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Building a Mathematical Classroom Community

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Building a Mathematical Classroom Community

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Classroom environments that foster a sense of community that allows students to express their mathematical ideas-together with norms that expect students to communicate their mathematical thinking to their peers and teacher, both orally and in writing, using the language of mathematics-positively affect participation and engagement among all students .

Principles to Action, NCTM

The beginning of the school year offers teachers and students a fresh start full of exciting possibilities. From the first day of class, as we begin to learn about each of the students in front of us, we have the opportunity to set the stage for how learning math will look, sound, and feel throughout the year. We also begin to foster the attitudes and beliefs that are important in shaping a mathematical classroom community in which each and every student is positioned as a capable learner and doer of mathematics, truly believes their voice is valued and heard, and understands that we learn math by doing deep and meaningful mathematics together. Building this classroom community requires a purposeful process that takes time and careful attention.

To build this community, it is first important to be mindful of who is involved in the process. While it may be fast and easy to simply tell students how they will engage in math this year by offering a given set of rules or norms, it completely removes student ownership in their own learning. It is also a missed opportunity to engage students in reflecting on the things they need to feel safe and successful in mathematics. To be invested in a classroom community, students should be active participants in identifying what it means for them to do math and the collective norms that allow each and every one of them the opportunity to do so.

Student-generated norms offer guidance and continuous reminders to students as to how they can work collaboratively and productively as individuals as well as in groups. Even with the best of intentions, however, all too often we establish norms at the beginning of the year only to struggle to maintain them. Creating norms within the context of building a mathematical community moves the norms from just a poster on the wall to a living, breathing culture in the classroom.

There are two important considerations when planning the student experiences through which to establish norms:

1. The experiences should be reflective of how learning math will look, sound, and feel all year.

2. The experiences should be connected to convey the message that learning math is a coherent journey.

If we want students to have access to, and engage in, deep and meaningful mathematics, their opportunities to do mathematics should be connected. A series of connected experiences that encourage mathematical discussions, collaborative work, and engagement in the Mathematical Practices not only create a mathematical classroom culture, but also give students a coherent picture of what it means to learn math. Through these experiences, the established norms are continuously reinforced.

T he first two weeks of class are often dedicated to giving students exciting math problems and establishing norms. While this is great for engaging students in mathematics, these activities are typically disconnected, isolated tasks that then create the need for the teacher to establish new routines and lesson structures when starting their first curriculum unit. These additional tasks take time and can add extra days into an already full year of learning, forcing teachers to make decisions about which content to cut later in the year because of pacing issues.

From the beginning of Unit 1 in the IM 6-8 Math curriculum, the problem-based lesson structure engages students in collaborative, connected mathematical experiences. Through warm-ups such as "Which One Doesn't Belong," "Notice and Wonder," and "Number Talks," and classroom activities that include card sorts and interactive Geogebra applets, the norms are intrinsic to the daily function of the mathematics classroom throughout the year.

Linked below is a process to start building a mathematical classroom community during the first week of school in Unit 1 of the IM 6-8 Math curriculum. In preparation for this work, we recommend teachers read the "What Is a Problem-based Curriculum?" section of the curriculum course guide to gain insight into the ways students actively participate in the learning throughout a lesson.

Download the Building a Mathematical Classroom Community plan.

Here are some ideas to help maintain your mathematical community norms throughout the year:

As the teacher, be a daily example of what it looks like to do math and be mindful of the community norms.

After the first week, be sure to revisit the "Mathematical Community" ideas and ask for revisions at least once a week. It is easy to focus solely on the math students are doing, but by revisiting this list it shows students that you value the mathematical community as much as you value the math.

To ensure this is a working and growing collection of ideas, make Post-its available to students and ask them to make suggestions or show evidence of either doing math or norms they experienced.

Before launching activities that require a lot of group interaction, remind students of their mathematical community ideas so the ideas are at the forefront of their work.

As students work during a lesson, occasionally monitor for evidence of their mathematical community in addition to the math. During the synthesis, highlight the actions and norms you saw being attended to during the lesson.

If time allows, periodically ask students to be more metacognitive about the norms by asking them which norms they think are the most difficult to follow, and why.

Organizational tip for the classroom: In the FB group, Lindsey K. posted, "I'm moving from elementary to middle school. I've always done collaborative norms and posted them. How do you do that for multiple classes? I was thinking of doing each class and then synthesizing all 5 on one anchor chart. Any other ideas?"

I thought this was a great question and one that many teachers face with limited wall space. I taught three 5th grade math classes and kept a separate piece of chart paper for each class because they were uniquely different. I also had an abnormally long room with a huge, empty wall that made it easy to do! If you are short on wall space, I think consolidating the class norms to one poster is a way to save space. And then, to value each classes' differences, you could make a 5×8 index card or copy of the norms on card stock to tape to the front of their workbooks or math journals.

If you use this process, we would love to see your students' ideas and hear about your experience. You can share your pictures, blog post links, and reflections in the comments section below, or on Twitter using our #LearnWithIM hashtag and tagging @IllustrateMath!

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Building a Mathematical Classroom Community - IM CERTIFIED® BLOG

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Classroom environments that foster a sense of community that allows students to express their mathematical ideas-together with norms that expect students to communicate their mathematical thinking to their peers and teacher, both orally and in writing, using the language of mathematics-positively affect participation and engagement among all students.

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Elements of Problem-Based Teaching and Learning

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Elements of Problem-Based Teaching and Learning

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By Max Ray-Riek, Senior Director, Teacher Professional Learning

Our vision at IM is world where all students know, use, and enjoy mathematics. Educators in our IM Community work toward this vision in classrooms day after day using our problem-based curriculum. What does an IM classroom look like? What does it sound like? We often get asked these questions, and one way we share the story of an IM classroom is through the elements of problem-based teaching and learning.
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You may have seen these "hexagons" before-in an IM booth, at a conference session, during a professional learning session, on a sticker, or in a social media post. Even if you've seen them before, take just a moment to look at them closely.
What do you notice? What do you wonder? Here are some things that may have stood out for you:

There are some gray hexagons without words on them.

Some hexagons are bigger than others.

Most of the hexagons are about students, but one is about teachers.

Several years ago, IM's curriculum and professional learning teams came together to talk about what we wanted to highlight for teachers learning about our approach to problem-based instruction. We thought about classrooms that we've visited (some of yours!), and reflected on questions and concerns from professional learning participants (some of you!). In response to these concerns, we created these elements of problem-based teaching and learning that now serve as an anchor for our teams as we design learning experiences.

We purposely included the gray hexagons as a visual reminder that we haven't created a conclusive list. What would you add? The larger hexagons are a premise and our hopes for a powerful outcome. For us, problem-based learning starts with curiosity and trust, specifically with teachers being curious about their students' ideas and excited to see where their students' thinking will lead. The other elements work in tandem to ensure students arrive at IM's vision of where all students know, use, and enjoy mathematics .

How do these elements play out in your classroom? What do they look like and sound like? Here are some added details based on our observations during our classroom visits.

Each element of problem-based learning on this list contributes to an ultimate goal: to create the conditions for every student to experience a sense of belonging so they feel empowered to know, use, and enjoy mathematics in class and in their daily lives. And even better than a list of suggested look-fors, we have examples of what these elements look and sound like in a school district in Iowa.
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To learn more about the work happening in Iowa, check out their case study.

Teachers and students in a New Mexico district got to reflect on the elements like you just did as they watched a live video feed of students participating in a MathLab summer program and noted the elements they saw.
Here are a few quotes from middle-grade teachers sharing what they learned: "You need to . . . witness these good teaching practices, and really be thoughtful of how the elements of problem-based teaching and learning are purposely laid out. I am always reminded of how Vince Lombardi is quoted to say 'Practice doesn't make perfect. Perfect practice makes perfect.' You need to witness and thoroughly think about what you as a teacher are going to do." "Let go of control. Trust your students and the curriculum to get the learning where you need to go. You don't need to steer." Here's what their students had to say as they reflected on their IM experience when the elements of problem-based teaching and learning were a focus: "I thought it was really cool how safe of a space it was, how everyone was able to share their thoughts and the way they thought and their questions without being judged." "A really good way that makes it safe is being able to talk with friends and share ideas. That just helps me a lot. It can be distracting at times but it can also be very helpful." "I wanted to add on to what [the previous student] shared; working together as a team was very helpful."
In these reflections we can see not only evidence of the elements of problem-based teaching and learning, but also how teachers' and students' beliefs about math and their roles in the classroom shifted. This connection between the elements and our beliefs about students and educators is important to us.

The elements of problem-based teaching and learning are grounded in IM's beliefs about teachers and educators:

This is what we believe and hope for in IM Classrooms, but we know that isn't enough. To thrive, teachers and students must also embrace these beliefs not only about themselves but also about others in their learning communities.

How have you seen these beliefs play out in your own classroom and school?

What connections do you see between these beliefs and elements on your journey to a world where all students know, use, and enjoy mathematics?

Whether you have encountered the "hexagons" before or this is your first time exploring them, we hope that you are making connections to your own practice. As you reflect on these elements, ask yourself what inspires you in the classroom and consider how your own beliefs about students and about educators influence the instructional decisions you make.

In Future of Math Teacher Professional Learning , the authors state, "A teacher's views of their student's math capabilities is a predictor of their student's math performance. A critical first step to real change for learners underestimated by the system is to engage teachers to critically examine their beliefs and assumptions."

As mathematics teachers, we respond daily to the call to action to provide equitable instruction and to position all students in a way that supports learning. The most impactful IM Experience will be the one that you and your students cocreate as you believe in, value, and get curious about each other's thinking.

As you plan for an upcoming lesson/math party, consider:

We invite you and your students to take some time to reflect.

How have you experienced the elements of problem-based teaching and learning?

What element or belief will you highlight and focus on in the coming weeks?

Max Ray-Riek
Senior Director, Teacher Professional Learning

Max Ray-Riek is the senior director of teacher professional learning at Illustrative Mathematics. Before joining IM, Max worked for The Math Forum. He is the lead author of Powerful Problem Solving: Activities for Sense Making with the Math Practices. Max is a former secondary mathematics teacher (and before that, preschool teacher) who finds the art and discipline of valuing each student's ideas, and supporting all students to see themselves as "mathers," to be hard, rewarding, and important work. Max and his partner Kaytee live in Delaware County, Pennsylvania, where they raise service dogs.

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Elements of Problem-Based Teaching and Learning - IM CERTIFIED® BLOG

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One way we share the story of an IM classroom is through the elements of problem-based teaching and learning. You may have seen...

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Building a Math Community with IM K–5 Math

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Building a Math Community with IM K–5 Math

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"I'm not sure this is working. Only five of my students are participating and commenting each day. The rest sit there and look at me."

By Tabitha Eutsler
This was my conversation with our math coordinator after my first few days of teaching IM K-5 Math TM with my third graders. Those five students were having great conversations. However, my other students just sat there wide-eyed, silent, and staring blankly at their papers. I felt lost. Was this the best for my students? Could we survive a whole year of math like this? I wanted my students to love math and have a deeper understanding of mathematical concepts. How would this get them there?

The next week, while outside at recess, a handful of my students came up and asked what we were doing next in class. I told them we were working on Illustrative Math and they cheered. I stood there looking confused. We were eight lessons into the first unit, and it didn't feel like a success worth cheering about. In my head I was thinking, "For real? You guys are enjoying this?" These were students who never said anything in math and rarely were able to explain how they got their answer. I walked away even more perplexed than I already was about my math instruction.

Heading into the following week I was beginning to see a difference in my kids. I started to get why they loved it so much: They all felt successful. There was an entry point for each student. They were all learning the same standard but it was designed in a way that allowed each student to contribute in math class each day. I had so many students wanting to show their work and defend their work that we couldn't get through them all in a day. They were also giving each other constant feedback on their work.

During one lesson, multiple students gave feedback on a bar graph a student had presented. All of these students agreed with the way the student had created the bar graph from a set of data. Another student signaled with her thumb and said she disagreed. The whole class turned to this student and listened intently. This was one of the first times a student had disagreed. She went up to the front with the student who was presenting their work and explained how their scale on the left hand side was incorrect due to the placement of their zero. They placed the zero on the first section of the bar graph and it should have been down on the x-axis. The whole class goes "Oh ya!" and the student who had originally shared immediately started fixing her bar graph. I had noticed this mistake as I was walking around the room monitoring their work, but had refrained from saying anything. This paid off big time! My students were now learning from each other and teaching math to one another. It was a huge moment in our classroom.

There were still days that were difficult-with only a few students participating-but we pushed through and continued to build our mathematical community. I began to examine how my facilitation shaped the experience in the classroom. There were days when I didn't ask my students the right questions or push them in their struggle. That is when I saw my students have less ownership in their learning. Whenever this happened, discourse flattened. When asked to give feedback to a peer, students would say "I agree with you because I did the same thing." However, when I stepped back and let students construct meaning from the task and strategies of others, our conversations completely changed. Students were defending their thinking and questioning the thinking of others.

Now my students' mathematical thinking blows my mind!

Each and every student in my classroom can explain their answer. Their strategies look different because they all approach and solve problems in different ways, but they can use words, diagrams, equations, skip counting, whatever it may be to explain how they got their answer. This started happening before we even completed Unit 1.

One more huge moment happened in our room when a student gave feedback to another student while presenting work to the class. The student had written 4 x 5 = 20 for the given array. A student popped her thumb to give feedback and she said she disagreed. Once again it was one of those problems where almost everyone had the exact same thing, so they were anxious to hear more. She said that the student had written an equation but the directions said to write an expression. She explained to the class that an equation has the whole number sentence with the equal sign and product but an expression doesn't have those things so it should just be 4 x 5. I think my mouth fell open as I heard her use those mathematical vocabulary words that we had only recently discovered. I watched my students immediately go through and start correcting their work without a teacher standing up there saying they needed to correct it. In fact, I rarely tell students to correct their work. They listen to each other and do it by themselves. Which is so much more powerful! I was in. This was the best. Only 30 days into the school year,I was watching and listening to students deeply discuss math. There could be nothing better than that!

In my classroom, there are still days in which we struggle, but we have committed to struggling productively and learning from our mistakes. Our greatest success is that my students love math. They feel successful in math. They have a growth mindset everyday in math. I firmly believe that having a growth mindset and being able to think about and reason in math will start to show on assessments in a positive way. I can't wait to continue this journey through IM with my students, and I truly cannot imagine the kind of math thinkers that I will have in my room after another 30 days.

Next Steps

If you are interested in piloting IM K-5 Math beta at your school or district for the 2020-21 school year, Illustrative Mathematics recently announced that they have opened the application process to interested districts. Participants of the pilot get early access to the highly anticipated K-5 math curriculum, professional learning, and the opportunity to provide regular feedback to influence future versions.

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Building a Math Community with IM K-5 Math - IM CERTIFIED® BLOG

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"I'm not sure this is working. Only five of my students are participating and commenting each day. The rest sit there and look at me." By Tabitha Eutsler This was my conversation with our math coordinator after my first few days of teaching IM K-5 MathTM with my third graders.

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**Before accessing ILC link, first you'll need to log into ILC by clicking the ILC square in your SSO, and then you will be able to click the below tile.

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Please e-mail math@philasd.org with any district related questions.

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Name: Annemarie Pesce

Email: annemarie.pesce@imaginelearning.com

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Name: Kerry Newby

Email: kerry.newby@imaginelearning.com

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Improve your classroom with our educational research and resources. SERP provides innovative and scalable solutions for our schools' most pressing problems.

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Creating a Mathematical Community is a key structure in the design of IM 

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Creating a Mathematical Community is a key structure in the design of IM 

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Ways in which to build this community is built into the teacher guidance in the introductory lessons of Unit 1.

Navigate to Unit 1 of your course to check out the teaching notes.

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Illustrative Mathematics® K-12 | IL Classroom

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8 indicators of facilitating a PBL lesson

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8 indicators of facilitating a PBL lesson

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#1 Cultivate a positive, inclusive environment

#2 Equitable learning environment

#3 Launch activities

#4 Questioning strategies

#5 Engage students in discussion

#6 Monitor student thinking

#7 Value student thinking

#8 Synthesize learning