As stated in our design principles, within a problem-based curriculum “students learn mathematics by doing mathematics.” Given the nature of math classrooms, however, students come with differing math identities, which means some students are more prone to see themselves as doers of mathematics than others. Furthermore, apparent inequities in math instruction suggest that some students have opportunities to bring their voice into the classroom, and others do not. In order to extend the invitation to all students to do mathematics, we must work to explicitly develop the math learning community.

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).

To support teachers to develop math learning communities in their classrooms, the first six lessons of each course embed structures to collectively identify what it looks like and sounds like to do math together, create, and reflect on classroom norms that support those actions.

Beyond the first six days, teachers should revisit these norms at least once a week to sustain the math learning community. Consistently returning to these ideas shows students that we value the math learning community as much as we value the math content. Students should also be provided with opportunities to reflect on the norms by stating which ones are the most challenging for them and why. Teacher reflection questions periodically remind teachers of points in a unit where it may be helpful to reflect on these norms.

Additional teaching moves can be used to support the development of math learning communities throughout the school year. The section below highlights teaching moves, put forth by Phil Daro and the SERP Institute, that are intended to support students' engagement in the mathematical practices. A solid math learning community exists when all students display these observable actions, called student vital actions.

Teaching Moves to Support Math Community

student vital actions	teacher moves
All students participate.	Assign rotating roles, and provide routines for collaboration so that every student is actively engaged in each task, and has experience in all roles over time. When students are confused ask them to show where they got lost or ask a question that can help them move forward (more than “I don’t get it” or “How do you do it?”). Check to see if there are recognizable patterns between participation and prior achievement or social groups (for example, ELL, race/ethnicity, or gender).
Students say a second sentence.	Ask and encourage students to ask: Can you tell me more about that? Why do you think that? What changed and what stayed the same? Is that an answer that makes sense for this problem? How do you know? How did you get that answer? Why did you (reference student work)? Is it always true? Sometimes true?
Students talk about each other’s thinking.	Show and discuss work generated by students when working with mathematics concepts. Questions that may be used to prompt students: Did anyone approach the problem a different way? How is your thinking different from theirs? What does their way of thinking help you understand? Do you think their method would work with this kind of problem? Why or why not? Try only responding to questions from groups when no one in the group can answer the question and everyone in the group can ask it.
Students revise their thinking.	If a student is presenting an explanation, play the role of not understanding and say “Could you help me make sense of your thinking? Could you revise your explanation?” Have a student quote a classmate’s statement that inspired them to revise. Have students confer in small groups after whole-class presentations to revise and refine their way of thinking.
Students engage and persevere.	Ask a student who has given a wrong answer additional questions to explore his or her thinking. Demonstrate curiosity about that thinking. Have students share their thinking and attempts even when they have not found a viable solution. When some groups are “finished” earlier than others, ask them to analyze their work and seek places to revise their explanation so more students will understand it, or look for an alternative approach.
Students use general and discipline- specific academic language.	Before beginning small group work, give students sentence frames and probing questions that feature important terms. Accept students’ everyday way of talking as a starting point for joining the math conversation. Teachers can refer to student statements using some student language while strategically incorporating more precise academic language with the addition of a key word or phrase.
English learners produce language.	For everyday words that have precise mathematical meaning, provide multiple contexts where the word is useful and have students explain what it refers to in that context. Ask them to use the word to make connections between the different representations. Encourage students to use language to construct meaning from representations with prompts such as: “Explain where you see…(length, ten, oranges) in the…(figure, equation, table). How do you know it represents the same thing?” Every student speaks, listens, reads, and writes.

For more details and a full list of teaching moves, visit the SERP Institute site.

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Developing a Math Community