Research on students' learning has made it clear that learning happens through an interaction with others and through communication. In the classroom, the more students talk and discuss their ideas, the more they learn. However, within a one-hour period, it is hard to give everyone an equal opportunity to talk and share their ideas. Organizing students in groups distributes classroom talk more widely and equitably (Cohen and Lotan 1997).
Stephanie M. Butman
D. Bruce Jackson
Given two slices of bread—a problem and the answer—students fill in the fixings: their own mathematics reasoning.
Amy F. Hillen and Tad Watanabe
Conjecturing is central to the work of reasoning and proving. This task gives fourth and fifth graders a chance to make conjectures and prove (or disprove) them.
Lisa A. Brooks and Juli K. Dixon
A second-grade teacher challenges the raise-your-hand-to-speak tradition and enables a classroom community of student-driven conversations that share both mathematical understandings and misunderstandings.
Sherri Ann Cianca
Communicating reasoning and constructing models fold nicely into a geometry activity involving the building of nesting boxes.
Wendy P. Ruchti and Cory A. Bennett
Solutions coupled with drawings can illustrate students' understandings or misunderstandings, particularly in the area of proportional reasoning.
Tutita M. Casa
This instructional tool helps students engage in discussions that foster student reasoning, then settle on correct mathematics.
Nicole R. Rigelman
Take a page from the humanities and have your students investigate mathematics in writing.
Jeffrey M. Choppin, Carolyn B. Clancy, and Scott J. Koch
Allowing students to reason and communicate about integer operations, or any idea, before these ideas are formalized can be an important tool for fostering deep understanding.
research matters for teachers
Kristen N. Bieda and Jerilynn Lepak
Research explores how to help students build from, instead of building with, examples when justifying mathematical ideas.