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Quick activities that can be used to check for understanding or emphasize key information at the end of a lesson.

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You may have come across the term "metacognition" recently and wondered if it was just another instructional buzzword. Metacognition is "thinking about thinking," but what exactly does that mean, why does it matter to learning, and how can teachers emphasize it in their instruction?

What is metacognition:

Metacognition is an awareness of one's own learning. It entails understanding the goals of the learning process, figuring out the best strategies for learning, and assessing whether the learning goals are being met. A metacognitive student sees him or herself as an agent in the learning process and realizes that learning is an active, strategic activity.

A useful analogy for understanding metacognition might be mastering an athletic skill: in the early stages, a novice player needs to think carefully about how his or her actions affect performance. For instance, in figuring out the best way to swing a golf club, a novice player might deliberately adjust his or her stance, assess whether the adjustment leads to better performance, and then decide whether to adopt the strategy going forward. This is essentially the active thinking about the learning process that we want to encourage with students.

Metacognition can include any of the following elements:

Understanding what one already knows about a topic

Figuring out what one wants to know about a topic

Realizing what one has learned in the course of a lesson

Monitoring one's understanding during the course of an activity

Choosing which learning strategies to employ and when

Evaluating whether a particular learning strategy was successful in a given circumstance

Why is metacognition important:

Metacognition has been linked to improved learning outcomes. It makes sense that individuals who are strategic in their learning are more successful than those who do not reflect on the learning process. For instance, metacognitive learners are more likely to notice when what they are studying does not make sense. These are the students who try to clarify their understanding rather than passively continuing on with the assignment. According to researcher John Hattie, the effect size for teaching metacognitive strategies is 0.69, making it one of the most effective teaching interventions.

Metacognition is also a significant factor in whether students can transfer their learning to new scenarios. Students who are metacognitive are actively embedding new information in their existing network of knowledge and creating connections among ideas. This is the sort of thinking that gets students beyond surface learning and drives them to deeper understanding.

How do students become metacognitive:

Though some individuals are naturally more metacognitive than others, metacognition is a skill that can be taught and learned. As with other learning skills, students will initially need explicit instruction, scaffolding, practice, and feedback in order to turn unfamiliar operations into habits of mind. Here are a few ideas on how to incorporate metacognition into instruction, particularly as it pertains to literacy.

Metacognition is a skill that can be taught and learned.

Model your thought processes

Teachers can model metacognition by demonstrating their own thought process while they read. They can let students see how they interact with the text: how they determine the purpose of their reading, where they pause to ask a question, how they connect new ideas to previous knowledge, how they track whether they understand the content, how they decide when to slow down and re-read, and how they assess what they have learned. Teachers can do this through read-aloud or by sharing their annotations with students. It is useful to repeat this modeling process, particularly at the beginning of more challenging assignments.

Create simple tasks for students to demonstrate thinking

Teachers can scaffold metacognition by asking students to demonstrate their thinking in writing or during discussion. Instructions on how to do this will need to be explicit; for instance, teachers can guide students to mark one moment in the text they found surprising, confusing, or erroneous and explain their reaction. Reviewing what students have noted is a great way to spur a discussion about the reading.

Increase writing

Writing is a particularly useful way to make metacognition visible because it enables students to look back on their previous notes and see how their thinking has changed. Some teachers find it effective to create portfolios of student learning, including rough drafts and pre-writing activities, then ask students to look back on the trajectory of their work and note how it has evolved with successive revisions.

Pre and post reading polls

To demonstrate the impact of learning, teachers can record students' attitudes and preconceived notions about a topic prior to reading a text, then follow up after the reading to gauge whether students have changed their minds based on what they've learned. This can be done via a pre- and post-reading poll, with the data ultimately driving a discussion about students' previous misconceptions and how the text informed their thinking.

Build in a one question for students to ask themselves

Teachers can encourage students to regularly practice metacognition simply by asking, "How did you figure that out?" after a student offers an answer to a question. This helps students reflect on the learning strategies they employ and gives their classmates an opportunity to see how their peers learn.

Peer assessment

Students can help get in the habit of assessing different learning strategies by judging work: after viewing a detailed answer to a question, students can discuss whether the answer shows an effective use of reasoning and how it can be improved.

Make revisions part of assignments

Finally, students benefit tremendously from opportunities to revise their work and reflect on how their thinking has improved. This gives them the chance to understand what errors they made the first time around and how the learning process has led them to see the problem differently.

RELATED:

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Mastering Metacognition: The What, Why, and How

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This post describes what metacognition is, why it matters, and how teachers can get students to reap the learning benefits of it.

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Find the connections between the Common Core State Standards for Mathematics

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Excerpt of Jo from "The Importance of Struggle" - YouCubed

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A one-minute clip of Jo Boaler from "The Importance of Struggle"

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Modified from Dr. Nikki Newton and Lanny Sammons

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Getting Started, Establishing Routines and Procedures for Math Workshop

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Getting Started, Establishing Routines and Procedures for Math Workshop

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Austin Independent School District

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Creating an inspiring space for young children has never been easier! Use the FREE myKaplan Classroom FloorPlanner to design the classroom perfect for your needs.

Design your own classroom space

Design, plan, visualize, and share your classroom with the myKaplan Classroom FloorPlanner. Use our FREE online classroom design tool to arrange your learning space and see how your favorite Kaplan products fit into the classroom. Simply enter the exact dimensions of your classroom then drag, drop, and rearrange the products until your design is complete.

Sample Classrooms

Choose from our sample classroom layouts or create your own 2D and 3D renderings for a realistic view of what your classroom will look like. When you're ready to bring your classroom to life, our Sales Support team is here to help!

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Creating an inspiring space for young children has never been easier! Use the FREE myKaplan Classroom FloorPlanner to design the classroom perfect for your needs. Design, plan, visualize, and share your classroom with the myKaplan Classroom FloorPlanner. Use our FREE online classroom design tool to arrange your learning space and see how your favorite Kaplan products fit into the classroom.

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Dr. Nicki Newton

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Prompts to Promote Mathematical Discourse

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Prompts to Promote Mathematical Discourse

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Flexible grouping is a data-driven teaching practice. With this practice, you put students into temporary groups to work together for only as long as is needed for them to develop an identified skill or to complete a learning activity. The groups can be heterogeneous (made up of varying skill levels) or homogeneous (made up of the same skill level). The groups change often based on the learning objective and students' needs or interests.

If you're like most teachers, putting students into groups is an important part of your day-to-day classroom life. That concept of grouping dates back to the days of the one-room schoolhouse, when teachers grouped students by age or ability.

In today's inclusive classrooms, we know age and ability don't correspond neatly across subjects. Students have different strengths, interests, and needs depending on the content area, specific lesson, or even the time of day. Few students engage at the exact same academic, social-emotional, or linguistic level every day. That's where flexible grouping comes in.

What is flexible grouping?

Flexible grouping uses a mix of heterogeneous groups (made up of students with varying skill levels) and homogeneous groups (made up of students with similar skill level) to help students achieve a learning goal. The size of the groups can vary - from two or three students in a small group to up to six students in a larger group.

Students work together, often with the guidance of a teacher, only for the length of time necessary for them to develop an identified skill or to complete a learning activity. That makes it different from static groups that don't change based on students' needs, acquisition of skills, or knowledge.

Flexible grouping is driven by data. You can use data you already have about students to group and regroup them to meet their evolving needs. The data doesn't have to be fancy. It can be as simple as observing students' work during a lesson. In doing so, you may see that some students could benefit from more practice in a small group before moving on.

A key component of flexible grouping is that while all students are working toward the same learning goal, the work addresses students' varying learning needs. The work is engaging and important for all students, but the task or how they show what they've learned may look different for each group.

Why use flexible grouping?

Flexible grouping is a powerful and effective practice for improving learning. It allows your students to get the right support, in the right way, at the right time.

When flexible grouping is part of the classroom routine, there's nothing out of the ordinary about one or more students working with the teacher on a specific project. Students who struggle don't feel singled out or embarrassed. Because groups change frequently and aren't based on ability level alone, all students have the chance to get to know and work with each other. In fact, according to research, all students in classrooms that use flexible grouping show academic gains.

Not being pigeonholed. Flexible grouping allows for regrouping for different content areas. That's beneficial to students who learn and think differently because they may have challenges in some content areas and not in others. For instance, a student who struggles with reading but not math can be grouped with other students who have similar support needs in reading. That student can then be regrouped for math.

Feeling valued. Students bring their own skills, talents, and life experiences to the group. In flexible groups, students see that everyone adds value to the learning community. This follows the culturally responsive teaching philosophy of identifying students' assets and using them to create student-centered instruction. Working in student-led groups means that non-academic strengths, like leadership skills, are important, too.

Language practice. Flexible grouping is particularly beneficial to English language learners. It gives them more chances to interact with classmates who speak English fluently and to practice both academic and interpersonal language. Students can also be placed in groups with other classmates who speak the same home language. In those groups, they can discuss content or concepts before sharing their ideas in English.

The opportunity to collect data. Because flexible grouping depends on data, it also gives you a routine for data collection. When students are working in groups, you can collect observational data, as well as more formalized data. For instance, you may ask students to take pictures of their work at the beginning, middle, and end of the lesson. Or you can have an exit ticket for all students, which asks students to do things like:

Summarize key points from the lesson

Show how they can use what they learned to solve a problem

Answer an essential question based on the lesson

Identify questions they may still have

All of this data can help you make adjustments to your instruction in the moment. It also helps you tailor your future instruction, which might include switching up your groups the next day.

What do flexible groups look like?

Flexible groups come in all types and sizes. They can:

Include partners, small groups of a couple of students, and large groups of up to six students

Be heterogeneous (made up of varying abilities) or homogeneous (made up of the same ability)

Be teacher-led or student-led

Be assigned or self-selected

Last for just one lesson or for a few weeks, depending on the purpose of the activity, learning goals, and data

In elementary grades, this might look like students rotating among different learning stations, working in guided reading groups that change from week to week, or engaging in a "turn and talk" with different partners each time.

In middle school and high school, this might look like collaborative learning groups in which students have clearly defined roles, like being the facilitator or timekeeper.

How do I put flexible grouping into practice?

1. Define the learning objective for your lesson to determine what type of groups you need.

Start with a clear idea of exactly what skills or concepts you want students to master. This will help you in two ways. First, the learning objective will help you be more intentional about what groups to create, including which students belong in the group and the size of the group. Second, with the end goal in mind, you can create checkpoints to monitor each student's progress and adjust groups when necessary.

Schedule time for group work in your lesson plans.

Plan how you and your co-teachers (or other support staff) will work together during a lesson. You can maximize flexible grouping instruction when you have more educators in the room to lead learning or circulate to support groups.

Plan to work with small groups and have work stations during independent practice times.

Try out flexible grouping with your students for short periods of time or to complete quick activities so they can practice. Give them feedback on what went well.

Incorporate Universal Design for Learning (UDL) practices into your flexible grouping lessons.

2. Review data to decide which students to group together.

Once you have your learning goal in mind, you can turn to student data to guide your decisions about how to group students. For instance, reviewing the exit tickets from a previous day can show you which students didn't fully master the learning objective. You can then group them together to practice that skill. Or the responses to an equation on the board can help you form groups for the day. The students who understood it can move on and those who didn't can be grouped to get more support and practice.

Review your students' learning profiles.

Know your students' interests.

Evaluate how previous groupings went.

Draw on several sources of data, including:

Formal assessment data, like information from the most recent standardized testingInformal observations of studentsStudent self-assessments or questionnaires, like exit tickets from the previous lessonPre- and post-testing around specific skillsUniversal screening data (such as DIBELS or other reading assessments) Data from response to intervention (RTI) programs Review of student writing

Start class with a Do Now and end with an exit ticket. They're great sources of data for future lessons.

Use data to identify student successes or misconceptions to address during upcoming lessons.

3. Set guidelines for how the groups will interact.

Use prompting and pre-correcting strategies to establish group behavior expectations and student roles.

Create a visual of the roles and expectations for each type of group.

Post directions.

Create visuals to support students with language needs.

Create a place for small group materials.

Color-code folders or baskets.

Determine set times for each group activity and provide time reminders for students to remain on task.

Assign a group member to be a materials manager.

Arrange furniture so that there is a whole group learning area and specific areas for small group work.

Teach routines for transitioning into small group work.

Teach students how to have meaningful conversations with each other (known as Accountable Talk®). Using these strategies provides a framework for interactions as well as prompts and precise language for how they are expected to speak with each other.

4. Prompt students to reflect.

Build in time at the end of a lesson for students to talk about what they learned. Did they meet the learning goal? What lingering questions do they have? How effectively did their group work together? What could they do better next time? Students can reflect in a whole group discussion, via an exit ticket, or as part of the group's assignment. This debriefing process can help you make decisions for the next groups you'll form, like which students may have the same unresolved questions or misunderstandings.

Use metacognitive strategies to ask students to reflect on their own learning. What advice would they give themselves for next time? What do they need to improve?

Ask students to tell you what they want more practice with.

Talk through how and from whom students got help when they needed it, and whether they feel they needed more support.

Ask targeted questions to gauge how well your students achieved the learning goal.

Ask students to give you specific feedback about what they may need in the future to be more successful learners.

Use the principles of UDL to give students multiple ways of sharing feedback. For example, students who need more time to process their thoughts can provide feedback later through a Google Doc or paper feedback form.

How can families support this at home?

Families may be more familiar with the idea of ability grouping than flexible grouping. If that's the case, they may be confused when their child comes home talking about moving from group to group.

To head off confusion, you can explain at back-to-school night or in a class email or newsletter that you'll be using flexible grouping. Emphasize that students will not change groups just when they need extra help - they'll switch groups as they make progress, too. Let families know that you'll keep an eye on how students are doing academically and with whom they work well. That will help you put them in groups and in turn, help students grow.

Now that you know more about flexible grouping, how do you plan on using grouping differently in your classroom? Try it out and see how flexible grouping helps you meet the needs of all learners.

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Flexible grouping: What you need to know

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Flexible grouping is a teaching practice that allows you to use data to group and regroup students for learning activities as their abilities change.

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Solve problems and explain your thinking in a digital math workspace.

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The standards for mathematical practices are the same for K-12 grade. Many times teachers need to know “How do I teach practice #1 at my grade level. The link above shows examples of the math…

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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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Introduction by Jo Boaler

It seems that taxis have been a part of my life for years. When I was a teacher and academic in London I would see the iconic Black cabs zipping around the streets of London, and I would occasionally travel in them. It was years later when these Black cabs became important again, as some of the first evidence on the plasticity of brains - even adult brains - came from studying the brains of drivers of Black cabs in London (see video link below). Researchers found that after their intensive spatial training the brains of the drivers of Black cabs strengthened and grew. Years later I was teaching my freshman class when I met Tessa, who proposed this taxi activity for youcubed.

The link below is an extract from my first online course, featuring the neuroplasticity research from the drivers of London Black cabs.
https://www.youcubed.org/resources/brain-science/
Directions:

How many different pathways exists to get the taxi from point A to point B?

You can only move directly to the right or directly You cannot move left, up, or diagonally.

Task

What do you notice & wonder?

Can you find how many paths there are in different dimension grids? What about a 2×2? 3×3? 4×4? 4×6?

Can you find a pattern for an m x n grid?

Can you make a visual proof?

Introduction by Jo Boaler

It seems that taxis have been a part of my life for years. When I was a teacher and academic in London I would see the iconic Black cabs zipping around the streets of London, and I would occasionally travel in them. It was years later when these Black cabs became important again, as some of the first evidence on the plasticity of brains - even adult brains - came from studying the brains of drivers of Black cabs in London (see video link below). Researchers found that after their intensive spatial training the brains of the drivers of Black cabs strengthened and grew. Years later I was teaching my freshman class when I met Tessa, who proposed this taxi activity for youcubed.

The link below is an extract from my first online course, featuring the neuroplasticity research from the drivers of London Black cabs.
https://www.youcubed.org/resources/brain-science/
Directions:

How many different pathways exists to get the taxi from point A to point B?

You can only move directly to the right or directly You cannot move left, up, or diagonally.

Task

What do you notice & wonder?

Can you find how many paths there are in different dimension grids? What about a 2×2? 3×3? 4×4? 4×6?

Can you find a pattern for an m x n grid?

Can you make a visual proof?

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Introduction by Jo Boaler It seems that taxis have been a part of my life for years. When I was a teacher and academic in London I would see the iconic Black cabs zipping around the streets of London, and I would occasionally travel in them.

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Download the Task
Watch the Video:

1. What do you wonder?

2. Estimate how many peas are in each pod. Large, medium, and small.

3. If all the peas were in one pod, how many peas would there be?

4. Make an estimate you know is too big. Too small.

How many peas in each individual pod Click the link here to find more of My 3-Act Lessons

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Act 1 - Peas in a Pod Download the Task Watch the Video: What do you wonder? Estimate how many peas are in each pod. Large, medium, and small. If all the peas were in one pod, ...