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Culturally Responsive Teaching in the Math Classroom - Haley Noel

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Culturally Responsive Teaching in the Math Classroom - Haley Noel

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While reading this article, I was thinking and relating back to our EDU 501 class about creating a space where students feel as thought they belong in the classroom. This article gave 5 different ways that teachers can become conscious to creating creative ways to implement inclusivity for the students who the system has failed. Researching culturally relevant pedagogy can share educator's experiences and beliefs through social justices and providing a curriculum in which students can see themselves in the material. Reflecting your own experience is crucial before making changes to the curriculum in order to provide better understanding before effective teaching a supportive social cultural classroom dynamic. The article went on to explain the teaching strategies we can use as educators to highlight and support student's voices in the classroom especially through student-centered environments. If students feel motivated by their peers and educators, they will succeed. Being able to ask students to provide their way of thinking or sharing their ideas on how they achieved the answer to the problem can create different pathways to the solution. The more we commit to incorporating to learning the student's backgrounds while providing a safe space for everyone, we can grasp student's attention and make real-world connections through building relationships and encouraging them to see mathematics in the world around them. I really enjoyed this article and it provided great insight in how we can not only create a equal learning opportunity for everyone in the classroom but how we can incorporate this into our mathematics lessons as well and helping our students to acquire the skills that will help them feel more connected to math through their own connections in and out of the classroom.

HALEY NOEL

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Help Students Understand Math - Haley Noel

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Help Students Understand Math - Haley Noel

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This article was well put when explaining how to keep your students engaged and having a positive and encouraging growth mindset. Helping students understand how to approach mathematics in multiple ways can open new windows for students with their comprehension. I related this article to not only being helpful with providing tips for an effective math class, but to also encourage confidence among your classroom. It stated that the ultimate goals of mathematics are to understand the material, apply skills and recall concepts in the future. This is all built on a foundation of confidence and effective teaching from an educator. I really enjoyed this article because it broke down parts in which students can become more effective and it proposed the effect of an engaging lesson. Something, I struggle with while substitute teaching is being clear and concise with math lessons. Math is a subject that does not come easily to me, and I find myself after every statement asking students, "Does this make sense?" Reading this article really opened my eyes to different possibilities on how to effective teach the subject of mathematics. I know for me, I am a visual learner, so the one tip that said to include multiple representations was something that stuck out to me. I'm hoping to be able to provide this kind of intel to my future students and be accommodating to their needs with comprehension of mathematics.

HALEY NOEL

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Math Classroom into a Thinking Classroom(comment) to Kalen

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Math Classroom into a Thinking Classroom(comment) to Kalen

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Yes, I agree thinking is an important part of learning. That is why it's important to create a positive environment for students to flourish. If the environment encourages thinking, learning, and engagement it will help students become more involved. I like how you talked about creating jobs to ensure that all the students are engaged and learning. As well as using whiteboards and dry-erase markers to help them map out their thinking and correct their mistakes. These strategies will boost their confidence in learning. - Ta'Nira Newton

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Typically when you think of math you visualize equations, formulas, numbers, variables and shapes, etc. You wouldn't think about using word walls, vocabulary lists and word-of-the-day activities in math. As we focus on word problems we have to think about what math terms will students have trouble with especially if they're seeing them for the first time. As you progress in math it becomes more complex, and so does the vocabulary. I thought about how students can see math terms and not understand them. Spending time to focus on keywords that are used in math problems can help students comprehend the meaning of the terms and recognize them as they appear in math problems. Using multiple activities and strategies helps make those connections. For example, creating your own vocabulary lists from a math text and defining those words. Getting creative and allowing the students to draw pictures, colorful posts it's and etc. Even games and the word-of-the-day, I tried similar activities as well. During our angles (right, obtuse, acute), line/line segments, and ray's unit I used an activity that required my students to get out of their seats and use their arms to show me what those words meant, looked like. We utilized an anchor chart/ word wall with the words and their meanings but allowed them to demonstrate what they mean. This activity checked their understanding of the terms and also engaged their thinking. - Ta'Nira Newton

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I loved your activity that you did with your students to get them involved in understanding and demonstrating math vocabulary. Some of these words can be complexed and can hold students back from understanding and solving math problems independently. I never thought to create word walls for tier 3 academic words, but it makes so much sense to help students understand the words to understand the word problems.

-Stephanie Page

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Ta'Nira, I love love love this! Vocabulary is tough in math - your strategy of getting students out of their seats and physically demonstrating the angles unit is fantastic! I also appreciate that you use different strategies to integrate the new vocabulary such as games, post its, drawing etc. I personally never came across a word wall with math growing up certainly never doing exercises to integrate the new vocabulary. I am excited to try some of these strategies and am so excited you already use them!

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Helping Students See Relevance in Math (comment) to Maddy

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Helping Students See Relevance in Math (comment) to Maddy

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I love how you stated that the article enlightened you to think about why it is important to make math inclusive and how teachers can help with that. Representation matters and including students in math problems will help engage their learning. As a kid, I remember my teachers including their students' names in math problems, using real-world examples, and doing simple things like allowing us to come to the board, and show the class how we solved the problem. That helped push our learning and motivated us to want to learn more. It made learning fun, relatable, and interesting. Especially in math, it's pretty cool to see what you're capable of and what you can learn. - Ta'Nira Newton

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6 Tips for Teaching Math Problem-Solving Skills

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6 Tips for Teaching Math Problem-Solving Skills

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This article tied perfectly into my thoughts on the other article I picked to read "5 Ways to Stop Thinking for Your Students." I enjoyed the way this article worded the topic of "think time." Providing the students their own time to tackle to problem, giving them the option to come back to the problem, or like number 2, give options for another operation. I personally struggled in math going through school and specifically struggled when I had to solve problems only one specific way. It is nice to know that we are encouraged to prompt students with more methods so that they can solve problems more independently. - Stephanie Page

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6 Tips for Teaching Math Problem-Solving Skills (Comment to Stephanie)

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6 Tips for Teaching Math Problem-Solving Skills (Comment to Stephanie)

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I agree with your comment about giving students time to think for themselves. This gives them the opportunity to work through the problem themselves before they are given the answer by the teacher or another student. I believe this would really help students become more confident and comfortable with how they can approach mathematical equations independently when it comes to in class work time, homework or tests and quizzes.

HALEY NOEL

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6 Tips for Teaching Math Problem- Solving Skills Comment  

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6 Tips for Teaching Math Problem- Solving Skills Comment  

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Stephanie, I too enjoyed the topic of "think time." I believe it is very important for students to have the opportunities and methods to learn in ways that best serves them. -Maddy

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5 Ways to Stop Thinking for Your Students

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5 Ways to Stop Thinking for Your Students

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This article was great for helping me to catch how often I want to do so many of these things when being in a classroom. It can be so easy for us as teachers to give immediate answers, grab a pencil, or assign a homework. We go the easier route enough times and the day is done and the students are sent home with their homework to figure out with not many ways to figure their work out on their own. I found it comforting that this is all common things that we do, but that there were attainable ways for us to resolve these reflexes. It is true that by doing these things we are teaching them to "mimic rather than think." By taking more time and thinking through our methods as teachers, we will be giving more students a variety of pathways for thinking for themselves. The one section that I feel would be difficult for me to adapt to would be section 4, "Stall your answer." At first glance, it feels to me like ignoring the students needs by not answering them in some capacity. I recognize the need to prompt the students to have more think time, but feel bad not answering them immediately. - Stephanie Page

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5 Ways to Stop Thinking for your Students (Comment)

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5 Ways to Stop Thinking for your Students (Comment)

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I like that you said it is easy to get into a routine of showing students how to do the work and then giving the students the answers. I often struggle with doing this myself. I always leave wondering did I teach the students something new or did they just learn how to simple copy down notes and copy what I already know what to do. Learning to let a student think and process the work for themselves. Not helping and letting them solve an answer for them is so hard, but it is vital to help them learn how to process and for themselves. -Kalen Dotson

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When reading this, this challenged me to get out of the way to help students to learn. Giving them tools to use to help them think and to let them struggle with a question so that they can learn. It is so easy to get caught in the work of getting your work done and following the curriculum speed, but slowing down to make sure they have skills in order to solve word problems is so much more beneficial. Once they are able to understand the skill this means that the students can download the information faster. Encouraging the students to work on a problem and think helps so much more than just simply giving them the answer. -Kalen Dotson

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Solving word problems is tougher than computing with numbers, but elementary teachers can guide students to do the deep thinking involved.

Consider this. When we're on the way to a new destination and we plug in our location to a map on our phone, it tells us what lane to be in and takes us around any detours or collisions, sometimes even buzzing our watch to remind us to turn. When I experience this as a driver, I don't have to do the thinking. I can think about what I'm going to cook for dinner, not paying much attention to my surroundings other than to follow those directions. If I were to be asked to go there again, I wouldn't be able to remember, and I would again seek help.

If we can switch to giving students strategies that require them to think instead of giving them too much support throughout the journey to the answer, we may be able to give them the ability to learn the skills to read a map and have several ways to get there.

Here are six ways we can start letting students do this thinking so that they can go through rigorous problem-solving again and again, paving their own way to the solution.

When we can remind students that they already have many comprehension skills and strategies they can easily use in math problem-solving, it can ease the anxiety surrounding the math problem. For example, providing them with strategies to practice, such as visualizing, acting out the problem with math tools like counters or base 10 blocks, drawing a quick sketch of the problem, retelling the story in their own words, etc., can really help them to utilize the skills they already have to make the task less daunting.

We can break these skills into specific short lessons so students have a bank of strategies to try on their own. Here's an example of an anchor chart that they can use for visualizing. Breaking up comprehension into specific skills can increase student independence and help teachers to be much more targeted in their problem-solving instruction. This allows students to build confidence and break down the barriers between reading and math to see they already have so many strengths that are transferable to all problems.

2. Avoid boxing students into choosing a specific operation

It can be so tempting to tell students to look for certain words that might mean a certain operation. This might even be thoroughly successful in kindergarten and first grade, but just like when our map tells us where to go, that limits students from becoming deep thinkers. It also expires once they get into the upper grades, where those words could be in a problem multiple times, creating more confusion when students are trying to follow a rule that may not exist in every problem.

We can encourage a variety of ways to solve problems instead of choosing the operation first. In first grade, a problem might say, "Joceline has 13 stuffed animals and Jordan has 17. How many more does Jordan have?" Some students might choose to subtract, but a lot of students might just count to find the amount in between. If we tell them that "how many more" means to subtract, we're taking the thinking out of the problem altogether, allowing them to go on autopilot without truly solving the problem or using their comprehension skills to visualize it.

3. Revisit 'representation'

The word "representation" can be misleading. It seems like something to do after the process of solving. When students think they have to go straight to solving, they may not realize that they need a step in between to be able to support their understanding of what's actually happening in the problem first.

Using an anchor chart like one of these ( lower grade, upper grade) can help students to choose a representation that most closely matches what they're visualizing in their mind. Once they sketch it out, it can give them a clearer picture of different ways they could solve the problem.

Think about this problem: "Varush went on a trip with his family to his grandmother's house. It was 710 miles away. On the way there, three people took turns driving. His mom drove 214 miles. His dad drove 358 miles. His older sister drove the rest. How many miles did his sister drive?"

If we were to show this student the anchor chart, they would probably choose a number line or a strip diagram to help them understand what's happening.

If we tell students they must always draw base 10 blocks in a place value chart, that doesn't necessarily match the concept of this problem. When we ask students to match our way of thinking, we rob them of critical thinking practice and sometimes confuse them in the process.

4. Give time to process

Sometimes as educators, we can feel rushed to get to everyone and everything that's required. When solving a complex problem, students need time to just sit with a problem and wrestle with it, maybe even leaving it and coming back to it after a period of time.

This might mean we need to give them fewer problems but go deeper with those problems we give them. We can also speed up processing time when we allow for collaboration and talk time with peers on problem-solving tasks.

5. Ask questions that let Students do the thinking

Questions or prompts during problem-solving should be very open-ended to promote thinking. Telling a student to reread the problem or to think about what tools or resources would help them solve it is a way to get them to try something new but not take over their thinking.

These skills are also transferable across content, and students will be reminded, "Good readers and mathematicians reread."

6. Spiral concepts so students frequently use problem-solving skills

When students don't have to switch gears in between concepts, they're not truly using deep problem-solving skills. They already kind of know what operation it might be or that it's something they have at the forefront of their mind from recent learning. Being intentional within their learning stations and assessments about having a variety of rigorous problem-solving skills will refine their critical thinking abilities while building more and more resilience throughout the school year as they retain content learning in the process.

Problem-solving skills are so abstract, and it can be tough to pinpoint exactly what students need. Sometimes we have to go slow to go fast. Slowing down and helping students have tools when they get stuck and enabling them to be critical thinkers will prepare them for life and allow them multiple ways to get to their own destination.

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6 Tips for Teaching Math Problem-Solving Skills

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Solving word problems is tougher than computing with numbers, but elementary teachers can guide students to do the deep thinking involved.

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I thought the comparison to using a map was very helpful. When students are not given the tools to solve problems, they will not be able to succeed in problem solving and they will just use the same tactics to move by. The article suggests that literature is very important in problem solving. Teaching students the literature and vocabulary will allow them greater access to understanding and solving problems in more than one way. -Maddy Svercel

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Great point about the importance of vocabulary! It is so important to give students tools to be able to independently solve problems without being held back by unknown words. The article was full of useful methods on how to help students understand complex math vocabulary.

-Stephanie Page

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The article “Build Strong Math Vocabulary Skills Using These Simple Strategies” by Stephen Noonoo made a lot of sense to me because it connects to the idea of fluency in reading if students have an extensive vocabulary, their reading comprehension is better.  With all the reading in mathematics, as well as the terms, numbers, equations, and wording for each set of rules, having a mathematics vocabulary seems to be a critical part of the learning process for mathematics.  The interesting thing this article delineates is how to go about gaining this vocabulary without writing words with their corresponding definitions in a repetitive way.  Using common classroom tools and shifting the focal points to mathematics can help with building fluency in math concepts.  Utilizing word walls that focus on math, glossary lists, games, and having a word of the day are all smart ways to facilitate a better understanding.  Practicing the “language of math” is important for engagement as well as the overall interpretations of math concepts.  Author Stephen Noonoo finds ideas from a small study conducted by fifth grade teacher Kathleen Palmieri.  She states that letting students be a big part of the lessons helps them learn.  They should do some of the defining so they can conceptualize words and be a part of the process. Making some tools more fun like word walls that add crafts and their unique touches also help to immerse them in the terminology. Another interesting take-away from this article is how word problems can be tackled with a “3-read” protocol.  The steps include first reading the word problem without numbers, then reading the complete problem, and finally reading the entire problem to pull out key terms and what the problem is asking for.  This helps students break down some of these tough problems.
-Cheri Enigk

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Vocab is not something I have ever associated with math.  But it makes a lot of sense!  There are many complex words when it comes to learning math that, at this point, I just take for granted.  Students have to learn the vocabulary and the math at the same time.  I can definitely see how someone who is not proficient in reading can struggle with math as well.  I wonder if someone is struggling with reading, if we rework their math lessons to exclude difficult words? - Fuad Suleiman

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Learning new vocabulary is a fundamental part of understanding math concepts. Use these strategies to build both fluency and engagement.

Math class doesn't seem like the most obvious choice for word walls, glossary lists, and word of the day games. But a strong understanding of math terms is essential for mastering concepts-meaning strategies for building robust vocabulary are surprisingly useful.

Recently, fifth-grade math teacher Kathleen Palmieri began to wonder how well her students understood the complex terms used in textbooks and word problems. So she performed some action research by pulling out 10 key terms-including exponent, base, equivalent, and estimate-and asked students to define those terms using words or numbers, she writes in a recent piece for MiddleWeb. About 40 percent of her kids could write a basic definition, exposing significant gaps in conceptual fluency.

"What I discovered in my students' responses was that learning math terminology is more than studying a list of words," she said, concluding that regular practice with new math terminology facilitates mathematical discourse and understanding. "It is much more of an architecture of learning where concepts need to be explored and a pathway of understanding needs to be blazed before a mathematical term can be attached to establish true meaning."

Here are a few of the ways Palmieri and other teachers "immerse students in the language of math"-while keeping student engagement high.

As an alternative to Palmieri's baseline assessment, have students pull out the key terms they think will be important later. Literacy specialist Rebecca Alber asked her students to skim a chapter from a textbook and identify their own vocabulary list. Students would then rate each term by whether they "know it," "sort of know it," or "don't know it at all." Afterward, they wrote out a definition or took their best guess at the term's meaning.

"Before they turn in these pre-reading charts, be sure to emphasize this is not about 'being right,'" she advised. "They are providing you with information to guide next steps in class vocabulary instruction."

Similarly,Palmieri provides some introductory context and asks students to add to an expanding glossary. Research has largely dispelled the practice of writing out memorized definitions from textbooks, so Palmieri takes a different tack. Students take an active role in coming up with definitions based on their learning. As students learn more about the terms and how they're used, they update definitions. At the end of the lesson, to consolidate learning, it may prove helpful to review all the terms as a class.

2. Get creative with word walls: Instead of writing terms on a word wall and hanging it up for students to glance at, Palmieri has students write terms on colorful Post-Its and affix them to bulletin boards. She also gets great engagement from letting students use art supplies to creatively show what they've learned: "Bubble letters, examples of problems and definitions with graphics are truly fun 'math' activities," she explains. "Students present and explain their term and then proudly display their poster in the classroom."

Unlike static word walls, these strategies involve principles of constructivism, an active and social learning theory where learners build on previous knowledge and create new learning themselves. As students learn new concepts, they can define terms in real-time, make adjustments as the concepts deepen, and hang them around the classroom for others to learn from.

3. Make it a game: Math instruction doesn't have to be drab, says Palmieri. You can introduce familiar word games like Pictionary, where students draw out clues and others try to guess the concept. She also plays a game called "What's My Term?" where "students verbally give clues as others listen."

Likewise, language specialist and Harvard lecturer Rebecca Rolland suggests a game where students show they know what terms mean by listing "non-examples" of things they are studying. For instance, acute angles can look "'sharp' but not 'curvy' or 'wavy' or 'square,'" she says. Ask students to come up with creative non-examples and explain their thought processes. "That same acute angle might look like a door that's partly shut, but not like a smile or a cloud."

Still others play match games with index cards face down on a table, or encourage students to create definitions that rhyme or fit to music. In these cases, the game itself is perhaps less important than the act of engaging students to commit the terms to memory.

4. Word(s) of the day: To reinforce specific concepts, Palmieri has the class come up with a word of the day or week, depending on the duration of the lesson. Students count how often the word is used and in which contexts (e.g., in word problems, during class discussion, in small group activities).

Inspired by research she had done that suggested students need to use a word between six and 30 times to truly learn it, sixth-grade teacher Megan Kelly began picking three words to focus on for a day and reviewing the terms at the start of class. During class, she emphasizes the words herself, and asks students to use the words as many times as they can with a partner.

"I used the words a ton in my directions and made a big deal whenever I heard a student say one of our goal words," she says. "Everyone wants to be in on the fun, so each time I praised someone for using the word, there was an increase in others using them too."

5. Break down word problems: Word problems are notoriously difficult, especially when challenging language obscures the intent of the question. Before students solve word problems numerically, Palmieri has the whole class perform a close read for sense-making. Together they pull out key words and create a written response. Working out word problems as a group is a well-established strategy. Teachers at Concourse Village Elementary School in New York City use a 3-read protocol: First, they read the word problem aloud to the class without numbers, then students read the complete problem on their own and pull out key terms before reading it together as a class. The 3-read protocol clarifies "what they're reading and helps to build their fluency," says Blair Pacheco, a teacher who has used the strategy with her students.

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Build Strong Math Vocabulary Skills Using These Simple Strategies

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Learning new vocabulary is a fundamental part of understanding math concepts. Use these strategies to build both fluency and engagement.

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I was surprised to read that only 40% of the students in the 5th-grade math class could write basic math definitions. This statistic clearly shows the gaps in conceptual fluency, the article states. When I first think of math, I think of numbers and formulas, vocabulary and words never really come to mind. I was really interested in the tips she gave for the word wall. I like how she gave ideas on how to spice up a word wall and make it more fun and engaging. Another idea from the article that I thought was important and effective was "word(s) of the day". This seems like a really good idea to truly drive a word and its definition home. The language of math is the foundation of a real understanding of mathematic processes.  KENDRA MACCAULL

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I agree with your statement about the thought of mathematics. Vocabulary is not the first thing that comes to mind for me as well! Although I can understand the importance of teaching students the difference between certain definitions when it comes to different mathematical equations. The word wall is a great tip to include with not only vocabulary that you may do with students for ELA but to incorporate one for math as well. I think it would be beneficial for students to learn words associated with their lesson in order to really get a great grasp of the concept that is being delivered. Great post! :)

HALEY NOEL

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I thought the exact same thing. When I think of math I immediately think about equations and numbers, not the words. Vocabulary in math is essential to helping students know how to solve math problems. It is interesting that one of the solutions is to have a word wall, because that reminds me of what we talked about in our last class last session. Having a word of the day is also interesting as well. -Kalen Dotson

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I also love the idea of creating unique word walls that the students personalize! They could have different characteristics than other word walls in the room and could really add some fun to important math concepts. -Cheri Enigk

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I agree! When I think of mathematics, I think of numbers, formulas, and all the different things you said and vocabulary would be the last thing that I would think of teaching. When I was in Geometry, I remember my class struggling with the definitions of the key words in a unit so much that my teacher began giving us vocabulary quizzes every unit to make sure we were studying the new words and definitions on the unit material. We all complained and thought it was stupid but I can assure once we started doing that, I performed and understood the material much better.
- Matt Hunter

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This article really pressed upon the idea of students truly understanding the material, rather than just memorizing formulas or equations. Simply memorizing might help you pass the test the next day, but it will not help you figure out different problems in the future. This article talked about 6 steps to help your students understand math better. I liked the step of showing the application. If you demonstrate how every concept can connect to the real world, the kids will easily understand. I liked the tip the article gave for situations where you cannot find real-life situations to connect the lesson to. The author suggests showing how the concept was developed through the history of math when you come across this problem. KENDRA MACCAULL

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I thought the article was very similar to the stuff we learned about in our classes from Summer session 1. Many times my students wanted to copy my work from the board as I went along and not pay any attention to how I got the answers because in the long run, if something was on their papers, at least it's a grade for something. But once the tests and quizzes came around, they struggled and blamed me for not teaching them better. They hardly put the blame on themselves for their lack of effort and threw it all on me. I have to do a better job in the future making sure that my students are doing all they can to follow along and reiterate the important processes that the math problems involve so they can do better and understand it more in the future.
- Matt Hunter

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Help students better understand math by presenting multiple examples, encouraging collaboration on alternative solutions, and framing the class with a clear agenda and effective summary.

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This article discusses strategies to help with critical thinking and connecting problem-solving to reading. It made me reflect on my teaching of math during this past school year. As far as what strategies I used to teach the material, what strategies did my students use to get their answers and did it stop them from thinking critically or doing less of the work? Often in math especially with word problems, reading can be a barrier for some students. It's important for students to learn multiple strategies to help them solve math problems but also utilize their reading and comprehension skills. Using manipulatives, breaking apart the question, read it draw it write method, visuals (anchor charts), drawings, etc. to help them solve the math problems. Be mindful that there is more than one way to solve a problem and avoid telling them exactly what to do this puts limitations on their deeper thinking. Also, allow students to have wait time so they can gather their ideas about what's being asked and how to go about finding a solution. We often feel so rushed to get everything done, this takes away from their learning. Slowing down, revisiting, and rereading these problems will help students be able to process the information better and faster. Including prompt questions will also push and encourage students to think critically. - Ta'Nira Newton

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I thought this article was very useful in getting students to better understand a math topic as it is laid out how a class lesson and instruction should be constructed to help increase retention. By starting out the class with a useful opener or entry ticket can allow the students to use their brains before they even collectively meet as a class. Using the "Think, Pair, Share" method is useful for students coming up with their own thoughts but also having the chance to talk with classmates to collaborate their ideas to see if they combine their thoughts. Once the lesson and the application starts, being able to relate it to a real-life application through models or pictures can help meet the learning needs for different students. Once they solve the problem, having them realize additional ways to solve the problem will help them down the line with problems that have the same strategy but require a different approach. Lastly, being able to share your thoughts with the teacher or another student is essential because it allows for you to walk through the steps that went through solving the problem and can lead to a deeper understanding of the principles. The moment you can teach someone your understanding of a problem, the more you will retain the knowledge.
- Matt Hunter

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Math can be opened up in many directions, this helps students connect to the lesson in a more conceptual way. Setting up the lesson effectively helps students understand what the goal of the day is. I really liked the concept of posting the learning objective so that students know the purpose and can self assess at the end of the class. I also appreciated the concept that the more ways a student is exposed to strategies and approaches for problems the deeper their conceptual understanding of the topic becomes.  - Sarah Finerghty

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I also think posting the learning objectives for all students to see is an effective method. In all of the classrooms I have visited, I have noticed the learning targets are usually on the whiteboard. I also like how you talked about how beneficial it is to students understanding when they know multiple strategies for a problem. I was thinking that teaching with many strategies also will help learners with different learning styles (visual learners, etc.) KENDRA MACCAULL

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Culturally Responsive Teaching in the Math Classroom

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Culturally Responsive Teaching in the Math Classroom

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Culturally Responsive Teaching

Teachers can help all students feel like they belong in math classes by creating connections between course material and students' lives.

Allison Shelley for the Alliance for Excellent Education

Throughout my experience in the secondary mathematics classroom, I have noticed many students, especially students of color, disconnecting from the content presented to them. Rochelle Gutiérrez, a professor of curriculum and instruction, has noted, "Mathematics education cannot truly improve until it adequately addresses the very students who the system has most failed.... We need a central focus on students who are Latinx, Black, and Indigenous in ways that build upon their strengths."

Creating inclusive classrooms is not a one-and-done fix; instead it is constant, conscious work that educators must do in any classroom. When students are learning math where culturally relevant pedagogy (CRP) strategies are utilized, they can develop an understanding of the importance and usefulness of mathematics as well as develop their ability to discuss relevant societal issues.

Affirming Diversity-Sonia Nieto and Patty Bode provide a rationale for the necessity of multicultural education. This book serves as a foundation for teachers who are looking to implement CRP that shows the benefit of teaching with a multicultural lens.

Culturally Responsive Teaching and the Brain-Zaretta Hammond investigates the neuroscience research behind culturally responsive teaching and describes brain processing systems relevant to culture and learning. This book provides physiological backing for CRP and more information for teachers.

Learning to Teach Mathematics for Social Justice-Tonya Gau Bartell highlights the implementation of social justice mathematics and teachers' experiences and beliefs doing so. She provides teachers' research about other educators who are already doing this work in the field.

Connecting Mathematics and Social Justice-Kyle Evans and Megan Staples provide users with free secondary social justice mathematics lessons in their online book.

"Mirrors, Windows, and Sliding Glass Doors"-Rudine Sims Bishop argues that students should be able to see themselves in the material, look into others' experiences, and engage with the worlds of others.

-In this documentary, Peter Nicks exposes some of the pitfalls in the current public school system, specifically in Oakland, California, and provides teachers with some of the realities of students' experiences inside and outside of school.

Waiting for Superman-In this documentary, David Guggenheim investigates the decline of the American educational system and how students are affected.

5 Ways to Implement Culturally Relevant Pedagogy

1. Research CRP. These resources are helpful places for teachers to begin researching what this pedagogy looks like in the classroom.

2. Reflect on your own experience. Just as your students bring a unique perspective to the classroom, so do you. It is crucial to analyze your sociocultural identity before making changes to your classroom, curriculum, and outlook regarding CRP. You may begin by completing an identity wheel to reflect on the different pieces of your identity that you bring to the classroom. Think about how your perspective may differ from your students' and how your past lived experiences influence the way you approach interactions within the school.

3. Adopt teaching strategies to highlight and support student voice in the classroom. A teacher's main role in the classroom is to teach content to students. Expecting high academic achievement catalyzes the creation of a supportive, motivational environment. If students feel as though their teachers believe they can become academic high achievers, they may feel more motivated and supported to do so.

At the same time, creating a classroom environment that recognizes and respects students' cultures requires teachers to teach using a student-centered lens. For example, mathematics educators can use materials that ask students to share their thinking. Teachers can implement written or oral prompts encouraging students to share their thinking about a problem, provide them with opportunities to analyze other students' mathematical thinking, and highlight when students use various paths to a problem's solution.

4. Begin units with connections to students' lives. To foster a culturally relevant and inclusive classroom, you must commit to learning about your students' backgrounds. This could involve facilitating classroom discussions around students' previous learning experiences, incorporating social and emotional learning, and providing a safe space for students.

For example, a teacher could begin a unit about ratios or proportions with an activity comparing the number of students in the school with teachers in the school as a ratio before diving into the traditional content. Other real-world examples could include analyzing various data or data trends for different racial, socioeconomic, and gender groups.

Providing this type of information within a diverse classroom provides a mirror for some students, a window for others, and a sliding glass door for all. "Notice" and "wonder" activities with real-world connections can be a good way to grasp students' attention and curiosity at the beginning of a unit, even if they are not familiar with the relevant mathematics yet.

5. Build relationships within schools and communities. Creating lessons and/or activities that bring other school staff members into your classroom can boost student engagement. This could include creating interdisciplinary lessons with other teachers (e.g., science, history) or retrieving data about the school from a staff member (e.g., secretary, cafeteria worker). A few examples of these data are finding the number of students who get hot lunch every day, the number of students in each grade, or the number of teachers and how long they have each worked at the school.
E. Jean Gubbins, PhD; Rachael Cody; and Gregory T. Boldt coauthored this article.
Similarly, consider building connections to your students' communities. This could include analyzing statistics from your students' communities, interviewing a community member who works in a STEM-related field, or organizing a community walk to help students see mathematics in the world around them. Students could look for geometric patterns in brick pavement, estimate the height of the school or other buildings or structures, or record quantitative data about the number of signs they see.

These strategies allow students to see the relevance of mathematics and how their culture and background relate to learned content. Implementing CRP into the mathematics classroom requires adequate preparation, a willingness to alter classroom expectations and curriculum, and an ongoing commitment to fostering an environment conducive to productive, engaging learning. When it's implemented, all students can feel connected to mathematics and acquire skills to help them engage as democratic, global citizens.

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5 Tips for Culturally Responsive Teaching in the Math Classroom

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Teachers can help all students feel like they belong in math classes by creating connections between course material and students' lives.

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Culturally Responsive Teaching- Fuad Suleiman

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Culturally Responsive Teaching- Fuad Suleiman

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The article makes a lot of good points about how underrepresented groups can struggle in math if they don't see themselves represented in the pedagogy. I found all of the points useful, but I especially liked number 2, "reflect on your own experience." I feel like for me to better understand my students' cultural identities, I would first have to understand what that means to me. The identity wheel provided has good prompts to help stimulate thinking about my identity. Once we can establish the identities of the students, we can bridge the gap between the curriculum and how it affects their lives and communities. I found the point about building relationships in the school and community very interesting. If we can present people around them that can connect to the material, than the students are likely to have an easier time making those connections for themselves. And if the students connect with the lessons, I believe they are more likely to enjoy it, learn from it, and see themselves involved with it in the future.

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I struggle with holding back and letting students explore until they find solutions. I really like the idea of opening up a curious classroom and thinking classroom. The tips in this article such as not carrying a pencil or marker around, stalling the answer, using we instead of I ( in group work it is difficult for an individual to get stuck once the rest of the mates are lopped in. ) and setting boundaries! This resonated with me the most in this article - "Are you asking me a thinking question? I am glad to give you a nudge but I can no take away YOUR OPPORTUNITY TO THINK".  It is exciting to think of math this way and I appreciate this take.  Sarah Finerghty

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I agree that the concepts in the article for keeping boundaries seem like they would be effective, but it will take some getting used to for a lot of teachers.  The reference to carrying a pencil also  hit home for me because I am a visual learner and drawing something or writing something is the first thing I go to!  Just getting the students used to the difference between a "thinking question" and a "stop thinking question" is making them think even more, so already a step in the right direction. -Cheri Enigk

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This article enlightened me to think about why it is important to make math inclusive and how teachers can help aid in that. If students can not see themselves in the material, it will be impossible to understand and learn further. Using real world examples will help the students be able to connect to what they are learning, it becomes more of a tangible thing as opposed to abstract concepts. Additionally, I found in this article that is important for the teachers to serve as a source of motivation to enhance the students' learning and motivation to continue learning. - Maddy Svercel

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I like how you mentioned the motivation that teachers must provide to enhance the students' learning.  There is so much time spent with teachers so without that as a key part to the learning process, it would be so easy for students to stop trying, or feel like it was all for nothing.  Staying positive and finding interesting methods to deliver math content can keep the energy up in the class so students motivate each other as well as the teacher motivating students. -Cheri Enigk

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I love the quote from the article that you included in your discussion. I have never heard of a thinking question in math, but it makes total sense to me. I could definitely see students getting frustrated with this response from a teacher, but I think they would feel even prouder when they finally figure out the problem on their own. KENDRA MACCAULL

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Quote response to response to boundaries

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Quote response to response to boundaries

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I would have been livid as a student, but only if it was out of the blue I think. If the classroom is set up in such a way where thinking and struggle are encouraged it wont come across as, hey you're own your own kid, as much as if it was in a typical classroom when we were kids. Sarah Finerghty

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The article “5 Ways to Stop Thinking for Your Students” by Crystal Frommert makes some interesting points that could be hard to implement in the classroom, but that seem necessary to get kids thinking on their own.  One thing that surprised me about this article was the negative reference to the “I do, we do, you do” format.  This, to me, still seems like a good way to get the students involved in class.  The other ideas in this article focus on how to get the students to think through problems without relying too heavily on answers from the teacher.  This could happen with increased group settings and a conscious effort by the instructor to learn how to re-structure questions asked by the students, so they must put more thought into finding answers.  Some concepts involve giving “verbal nudges or hints”, using other group examples for visuals, and stalling immediate answers because it is likely the student will get there with exploration and patience.  With boundaries set for questions that will be answered, the theory is that the students will put more thought into their work before asking questions and the questions they do ask will be focused, specific, and well thought out. This would be interesting to watch as it progressed throughout a school year. -Cheri Enigk

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I enjoyed reading your comment and agree that "I do, we do, you do" is still a good strategy. It is interesting that some strategies that may work in a content area like literature, may not work for Math. - Maddy

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5 Ways to Stop Thinking for Your Students

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5 Ways to Stop Thinking for Your Students

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Too often math students lean on teachers to think for them, but there are some simple ways to guide them to think for themselves.

Who is doing the thinking in your classroom? If you asked me that question a few years ago, I would have replied, "My kids are doing the thinking, of course!" But I was wrong. As I reflect back to my teaching style before I read Building Thinking Classrooms by Peter Liljedahl (an era in my career I like to call "pre-thinking classroom"), I now see that I was encouraging my students to mimic rather than think.

My lessons followed a formula that I knew from my own school experience as a student and what I had learned in college as a pre-service teacher. It looked like this: Students faced me stationed at the board; I demonstrated a few problems while students copied what I wrote in their notes. I would throw out a few questions to the class to assess understanding. If a few kids answered correctly, I felt confident that the lesson had gone well. Some educators might call this " I do, we do, you do."

What's wrong with this formula? When it was time for them to work independently, which usually meant a homework assignment because I used most of class time for direct instruction, the students would come back to class and say, "The homework was so hard. I don't get it. Can you go over questions 1-20?" Exhausted and frustrated, I would wonder, "But I taught it-why didn't they get it?"

Now in the "peri-thinking classroom" era of my career, my students are often working at the whiteboards in random groups as outlined in Liljedahl's book. The pendulum has shifted from the teacher doing the thinking to the students doing the thinking. Do they still say, "I don't get it!"? Yes, of course! But I use the following strategies to put the thinking back onto them.

5 Ways to Get Your Students to Think

1. Answer questions with a refocus on the students' point of view. Liljedahl found in his research that students ask three types of questions: "(1) proximity questions-asked when the teacher is close; (2) stop thinking questions-most often of the form 'is this right' or 'will this be on the test'; and (3) keep thinking questions-questions that students ask so they can get back to work." He suggests that teachers acknowledge "proximity" and "stop thinking questions" but not answer them.

Try these responses to questions that students ask to keep working:

"What have you done so far?"

"Where did you get that number?"

"What information is given in the problem?"

"Does that number seem reasonable in this situation?"

3. We instead of I. When I assign a handful of problems for groups to work on at the whiteboards, they are tempted to divvy up the task. "You do #30, and I'll do #31." This becomes an issue when they get stuck. I inevitably hear, "Can you help me with #30? I forgot how to start."

I now require questions to use "we" instead of "I." This works wonders. As soon as they start to ask a question with "I," they pause and ask their group mates. Then they can legitimately say, " We tried #30, and we are stumped." But, in reality, once they loop in their group mates, the struggling student becomes unstuck, and everyone in the group has to engage with the problem.

4. Stall your answer. If I hear a basic computation question such as, "What is 3 divided by 5?" I act like I am busy helping another student: "Hold on, I need to help Marisela. I'll be right back." By the time I return to them, they are way past their question. They will ask a classmate, work it out, or look it up. If the teacher is not available to think for them, they learn to find alternative resources.

5. Set boundaries. As mentioned before, students ask "proximity" questions because I am close to them. I might reply with "Are you asking me a thinking question? I'm glad to give you a hint or nudge, but I cannot take away your opportunity to think." This type of response acknowledges that you are there to help them but not to do their thinking for them.

When you set boundaries of what questions will be answered, the students begin to more carefully craft their questions. At this point of the year, I am starting to hear questions such as, "We have tried solving this system by substitution, but we are getting an unreasonable solution. Can you look at our steps?" Yes!

Shifting the focus to students doing the thinking not only enhances their learning but can also have the effect of less frustration and fatigue for the teacher. As the class becomes student-centered, the teacher role shifts to guide or facilitator and away from "sage on the stage."

As another added benefit, when you serve as guide or facilitator, the students are getting differentiated instruction and assessment. Maybe only a few students need assistance with adding fractions, while a few students need assistance on an entirely different concept. At first, you might feel like your head is spinning trying to address so many different requests; however, as you carefully sift through the types of questions you hear, you will soon be comfortable only answering the "keep thinking" questions.

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5 Ways to Stop Thinking for Your Students

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Too often math students lean on teachers to think for them, but there are some simple ways to guide them to think for themselves.

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5 Ways to Stop Thinking for Your Students

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5 Ways to Stop Thinking for Your Students

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One thing I found interesting in the article is that we think that the students are doing the majority of the thinking throughout the class but in reality us teachers are the ones who are doing the majority of the thinking and eliminating the chances for our students to use their critical thinking skills. I subconsciously have previously implemented these strategies in my classroom pedagogy but the one that I never thought of was carrying around a pencil myself encourages students to think that I will write for them and get them out of the struggling problem. That was one thing that I was guilty of doing in my classroom that I will have to get better at moving forward to be able to allow my students a chance for them to write it down and retain some of the information themselves. By answering follow up questions to students' questions rather than yes or no allows more room for communication amongst the student and the teacher and engages in critical thinking on how to solve problems.
- Matt Hunter

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Math Classroom into a Thinking Classroom

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Math Classroom into a Thinking Classroom

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Thinking is an important part of learning. Instead of having students work in a setting that is not working. They should be placed in an environment that they can thrive thinking. Placing students in a group and assigning jobs for each person in a group ensures that each person will be actively participating and learning. Having the students "vertically learn" is another way that they will be able to get them involved. Working with dry erase markers and whiteboards help students not to focus on getting everything correct, but to write out what can do and know that they can correct the work by simply erasing it. This not only helps the student to think, but to also persevere even when they did not answer correctly. The focus on being able to understand the work, not just to answer correctly. Lastly, in order for this to work in a classroom there needs to be strategies taught that allow students to be in a learning environment. -Kalen Dotson

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I really liked the part about assigning jobs to members of the group. Often times, students can be anonymous in group work if other students take over. But like you said, if we assign different tasks to each student, we can ensure active participation by each member of the group. That way everyone will be involved and will hopefully stay engaged with the lesson at hand. - Fuad Suleiman

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Math Classroom into a Thinking Classroom

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Math Classroom into a Thinking Classroom

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In traditional math classrooms-and in classrooms where challenging, unfamiliar work is often assigned, more generally-the progression " I do, we do, you do" often becomes the default approach to learning, according to researcher and professor of mathematics at Simon Fraser University, Peter Liljedahl.

It makes sense in many cases, particularly when difficult concepts need to be addressed in time windows that are compressed by bell schedules, holiday breaks, andsummer vacation.But used too frequently, this approach, Liljedahl recently told the Cult of Pedagogy, inhibits higher order thinking and results in students who "mimic" teachers. Students who engage in too much rote work miss out on some of the challenging, sometimes confusing work that builds up their self esteem to face difficult thinking tasks in the future.

"By and large students spend most of their class time not thinking, at least not in ways we know they need to think in order to be successful in mathematics." Liljedahl explains. "If they're not thinking, they're not learning."

Liljedahl, the author of Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning advocates for "Thinking Classrooms", which offers a different take on how classroom work is organized, how tasks are assigned, and how students learn and work together. His conclusions are based on more than a decade of research, experimentation, and collaboration with over 400 K-12 teachers.

In a 2017 article for Edutopia, Liljedahl clarified that a "non-thinking" classroom is "predicated on an assumption that the students either could not or would not think." When presented with difficult problems, students in these classrooms have a hard time pushing through to find their own solutions, he argued, and often wait for teachers to step in to do the heavy lifting for them.

To stimulate independent thinking, Liljedahl says, reorganize some of your classroom approaches: Start with hard puzzles and problems that push kids to their limits; confront the fundamental passivity of classroom seating; and use highly structured group activities to promote discussion, peer review, and iterative thinking.

Starting With 'Thinking Tasks'

Instead of starting a lesson with direct instruction, give students novel "thinking tasks" they can work on, ideally in groups. Liljedahl describes these tasks as problem solving activities and mental puzzles that, early on in the school year, should be "highly engaging, non-curricular tasks" to motivate students and get them in the mindset of challenging themselves. As the school year progresses and students become more accustomed to this mode of working and thinking, the activities and challenges can be replaced with tasks directly related to the curriculum.

Liljedahl points out that the tasks should be carefully sequenced so they get incrementally more challenging. "The goal of thinking classrooms is not to get students to think about engaging with non-curricular tasks day in and day out-that turns out to be rather easy," he told Cult of Pedagogy. "Rather, the goal is to get more of your students thinking, and thinking for longer periods of time, within the context of curriculum, which leads to longer and deeper learning."

Liljedahl has a long list of sample "thinking tasks" to look through. They include challenging dice-related problems, such as: Imagine a typical 6-sided die, and notice that the sum of opposite faces is always seven. The one is across from the six, the two is across from the five, and so on. Now imagine that you were making your own six-sided die that did not have this restriction. How many different dice could be made?

Use Standing, Randomized Group Work

Central to Liljedahl's approach is student collaboration and group work. Instead of grouping students by ability, or allowing them to choose their own groups to work in, his research has shown him students work more effectively-and are more likely to contribute-in randomized groups. According to Liljedahl, interviews with students show that randomized groups "break down social barriers within the room, increase knowledge mobility, reduce stress, and increase enthusiasm for mathematics."

At Design39Campus, a K-8 school in San Diego, eighth grade math teacher Kyle Asmus puts Liljedahl's approach into practice by using a random group generator (such as this one from Classtools or this one from Keamk) to ensure that different kids work together across multiple exercises.

To ensure that all students feel included, Asmus assigns group roles: The scribe writes down possible solutions; the speaker communicates the group's thinking to the broader classroom; the inquirer asks the teacher questions; and the manager makes sure the rest of the group stays on track.

Having students stand while they engage in this collaborative, messy thinking is yet another way to engage them, according to Liljedahl: It makes them much less likely to withdraw from the work, or assume that others will handle it. "It turns out that when students are sitting, they feel anonymous," Liljedahl told Cult of Pedagogy. "And when students feel anonymous, they disengage."

Work on Non-Permanent, Vertical Surfaces

In a thinking classroom, students put notebooks away and participate in group work while standing at vertical non-permanent surfaces such as whiteboards, blackboards, or windows-surfaces that Liljedahl believes promote more risk-taking.

According to Liljedahl, his experimentation with students shows that when comparing a group working on a whiteboard versus a group working on flip chart paper, the group working on whiteboards start working within 20 seconds.

"They'll start making notations on the board. They'll try anything and everything because they feel like they can just erase it if it's wrong," he told Cult of Pedagogy. Meanwhile, students working on chart paper take upwards of three minutes to make a single notation, because, Liljedahl said, they often wait until what they write is perfect-"and that hesitation leads to a lower form of thinking."

Design39 students also practice Liljedahl's "vertical surfaces" learning technique, which Asmus says promotes "high quality collaboration" and facilitates "questions and rich conversations" among students. According to Asmus, when students are presented with challenging tasks and work vertically, the time for students to get to a task is not only quicker, but the time they spend on a task is longer.

The large surfaces spread out around the room also allow students to see the work their peers are doing in other groups, and build off of each other's understanding. "It makes it easy for the whole class to see what everybody else is doing so we can be inspired by each other's ideas," said Iniyaa, a student in Asmus' class.

Answer the Right Questions

As students work vertically in groups, teachers can easily see how they're progressing and bounce around the room. Questions will undoubtedly arise, but Liljedahl says teachers should avoid answering questions asked for the purpose of reducing student effort and getting to an answer more quickly-such as "is this right?" Instead, they should prioritize addressing student questions that will lead to further independent thinking.

In her elementary school classroom in Brooklyn, teacher Tori Filler says that instead of rushing to provide hints and solutions to the hard parts of a lesson, she often asks them to evaluate what's tough about it, and encourages them to sort it out on their own before stepping in to help.

If most of the class is struggling, ask more questions and turn the struggle into a productive discussion for everyone. Asking questions like "What makes this hard?" or "What have we tried?" gets students to think metacognitively and develop the skills to push through challenging work on their own.

Evaluate What You Value

To succeed in a thinking classroom, students need to develop skills like perseverance, academic courage, collaboration, and curiosity, among others. But according to Liljedahl, if we want students to develop these competencies, then we should find ways to evaluate them on it.

"What we choose to evaluate tells students what we value, and, in turn, students begin to value it as well," he writes.

He argues for a mix of both formative and summative assessment in math classrooms that focus less on end products and student ranking, and more on the work leading up to those end products and collaboration between groups to get there.

The educators at Bite Sized Learning, for example, suggest evaluating students on the work they produce, but also on how well they persevere and make an effort in response to challenges, how well they set individual goals and monitor progress toward achieving them, and how well they share information and resources with group members to solve problems and make decisions.

Liljedahl's own formative assessments focus on informing students "about where they are and where they're going in their learning." This can take the form of observations, check-for-understanding questions, or even unmarked quizzes. Summative assessments, meanwhile, "should focus more on the processes of learning than on the products, and should include the evaluation of both group and individual work," Liljedahl writes.

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How to Turn Your Math Classroom Into a 'Thinking Classroom'

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The researcher Peter Liljedahl evangelizes for practices that prioritize and stimulate more hard thinking in classrooms.

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The thinking classroom discussed actually sounds a lot like the classes we have been a part of thus far in our MST program. Personally, I have found this style of teaching and learning more preferrable to my undergraduate classes which were mostly lectures. I felt like a lot of what the author was saying about traditional classrooms was accurate. In a lecture, I was much more likely to "check out" mentally even when trying to keep up with the lesson. It is difficult to stay focused on a lesson when the professor just reads the material to you for an hour. I find environments that promote discussion, movement, and student involvement keep me engaged and I retain more from the lesson. I especially like to hear what my peers are thinking about the lesson because it can help me sort out my own thoughts on what is being discussed. Hearing from more perspectives than just the teacher's can be very helpful for me to internalize the lesson. I really liked the idea of starting a new lesson with something challenging that can push thinking rather than just starting with something easy to get the lesson going. I feel like that can set the stage for more complex thinking rather than surface thinking.