As Catherine Bruce points out in this monograph, the research shows that in “rich talk” math classrooms, “benefits increase further when students share their reasoning with one another”, and that the teacher plays a critical role in ensuring this happens effectively, because “left to their own devices, students will not necessarily engage in high-quality math-talk”!
In addition to skill-building oral language in my Grade 3 classroom this year through the use of “Grand Conversations”, I have recently (over the past two months) begun to use Fosnot’s “optimal mismatch” pairings in math: Rather than have students
Each student in my room is partnered with another student who is either just slightly stronger or slightly weaker than they are in some area. This way each person is working more or less with his/her intellectual peer, but has the opportunity to pull another learner along, or learn from the partner, since they are close but not precisely equal in skill and demonstrated understanding.
Pairing students in such a fashion is a trick I picked up during one of our trips to a classroom in a neighbouring school board. The teacher there not only had students working with teacher-selected math partners, but also organized her materials according to this match. For example, each pair of students was assigned a number, and the student whiteboard markers were labelled with each pair’s number, so that they are responsible for looking after their own marker. If it gets lost or damaged, oh well, too bad, so sad, now they have to use paper and pencil. (Interestingly, since I have implemented this system in my own classroom, we have had very few lost markers!!)
Having students paired up allows me to visit with two students at a time quite easily, and observe their individual work within the pair. It also allows students who prefer to work alone to do so periodically, without alienating a whole group of peers: We have an agreement in my classroom that most of the time, you work with your partner, and try to help one another reach a common math goal, but if you need to work alone sometime, you simply let your partner know – politely – that you prefer to work alone today, and your partner has to respect that. In this way, each student benefits from the acquisition of necessary social skills while still having some independence as a learner.
With a few small tweaks here and there, the original pairings I started in early winter are holding up, even through different strands of math. The odd time when I give students a choice of working with anyone they want to on a math problem, many will choose to work with their regular math partner!