Learning through explaining and engaging with others’ mathematical ideas

Abstract

Educators, researchers, and policy makers recognize that student participation in classroom mathematics conversations, especially explaining one’s own thinking and engaging with others’ ideas, can promote students’ mathematics learning. However, precisely how participating in these ways supports learning has not often been examined in detail. Using in-depth analyses of videotaped whole-class discussions, small-group collaborative work, and private partner conversations in two third-grade mathematics classrooms on six occasions over a five- month period, we show advances that students made in their mathematical thinking or mathematical work in the context of explaining their thinking and/or engaging with others’ ideas. The detailed analyses focus on students who had previously scored low on standardized tests of mathematics proficiency. The results show how students not considered to have extensive mathematics knowledge can forge new connections between mathematical ideas and representations, and extend their problem-solving strategies in ways that are directly related to their participation.