“Equitable teaching and learning of mathematics can only take place in an environment where students engage deeply with significant mathematical ideas,” have opportunities to express their math thinking and interact with the thinking of others, take responsibility for their learning, and work together in productive ways. (Russell, et. al., 2022, p. 3) Discussions, Math Workshop, and partner work are Investigations 3 structures that offer critical opportunities to develop and support an equitable math learning community. This 3-part blog series offers guidance about how these structures can promote equity in the mathematics classroom and support the identity and agency of all students, especially those who have been historically marginalized in mathematics.
How Discussions Support Equity
Whole-class discussions are an essential feature of the Investigations 3 curriculum. Discussions provide students with the opportunity to articulate their ideas and consider the ideas of others, develop mathematical language, and compare and connect ideas, representations, and solutions. However, “classrooms that are rich in mathematical discourse…are…high-risk for reproducing patterns of racism and marginalization.” (Ball, 2019, slide 11). It is important to think about and plan for how to make participation in such discussions equitable and how to establish a “community in which students are prepared to listen actively and contribute ideas.” (See Implementing Investigations in Grade [2], p. 30.)
The following factors, in bold, are important to consider in working to make discussions an opportunity to develop students’ mathematical identity. In blue, you’ll find questions you can discuss with students as you reflect on whose voices are being heard, whose work is being shared and discussed, and whose ideas are not yet present in math discussions.
Organizing the Physical Space
The set-up of the classroom should encourage students to participate in whole class discussions, as both a contributor and a listener. Being able to see each other’s faces, and any work being shared, helps students focus their attention and encourages them to speak directly to each other. Ask students to share ideas about how to make discussions good learning opportunities for everyone.
- What helps you stay focused during a discussion? What makes it hard to stay focused?
- Are there changes we could make to how our seats are arranged that would improve our discussions?
Supporting Students’ Interactions
Productive discussions require the interaction of the various participants. Signals that indicate a student would like to share a thought, build on an idea, or ask a question of or disagree with a classmate, support students in conversing with each other. Gather ideas from students about sharing ideas, and about listening and responding to the ideas of others.
- When someone is sharing, what helps you really listen to their idea?
- How can you show that you are listening to other peoples’ ideas?
- How can you respond to someone else’s idea? (ask a question, add on, agree, disagree) How can you disagree in a respectful way?
Using Targeted Facilitation Moves
Targeted facilitation moves (e.g. turn and talks, asking students to rephrase someone’s idea or to share a partner’s idea, sufficient wait time) can support students in participating and in listening to others. For example, a “turn and talk” offers every student the opportunity to express their thinking and to listen to the thinking of a peer. For turn and talks to be successful, students need to know how they will partner, what’s expected of them, and practice. Encourage students to reflect on what makes for a “good” turn and talk.
- What does a turn and talk look like in our community?
- What does each person do in a turn and talk?
- How does talking with a partner help you during a discussion?
Using Mistakes As Opportunities
Mistakes are important opportunities to revisit and clarify math thinking, and to learn. This stance requires a community that carefully considers the ideas of others and can ask questions and offer different ideas. Discuss ways to comment on others’ work and to disagree respectfully.
- If you think your partner made a mistake, what could you say? What are helpful ways to talk with someone about a mistake?
- Someone solved this problem this way. [Share a mistake.] What do you think they were thinking? What suggestion could you give them? How could you express that in a supportive way?
Supporting the Participation of All Students
Productive and equitable discussions invite and acknowledge the contributions of each and every student. Consider how to support students who are reluctant to participate. For example, when selecting work to discuss, use this as an opportunity to position students who do not share often in the whole group. Explain why you would like them to share and ask if they would like to “rehearse” with you beforehand. If students are hesitant, ask if you can share their work or if you could do it together. The class should know that you want different approaches to be shared during discussions, and that you want everyone to have an opportunity to explain their thinking over time.
- What was it like for you to share your work today?
- How did rehearsing ahead of time help you? (for students who did)
- What would help you feel comfortable sharing your work/ideas in a future discussion?
- What might make help you share an idea you’re not sure of yet?
Making Equitable Participation Explicit
Creating an equitable math learning community is not just the work of the teacher. Engage students in working together with you to achieve equitable participation.
- How can you invite people into the conversation? Make room for others to contribute? Are you aware of how often you are speaking?
- What might help you share your ideas or work? What doesn’t help?
- How can we as a community support each other during discussions?
While the beginning of the school year is a natural place to lay the foundation for discussions in which all students are engaged and encouraged to share their thinking and listen to the thinking of others, it is important to continually revisit and reflect with students on how they are experiencing discussions. For support thinking about how to develop equitable math discussions from the start of the year, see Developing an Equitable Math Learning Community in Unit 1.
If you are interested in reflecting further on whole class discussions, see the Teacher Reflection Tools offered by the Forum for Equity in Elementary Mathematics.
Discussions are one of the structures in Investigations 3 that offer students opportunities to see themselves and each other as active and contributing members of their math community. Part 2 of this series will explore how another structure, Math Workshop, engages students in taking responsibility for and becoming agents of their own learning.
References
Ball, D. L. (2019, April 4). The power of teaching [PowerPoint slides]. National Council of Teachers of Mathematics. Retrieved from https://static1.squarespace.com/static/577fc4e2440243084a67dc49/t/5ca76 a3b90b1e600012f7c7c/1554475585731/040419_NCTM_lead+speaker+presentation.pdf
Russell, S.J. et al. (2022, September). A Framework for Reflecting about Equity in the Elementary Mathematics Classroom. Investigations Center for Curriculum and Professional Development.
TERC (2017). Implementing Investigations. Investigations in Number, Data, and Space®, (3rd ed.). Savvas Learning Company.
