[Adapted from Interweaving Equitable Participation and Deep Mathematics: Building Community in the Elementary Classroom by Susan Jo Russell and Deborah Schifter]
Many students are, at first, reluctant to contribute their ideas in whole-class mathematics discussion. Some students may have had classroom experiences in which only a few students, who typically provided the “right” answer, were called on. They may assume their own ideas are not of interest. Some students know they have mathematical ideas but are not sure how to get their words out in order to express those ideas in a whole-group setting.
Many students don’t realize that expressing partial ideas can help everyone move their thinking forward.
Having an idea and articulating it in a way that others can understand it—as we have all experienced ourselves—are two different things. While there are those who seem to be able to fluently articulate what they want to say on their first try, most of us are figuring out the words we want as we say them. This may be even more true for young students, who are learning both everyday language and mathematical language, or for multilingual students who are learning the language predominantly spoken in the classroom. Do we give our students enough time and encouragement to get their ideas out? Do they know that this is an important effort and will be not just tolerated, but appreciated?
Often students in elementary grades need more time to articulate their thoughts than might be comfortable for their teachers. Students may hesitate, stop in the middle of their thought, backtrack, repeat themselves, break off what they are saying and seem unable to continue, or simply take what seems like a long time to get started. As teachers, it can be difficult to balance support for the participation of all students, not just the most articulate, with the natural restlessness and straying attention of a class full of young students. There is, of course, no set of rules to make finding this balance easier. The point is, rather, that both of these goals must be present and in tension—supporting each student to express ideas and keeping the discussion going in a way that engages the whole class.
Consider what is involved in attending to both the needs of the group as a whole and the individuals in it as you facilitate mathematics discussions in your own context. Here are some explicit moves to think about:
- Encourage persistence. There is an unfortunate myth about mathematics learning that you either know the correct response or you don’t. Rather, help students learn that you are challenging them to think about hard ideas and that you expect them to need time and effort to make sense of them.
- Embrace pauses, backtracking, silences. In order to tolerate the repeating, backtracking, rewording, and rethinking that are essential parts of mathematical discourse, we have to come to terms with our own discomfort when students are uncertain, our own tendencies to want to save them from frustration, and our own difficulties in tolerating the time students take to articulate their thoughts.
- Reflect back students’ own words to them. When students hesitate or break off, help them see that they have kernels of mathematical ideas by reflecting back to them their own beginnings of sense-making. This can be as simple as, “you started to say something about multiplication” or “you said something about a 1—where were you seeing a 1?” Reflecting back in this way indicates that you are listening hard and that you expect students to have ideas.
- Give students opportunities to rehearse their ideas. While you circulate during individual and small group work, engage students to explain their thinking. Identify ideas that could be shared with the whole group, keeping in mind which students often share and which do not. Ask more reluctant students in advance about how they might share their ideas, and give them opportunities to rehearse what they might show or say.
Making space and time for every student’s ideas is necessarily a collaborative effort of the whole community, and for that to happen, community commitments about including and listening to all voices must be established collaboratively and reinforced frequently.
When both students who are eager to articulate their ideas and students who need more time or support to articulate their ideas are included and affirmed, students are learning that everyone has mathematical ideas that are worthy of being heard and considered.
