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by LaToya Byrd and Jenna Laib
School looks different this year. It's easy to focus on the changes that will need to be made-the new practices, the new routines, the new technologies-but we must first focus on our central beliefs about teaching and learning, and use those beliefs to determine what's important. It is essential to build a strong classroom community.

What does it look like?

This community should strive to be one where learners know, use, and enjoy mathematics. How do you envision this math class? And how does that relate to your own mathematical experiences?

Think back to your time as an elementary school student. How would you have defined "mathematics"? How did you feel about math class? There's no monolithic experience for teachers. When we ask this at professional development, we have heard teachers say things like:
Math was always about getting the right answer. No collaboration or sharing out our thoughts. Now that I am a classroom teacher, I ensure students get think time and encourage group work. We all have something to learn from each other. I also don't want my students to think I hold all of the answers. We are a team. I thought I was a good math student and smart, because that's what I was told. I knew my math facts and I completed assignments fast. That stopped when I was sitting in an Algebra I class with no reasoning skills. I didn't know what to do or how to ask for help. Math was fun! It was a different game every game. We had to work together to solve math mysteries. My teacher kept everyone engaged so we learned without knowing we were learning.
The kind of community we want to create rarely happens by accident. As educators, we can make deliberate choices that support and sustain our math communities. To support this, the authors of IM K-5 Math (currently in beta pilot across the US) embedded plans to build community into the first two weeks of lessons in the curriculum. This work then continues and is regularly reinforced throughout the school year.

At the Heart of Building a Math Community

Students need to feel ownership and agency within the math community. IM K-5 Math builds in opportunities for students to explore what it means to learn math by doing math, identify the associated actions, and relate the actions of doing math to norms that support that work.

There are two important considerations when planning the student experiences used 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.

Understanding What It Means to Learn Math by Doing Math

The work on community in IM K-5 Math is not a detour; it fits seamlessly into the curriculum. Lessons provide students opportunities to build on their prior understandings and experiences, to share their thinking, and to interact with the thinking of others. They begin with an invitational warm up, like the one below.

From IM K-5 Math, Grade 2, Unit 1

After engaging in authentic and meaningful mathematical ways, students are asked to reflect on what it felt like, looked like, and sounded like. The teacher records this in a T-chart titled "Mathematical Community," like the one below. For the first 3 days, the focus is on the left side of the chart: Doing Math.

Students mathematize. This might be in a classroom, or at home, or anywhere in between, but first things first: students must do some math!

Afterwards, students contribute to this chart in person or virtually. In the virtual environment, students might share out during a synchronous session while the teacher records responses on a slide, doc, or even paper or chart paper that the teacher is able to show on the camera. Students could also contribute ideas asynchronously that the teacher then consolidates into one chart.

Here is an example from a IM K-5 Math alpha pilot classroom after the first day.

Photo c/o Viri Hawkins, Grade 5

Identifying Actions Associated with Doing Math

The work continues the next day. After the second lesson of the unit, which again follows the same design structure as all IM K-12 Math curricula, students are asked to review the chart, and to revise or add to it based on their experience during the second lesson. The process continues on day 3, as students are prompted to think about the actions associated with doing math. What specifically did students and teachers do?

For classes that are meeting in person, the T-chart can be hung up in the room for students to review. The teacher should direct students to it before the lesson. After the lesson synthesis, the teacher may again direct students to review the chart, but this time to consider any revisions or additions.
The teacher may make similar moves in a virtual setting. The teacher can show the slide with the chart at the start of the lesson, and lead a brief reflection. The teacher cues the class to revisit the chart to close the lesson, as well.

Affirming and Reaffirming Norms

After the class has spent a few days fleshing out the Doing Math side of the T-chart, it is time to discuss explicit norms that make these actions possible. For example, "it may help us share our ideas as a whole class if we have the norm 'listen as others share their ideas.'" It helps to spotlight different norms, and to pause the class while working to call attention to them.

Photo c/o Valerie Effland, Kindergarten

For classes that are held in person, it is helpful to continue to reference the physical recording of the T-Chart. For virtual classes, the teacher can make the decision to show the entire record of the T-chart, or just the one norm in focus that day.

By week two, the teacher can start the class with a quick refresher of the agreed upon norms, and then end the class by asking students to share what norms they experienced during that class session. Or the teacher may ask students, "which one of the norms did you feel was most important in your work today, and why?" This could be done as a journaling exercise, or, e.g. in a synchronous setting, a class or small group discussion.

This work is not completed in September. Classes should revisit the T-chart throughout the year, to reflect on the state of collaboration and discourse, and recommit to class norms.

Impact on Classroom Community

Co-crafting explicit norms alongside students does more than create shared ownership and a productive atmosphere. This process is designed to promote equitable teaching practices, and impact teacher beliefs.

Co-crafting norms honors student voices. It centers student ideas, and positions teachers as learners, too. In a recent professional learning session with IM K-5 Math beta pilot teachers, one educator stated that they "[couldn't] think of a math training that talked about giving a voice to marginalized students the way [IM] did." Other teachers noted that crafting norms builds community, and that this work echoes how lessons emphasize community, from the invitational warm up to the lesson synthesis.

Co-crafting norms with students also asks a teacher to examine their own beliefs about math learning and teaching. "IM's curriculum is different," a teacher shared. "Different in a good way. Being forced to think about my beliefs and positioning can only make me a better teacher. I think we call that humanizing math."

Resources

There have been two IM featured blog posts about co-crafting norms with students: (1) Building a Mathematical Classroom Community; and (2) Co-Creating Classroom Norms with Students. The first post offers a downloadable resource that is similar to what is written into IM K-5 Math. Educators participating in the beta pilot benefit from having this built into their lesson plans, but it would be easy enough to incorporate into any lesson!

Next Steps

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!

Get more support with IM's collection of distance learning resources. This includes curriculum adaption packs for the 2020-21 school year that incorporate this work.

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Helping Elementary Students Cultivate a Strong Math Community - IM CERTIFIED® BLOG

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by LaToya Byrd and Jenna Laib School looks different this year. It's easy to focus on the changes that will need to be made-the new practices, the new routines, the new technologies-but we must first focus on our central beliefs about teaching and learning, and use those beliefs to determine what's important.

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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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