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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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By Ashli Black, Algebra 2 Lead

Students need a chance at the beginning of the year to shake off the summer dust. Learn how IM's curricular design builds in opportunities for review while starting the year with inviting, grade-level mathematics.

One of the things I love about the IM 6-8 Math curriculum and the forthcoming HS curriculum is that none of these courses start with review. While starting with a short unit of review was something I tried when I first started teaching, I later decided on a different route because the review time wasn't helping my students in any way I could measure. If a student already had graphing and fractions and factoring down, how did the review help? If a student didn't have those sorts of skills down, how could a single week or two be enough? And how long would the classroom status issues revealed during the review time last?

I eventually changed from review to giving a short quiz during the first week of class. This quiz always had two purposes: to introduce students to what my quizzes looked like and communicate to my classes how I interpret the results of a quiz. Question 1 was always to plot a few points on the coordinate plane. I never had a class get over 80% on the first go. Not even the precalculus classes. Does a result like that mean pausing to spend a day on graphing points?

The next day, after handing back the quizzes-ungraded, comments only-I would display the class average for that question. There was always at least one student who would shout out that they forgot what negatives were, or mixed up $x$ and $y$. Others would then murmur agreement or argue that their brains were still in summer. They would do better next time.

And they did. Always. One thing I know about myself is that it takes time to get back into a groove. The same was true for my students and their mathematical selves. I ask a straightforward question like "plot these points" and then have a discussion about the results to communicate to my students that I knew their brains were still a bit in summer mode and that I wasn't going to expect they come into class right where they left off at the end of last year. The quiz gave me an opportunity to clearly make the point that review of a variety of skills would be built into our daily work. I also needed that quiz to remind me that the faces I was looking at were not the same as the students I'd last seen sitting in those chairs after a full year of instruction.

The results of that question on the quiz didn't mean to stop everything and work on that skill, they meant that I needed to look for an opportunity within the grade-level work to highlight things to remember about graphing points. Each course in the IM curricula starts with a unit that has built in opportunities for students to shake off the summer dust and show who they are as mathematicians while keeping the focus on grade-level mathematics. In IM 6-8 Math, that meant a focus on geometry at the start of the year. In Algebra 1 it's one-variable statistics. In Geometry it's Constructions and Rigid Transformations. In Algebra 2 it's Sequences and Functions.

In all of these courses, the first unit gives time to introduce students to the instructional routines they will use throughout the school year, in particular those they are likely less familiar with such as Info Gap Cards. Students have fewer preconceptions about their abilities (and those of their peers) when we focus on new ideas at the start of a year, so these units give an opportunity to set classroom norms for communication, collaboration, and making connections.

In the first unit of Algebra 2, attention was given to the fact that a student who has followed the "traditional" sequence of Algebra 1, Geometry, Algebra 2, may be out of practice with some key algebraic ideas. This unit takes a look at the familiar concepts of linear and exponential functions through the new lens of geometric and arithmetic sequences. The activities ask students to represent relationships using words, tables, graphs, and equations. They learn to define sequences recursively using function notation in a new way, giving contrast to how they have written equations for linear and exponential functions in the past.

As they build new skills while honing older ones, students also get to experience the beginnings of an important part of Algebra 2: modeling. In viewing the IM high school pacing guide, you may notice that Algebra 2 looks a bit shorter than the courses preceding it. This was purposeful to give space for teachers to make use of the modeling prompts that will be part of the course. Here in Unit 1, students address an aspect of mathematical modeling when they make the decision for what input value goes with the first term of the sequence. Often this boils down to choosing 0 or 1, which is highlighted in the task A Sierpinski Triangle. While this choice can appear trivial, making a decision and recognizing the consequences that decision has on different parts of the modeling process is necessary training for students if we want them to be powerful mathematical modelers. And while this is going on, students are plotting points on graphs and thinking critically about equations for linear and exponential functions, blowing summer dust away.

Next Steps

Check out the Unit 1s for the high school courses (Algebra 1, Geometry, and Algebra 2). Where do you see embedded review in these lessons? Where could you build in review to your Unit 1 for the skill practice some students need more time on?

Give your students an ungraded quiz on something you would expect them to get 100% on. What do you notice about the results?

Check out the demo of IM 9-12 Math Algebra 1, Geometry, Algebra 2 which is now available on our website. To access the full curriculum, please see our IM Certified™ partner page.

See unit 1s for the high school courses. Where do you see embedded review in these lessons? Where could you build in review to your Unit 1 for the skill practice some students need more time on?

Give your students an ungraded quiz on something you would expect them to get 100% on. What do you notice about the results?

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How do you start the year? - IM CERTIFIED® BLOG

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By Ashli Black, Algebra 2 Lead Students need a chance at the beginning of the year to shake off the summer dust. Learn how IM's curricular design builds in opportunities for review while starting the year with inviting, grade-level mathematics. One of the things I love about the IM 6-8 Math curriculum and the forthcoming [...]

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Group students in 4, give them a piece of paper and make a large diamond in it. Challenge the group to find 5 or more things that they have in common, the more unique the better. Have them write those down inside the diamond. Then on the spaces outside the diamond have them find 3 things that are unique about each of them.