's process using a self-assessment of the process skills you are emphasizing. These process skills may include, among others, respectfully listening to and considering opposing views or a minority opinion, effectively managing conflict around differences in ideas or approaches, keeping the group on track both during and between meetings, promptness in meeting deadlines, and appropriate distribution of research, analysis, and writing.

Hold individuals accountable.

To motivate individual students and discourage the free-rider phenomenon, it is important to assess individual contributions and understanding as well as group products and processes. In addition to evaluating the work of the group as a whole, ask individual students to demonstrate their learning. This can be accomplished through independent write-ups, weekly journal entries, content quizzes, or other types of individual assignments.

Ask students to evaluate their group's dynamics and the contributions of their teammates.

Gauge what various group members have contributed to the group (e.g., effort, participation, cooperativeness, accessibility, communication skills) by asking team members to complete an evaluation form for group processes. This is not a foolproof strategy (students may feel social pressure to cover for one another). However, when combined with other factors promoting individual accountability, it can provide you with important information about the dynamics within groups and the contributions of individual members. If you are gathering feedback from external clients - for example, in the context of public reviews of students' performances or creations - this feedback can also be incorporated into your assessment of group work. Feedback from external clients can address product (e.g., "Does it work?", "Is it an effective design?") or process (e.g., the group's ability to communicate effectively, respond appropriately, or meet deadlines) and can be incorporated formally or informally into the group grade.

Grading Methods for Group Work
Instructor and student options for assessing group work.
Example of Group and Self-Assessment Tool

( download .pdf | download .doc)

CONTACT US to talk with an Eberly colleague in person!

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Assessing Group Work - Eberly Center - Carnegie Mellon University

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All of the basic principles of assessment that apply to individual students' work apply to group work as well. Assessing group work has additional aspects to consider, however. First, depending on the objectives of the assignment, both process- and product-related skills must be assessed.

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Using Concept Maps - Teaching Excellence & Educational Innovation - Carnegie Mellon University

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Using Concept Maps - Teaching Excellence & Educational Innovation - Carnegie Mellon University

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Concept maps are a graphic representation of students' knowledge. Having students create concept maps can provide you with insights into how they organize and represent knowledge. This can be a useful strategy for assessing both the knowledge students have coming into a program or course and their developing knowledge of course material.

Concept maps include concepts, usually enclosed in circles or boxes, and relationships between concepts, indicated by a connecting line. Words on the line are linking words and specify the relationship between concepts. See an example (pdf).

Designing a concept map exercise

To structure a concept map exercise for students, follow these three steps:

1. Create a focus question that clearly specifies the issue that the concept map should address, such as "What are the potential effects of cap-and-trade policies?" or "What is materials science?"

2. Tell students (individually or in groups) to begin by generating a list of relevant concepts and organizing them before constructing a preliminary map.

3. Give students the opportunity to revise. Concept maps evolve as they become more detailed and may require rethinking and reconfiguring.

Encourage students to create maps that:

Employ a hierarchical structure that distinguishes concepts and facts at different levels of specificity

Draw multiple connections, or cross-links, that illustrate how ideas in different domains are related

Include specific examples of events and objects that clarify the meaning of a given concept

Using concept maps throughout the semester

Concept maps can be used at different points throughout the semester to gauge students' knowledge. Here are some ideas:

Ask students to create a concept map at the beginning of the semester to assess the knowledge they have coming into a course. This can give you a quick window into the knowledge, assumptions, and misconceptions they bring with them and can help you pitch the course appropriately.

Assign the same concept map activity several times over the course of the semester. Seeing how the concept maps grow and develop greater nuance and complexity over time helps students (and the instructor) see what they are learning.

Create a fill-in-the-blank concept map in which some circles are blank or some lines are unlabeled. Give the map to students to complete.

CONTACT US to talk with an Eberly colleague in person!

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Using Concept Maps - Eberly Center - Carnegie Mellon University

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Concept maps are a graphic representation of students' knowledge. Having students create concept maps can provide you with insights into how they organize and represent knowledge. This can be a useful strategy for assessing both the knowledge students have coming into a program or course and their developing knowledge of course material.

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Protocols and Engagement Strategies Videos | Expeditionary Learning

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Protocols and Engagement Strategies Videos | Expeditionary Learning

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Pride of Profession: Striving to Become a Great Teacher | Edutopia

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Pride of Profession: Striving to Become a Great Teacher | Edutopia

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This is the second post in a two-part entry. Read part one.

In the first part of this entry, I discussed the process of achieving greatness as educators. In this part, I want to share some of the greatness I have seen in my career. One of the privileges I have had is to be able to go into the classroom and witness teacher greatness in a variety of forms:

I have seen a teacher treating her students like adults, and those first graders responded accordingly by doing fourth-grade work and mastering parts of speech as if they were in high school.

I have witnessed a brand-new teacher vividly and effectively demonstrate the three states of matter by having the students be molecules and act out what the molecules are doing in the different states. Because of this, the second graders easily used the scientific method to establish the three states of matter in a hands-on experiment.

I have seen self-assured and responsible eighth-grade students catching the vision of how school can be a stepping-stone for college and careers in an AVID (Advancement Via Individual Determination) class. They learned the unspoken curriculum of how to overcome fear and doubt and how to effectively work with their teachers. Everything about this class empowered them to actually believe that through individual determination, they truly can advance.

I have struggled to follow the swift movements of students fluently speaking the language of logic with hand motions that their teacher had taught them in order to aid them in remembering the AND, OR and XORs.

I have been amazed as a teacher's chemistry students demonstrated their knowledge by doing the chemical dance showing how covalent bonds are made and broken in chemical reactions.

I have witnessed a teacher expertly using the smart board to show pictures, words, and symbols to help English speaking and ELL students to understand the algebraic properties of equality.

I have stood in awe as a teacher mesmerized a group of rowdy 5th graders by creating a project based learning pizza parlor to help the students understand proportionality and the dreaded math of fractions.

I have tapped my foot to the rhythm of fourth-grade science students enthusiastically chanting the vocabulary and concepts related to mixtures and solutions.

Greatness can be found on every campus and in every school. Perhaps you are one of those teachers on your campuses that exhibits greatness in such abundance that others aspire to be like you. Greatness is not always found in the most flamboyant or gregarious teachers. For example, a regular, everyday English teacher, Mary Catherine Swanson, was the one that started AVID because she wanted to help her students be truly successful and to be able to find and believe in their own greatness. In doing so, she demonstrated her greatness. (If you want to learn more about it, read Wall of Fame, by celebrated journalist Jonathan Freedman.)

In my wonderful visits to the classrooms of great teachers, I have seen many other elements of greatness in both the students and the teachers. This privilege has helped me come to the conclusion that if we have progressed to the self-actualization stage in our careers, we should all believe that our students are the best in the entire world and that they are capable of being great. It is their right and our responsibility to help them achieve it.

This thought, brings me to the point of my post: How can we expect the students to aspire to be great if we are not also aspiring for greatness? As demonstrated above, we all have a certain amount of greatness that we demonstrate frequently, but according to Jim Collins, author of Good to Great: Why Some Companies Make the Leap . . . and Others Don't, the biggest enemy of success (greatness) is an attitude of "That's good enough." In that spirit, I would like to inspire all of us to do some self-reflection.

Consider these questions:

These are also great questions for you to discuss with a friend in your department, with a partner teacher, with your professional-learning communities, and at grade-level meetings. If you can spare the time, I would like you to answer the following questions, at least to yourself. But I welcome you to share your responses with the Edutopia readership in the comment section below.

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Pride of Profession: Striving to Become a Great Teacher

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This is the second post in a two-part entry. Read part one. In the first part of this entry, I discussed the process of achieving greatness as educators. In this part, I want to share some of the greatness I have seen in my career.

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35 Useful Apps And Web Tools For Math Teachers | Edudemic

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35 Useful Apps And Web Tools For Math Teachers | Edudemic

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Let It Marinate: The Importance of Reflection and Closing | Edutopia

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Let It Marinate: The Importance of Reflection and Closing | Edutopia

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I am one of those people who regularly figures out exactly what to say after the moment has passed. I will be deep in conversation with someone, sharing thoughts and bouncing around ideas. Yet, as the thoughts swirl, I'll have an unsettled feeling. Often it is not until some time later, when the ideas have marinated, that I realize what matters most to me and how to say it. I find that the flow of learning for many of my students matches my personal need for intellectual reflection.

A Classroom Example

Recently, we spent a chunk of one of my world history classes discussing an excerpt from The Power of Myth, a conversation that Joseph Campbell had with Bill Moyers about enduring myths and the human condition. The students read the text during the previous class and had done a writing exercise that helped them begin to explore some of the different ideas contained in the dialogue.

The discussion was interesting but felt aimless. Some students were interested in the idea of learning deeper messages by reading the myths of others. Others were struck by Campbell's idea that we are all imperfect. For many, it was unclear if they found anything of meaning in the reading. The body language in the classroom was mixed. Some students turned to face whoever was speaking and eagerly responded, often referring to the text in front of them. Others were slouched in their chairs rarely looking at the text or at the speakers.

Students knew that this was the beginning of our religion unit and had spent time earlier in the week attempting to create a definition of religion, yet if felt as if no one knew how to successfully put these different pieces together into larger, coherent ideas with greater meaning. As teacher, I felt unsure about our status in this early part of our unit.

As the discussion slowed down and the clock began approaching the end of the period, I asked everyone to jot down a one-sentence final thought. After two silent minutes, we started in one corner of the room and quickly whipped around as, one after another, students shared final thoughts from the reading and/or discussion. It quickly became clear that a lot more deep and rich thinking had happened than I previously realized. "Religions are glorified myths," said a student who had been quiet all period. "We all need ways to find meaning in our lives," offered a young man who had previously seemed to find very little meaning in the discussion.

Deepening Learning

In his book Pedagogy of the Oppressed, the Brazilian educator Paolo Freire reinforces the idea that reflection is an essential part of learning and of becoming an agent of change in the world:

Within the word we find two dimensions, reflection and action, in such radical interaction that if one is sacrificed -- even in part -- the other immediately suffers . . .

Freire also reminds us that this process (that he has named concientizacion) involves a true exchange of ideas:

If it is in speaking their word that people, by naming the world, transform it, dialogue imposes itself as the way by which they achieve significance as human beings. Dialogue is thus an existential necessity. And since dialogue is the encounter in which the united reflection and action of the dialoguers are addressed to the world which is to be transformed and humanized, this dialogue cannot be reduced to the act of one person's "depositing" ideas in another, nor can it become a simple exchange of ideas to be "consumed" by the discussants.

The end of a class period may often feel like a time to slow down and regroup before another set of students arrives. An alternate view is that these last moments, which usually occur when ideas have had a chance to marinate, can be a time when quiet thinkers finally articulate their ideas and move toward Freire's idea of concientizacion. In these moments, students can deepen their own learning, and entire groups can share ideas and make meaning of content. Additionally, the time when a large piece of work is submitted is an important opportunity for students to articulate their own learning and self-evaluate in order to improve learning and the quality of their work for the future.

Closings and Reflective Activities

There are many different ways to integrate closings and reflective activities into classroom practice. Depending on the circumstances, closings and reflective activities can be quickly jotted down and shared out loud, or they can be larger writing assignments that are submitted with projects or posted as an introduction to blog posts of student work.

The following is a list of different reflection and closing prompts:

Share one thing you learned.

Share a question for future investigation.

Respond with a word.

What worked? What didn't work?

What is one part of your work that you are proud of?

How would you do this differently next time?

School is generally not structured in a way that easily accommodates ambiguity and differentiation. While this presents a challenge, the strategic integration of meaningful closings and reflection into classroom practice gives students multiple avenues for engaging with complex ideas and allows more students to find broader meaning in their work. Additionally, these activities help teachers to more deeply understand and adapt to the intellectual processes of our students.

In what different ways do you structure reflection and closings in your classroom?

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Let It Marinate: The Importance of Reflection and Closing

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I am one of those people who regularly figures out exactly what to say after the moment has passed. I will be deep in conversation with someone, sharing thoughts and bouncing around ideas. Yet, as the thoughts swirl, I'll have an unsettled feeling.

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20 Collaborative Learning Tips And Strategies For Teachers

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20 Collaborative Learning Tips And Strategies For Teachers

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contributed by Miriam Clifford
This post has been updated from a previous post.
There is an age old adage that says "two heads are better than one."

Consider collaboration in recent history: Watson and Crick or Page and Brin (Founders of Google). But did you know it was a collaborative Computer Club about basic programming at a middle school that brought together two minds that would change the future of computing?

Yes, those two were, of course, Bill Gates and Paul Allen, the founders of Microsoft.

Collaborative learning teams are said to attain higher level thinking and preserve information for longer times than students working individually. Why is this so?

Groups tend to learn through "discussion, clarification of ideas, and evaluation of other's ideas." Perhaps information that is discussed is retained in long-term memory. Research by Webb suggests that students who worked collaboratively on math computational problems earned significantly higher scores than those who worked alone. Plus, students who demonstrated lower levels of achievement improved when working in diverse groups.

Collaborative learning teams are said to attain higher level thinking and preserve information for longer times than students working individually.

Many consider Vygotsky the father of 'social learning.' Vygotsky was an education rebel in many ways. Vygotsky controversially argued for educators to assess students' ability to solve problems, rather than knowledge acquisition. The idea of collaborative learning has a lot to do with Vygotsky's idea of the "zone of proximal development". It considers what a student can do if aided by peers and adults. By considering this model for learning, we might consider collaboration to increase students' awareness of other concepts.

What are some ways to include best practices for collaborative learning in our classroom?
1. Establish clear group goals
Effective collaborative learning involves the establishment of group goals, as well as individual accountability. This keeps the group on task and establishes an unambiguous purpose. Before beginning an assignment, it is best to define goals and objectives to save time.
2. Keep groups midsized
Small groups of 3 or less lack enough diversity and may not allow divergent thinking to occur. Groups that are too large create 'freeloading' where not all members participate. A moderate size group of 4-5 is ideal.
3. Establish flexible group norms
Research suggests that collaborative learning is influenced by the quality of interactions. Interactivity and negotiation are important in group learning. In the 1960's studies by Jacobs and Campbell suggested that norms are pervasive, even deviant norms were handed down and not questioned.

If you notice a deviant norm, you can do two things: rotate group members or assist in using outside information to develop a new norm. You may want to establish rules for group interactions for younger students. Older students might create their own norms. But remember, given their durable nature, it is best to have flexible norms. Norms should change with situations so that groups do not become rigid and intolerant or develop sub-groups.
4. Build trust and promote open communication
Successful interpersonal communication must exist in teams. Building trust is essential.Deal with emotional issues that arise immediately and any interpersonal problems before moving on. Assignments should encourage team members to explain concepts thoroughly to each other.Studies found that students who provide and receive intricate explanations gain most from collaborative learning. Open communication is key.
5. For larger tasks, create group roles
Decomposing a difficult task into parts to saves time. You can then assign different roles. A great example in my own classroom was in science lab, fifth grade student assumed different roles of group leader, recorder, reporter, and fact checker. The students might have turns to choose their own role and alternate roles by sections of the assignment or classes.
6. Create a pre-test and post-test
A good way to ensure the group learns together would be to engage in a pre and post-test. In fact, many researchers use this method to see if groups are learning. An assessment gives the team a goal to work towards and ensures learning is a priority. It also allows instructors to gauge the effectiveness of the group. Changes can be made if differences are seen in the assessments over time. Plus, you can use Bloom's taxonomy to further hone in on specific skills.

Individuals should also complete surveys evaluating how well the group functioned. "Debriefing" is an important component of the learning process and allows individuals to reflect on the process of group learning.
7. Consider the learning process itself as part of assessment
Many studies such as those by Robert Slavin at Johns Hopkins have considered how cooperative learning helps children develop social and interpersonal skills. Experts have argued that the social and psychological effect on self-esteem and personal development are just as important as the learning itself.

In terms of assessment, it may be beneficial to grade students on the quality of discussion, student engagement, and adherence to group norms. Praise younger groups for following (for digital collaborative learning, for example) standards. This type of learning is a process and needs explicit instruction in beginning stages. Assessing the process itself provides motivation for students to learn how to behave in groups. It shows students that you value meaningful group interactions and adhering to norms.

8. Consider using different strategies, like the Jigsaw technique.

The jigsaw strategy is said to improve social interactions in learning and support diversity. The workplace is often like a jigsaw. It involves separating an assignment into subtasks, where individuals research their assigned area. Students with the same topic from different groups might meet together to discuss ideas between groups.

This type of collaboration allows students to become "experts" in their assigned topic. Students then return to their primary group to educate others. There are other strategies discussed here by the University of Iowa, such as using clusters, buzz groups, round robin, leaning cells, or fish bowl discussions.
9. Allow groups to reduce anxiety
When tackling difficult concepts, group learning may provide a source of support. Groups often use humor and create a more relaxed learning atmosphere that allow for positive learning experiences. Allow groups to use some stress-reducing strategies as long as they stay on task.
10. Establish group interactions
The quality of discussions is a predictor of the achievement of the group. Instructors should provide a model of how a successful group functions. Shared leadership is best. Students should work together on the task and maintenance functions of a group. Roles are important in group development. Task functions include:

Initiating Discussions

Clarifying points

Summarizing

Challenging assumptions/devil's advocate

Providing or researching information

Reaching a consensus

Maintenance involves the harmony and emotional well-being of a group. Maintenance includes roles such as sensing group feelings, harmonizing, compromising and encouraging, time-keeping, relieving tension, bringing people into the discussion, and more.
11. Use real-world problems
Experts suggest that project-based learning using open-ended questions can be very engaging. Rather than spending a lot of time designing an artificial scenario, use inspiration from everyday problems. Real world problems can be used to facilitate project-based learning and often have the right scope for collaborative learning.
12. Focus on enhancing problem-solving and critical thinking skills
Design assignments that allow room for varied interpretations. Different types of problems might focus on categorizing, planning, taking multiple perspectives, or forming solutions. Try to use a step-by step procedure for problem-solving. Mark Alexander explains one generally accepted problem-solving procedure:

1. Identify the objective

2. Set criteria or goals

3. Gather data

4. Generate options or courses of action

5. Evaluate the options using data and objectives

6. Reach a decision

7. Implement the decision

13. Keep in mind the diversity of groups
Mixed groups that include a range of talents, backgrounds, learning styles, ideas, and experiences are best. Studies have found that mixed aptitude groups tend to learn more from each other and increase achievement of low performers. Rotate groups so students have a chance to learn from others.
14. Consider demographics
Equally, balanced gender groups were found to be most effective.

Some research suggests that boys were more likely to receive and give elaborate explanations and their stances were more easily accepted by the group. In majority male groups girls were ignored. In majority girl groups, girls tended to direct questions to the boy who often ignored them. You may also want to specifically discuss or establish gender equality as a norm. This may seem obvious, but it is often missed. It may be an issue you may want to discuss with older students.

15. Use scaffolding or diminished responsibility as students begin to understand concepts.

At the beginning of a project, you may want to give more direction than the end. Serve as a facilitator, such as by gauging group interactions or at first, providing a list of questions to consider. Allow groups to grow in responsibility as times goes on. In your classroom, this may mean allowing teams to develop their own topics or products as time goes on. After all, increased responsibility over learning is a goal in collaborative learning.
16. Include different types of learning scenarios
Studies suggests that collaborative learning that focuses on rich contexts and challenging questions produces higher-order reasoning. Assignments can include laboratory work, study teams, debates, writing projects, problem-solving, and collaborative writing.
17. Technology makes collaborative learning easier
Collaboration had the same results via technology as in person, increased learning opportunities. Try incorporating free savvy tools for online collaboration such as Stixy, an online shared whiteboard space, Google groups, or Mikogo for online meetings. Be aware that some research suggests that more exchanges related to planning rather than challenging viewpoints occurred more frequently through online interactions.

This may be because the research used students that did not know one another. If this is your scenario, you may want to start by having students get to know each other's backgrounds and ideas beforehand on a blog or chat-board.
18. Avoid 'bad group work'
As with any learning strategy, it's important to have a balanced approach. Cynics usually have a valid point. A recent New York time article, cites some criticism of collaboration for not allowing enough time for individual, creative thinking. You may allow some individual time to write notes before the groups begin. This may be a great way to assess an individual grade.
19. Be wary of "group think"
While collaborative learning is a great tool, it is always important to consider a balanced approach. At times, group harmony can override the necessity for more critical perspectives. Some new research suggests that groups favored the more confident members. Changing up groups can help counter this problem.
20. Value diversity
Collaborative learning relies on some buy-in. Students need to respect and appreciate each other's viewpoints for it to work. For instance, class discussions can emphasize the need for different perspectives. Create a classroom environment that encourages independent thinking. Teach students the value of multiplicity in thought. You may want to give historical or social examples where people working together were able to reach complex solutions.

By definition, learning is social in nature. Using different mediums, whether it be books, discussions, technology or projects we study and develop new ideas. We impart ideas and share perspectives with others. Collaboration is a learned process. If managed correctly, it is a powerful tool that can allow educators to tap into new ideas and information.
This is a cross-post from opencolleges.edu.au; image attribution flickr user flickeringbrad

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20 Collaborative Learning Tips And Strategies For Teachers

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contributed by Miriam Clifford This post has been updated from a previous post. There is an age old adage that says "two heads are better than one." Consider collaboration in recent history: Watson and Crick or Page and Brin (Founders of Google).

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Education World: Daily Numbers: A Daily Math Skill Reinforcement Activity

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Education World: Daily Numbers: A Daily Math Skill Reinforcement Activity

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Subjects: Mathematics: Algebra, Geometry, Measurement, Probability, Process Skills, Statistics

Brief Description

Use this daily lesson to reinforce skills taught throughout the school year. Then, when students must take state achievement tests, they have had frequent practice in all skills.

Note: This is a math activity by nature, but the concept could be easily adapted for other subject areas.

Objectives

Students

experience math success on a daily basis.

receive daily reinforcement in a wide variety of math skills.

achieve higher scores on statewide tests.

algebra, computation, daily, math, measurement, money, practice, reinforcement, telling time, whiteboard

Materials Needed

Lesson Plan

Daily Numbers is a great "bell-ringer" activity. As soon as students arrive in class, have them get out their whiteboards and do the ten math exercises on that day's Daily Numbers chart. Each student has in his or her desk a pad of scrap paper to perform math operations on. They write only the answers to the problems on their whiteboards.

Daily Numbers is the name given to this classroom bell-ringer activity because it's the name of a state lottery game. The owner of a local store provided one teacher with a Daily Numbers sign to hang above the chart on which the Daily Numbers math exercise is posted. Using the lottery game theme adds interest to the activity!

The ten problems that are part of each day's Daily Numbers exercise always include a variety of skills. Previously taught skills are continuously reinforced. For example, a third-grade teacher might post each day at least one addition problem that involves carrying (renaming) and one subtraction problem that involves borrowing. At least twice a week, students might be asked to do a problem that relates to other skills taught during the year. Examples:

Determine the cash value of a series of drawn coins.

Write in digital format (XX:XX) the time shown on a drawn clock face.

Draw a line of a precise measure, such as 2 1/2 inches long or 12 centimeters long.

In short, all skills are regularly reinforced and no skill is allowed to die.
This approach pays great dividends when state testing time comes around. All math processes students face on the test are fresh in their minds -- thanks to Daily Numbers!

As students complete the Daily Numbers activity -- it can usually be done in ten minutes -- they can get started on their daily work. When all students have completed the Daily Numbers activity, review it one problem at a time. Call on a student to solve each problem. When the student has finished, ask all those who have the same answer to raise their boards.

Assessment

Assess students' math skills by monitoring their responses on the Daily Numbers activity. Once a week or once every two weeks, have students do their Daily Numbers work on paper for a grade. Every student should solve at least eight of the ten problems.

Lesson Plan Source

Education World

Submitted By

Gary Hopkins

National Standards

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Daily Numbers: A Daily Math Skill Reinforcement Activity

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Subjects: Mathematics: Algebra, Geometry, Measurement, Probability, Process Skills, Statistics Brief Description Use this daily lesson to reinforce skills taught throughout the school year. Then, when students must take state achievement tests, they have had frequent practice in all skills. Note: This is a math activity by nature, but the concept could be easily adapted for other subject areas.

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Dark text on a light background is best. This combination offers the most visibility. Sometimes, though, you may want a dark background for effect, to dazzle the crowd. In that case, be sure to make text a light color for easy reading in a classroom presentation.

Text is often difficult to read on patterned or textured backgrounds. Keep your color scheme consistent throughout your classroom presentation.

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9 PowerPoint Presentation Tips for Students

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Dark text on a light background is best. This combination offers the most visibility. Sometimes, though, you may want a dark background for effect, to dazzle the crowd. In that case, be sure to make text a light color for easy reading in a classroom presentation.