Using this strategy, a teacher facilitates a short conversation during which students verbally explain and justify reasoning. We have found that a coordinated series of number talks supports students’ reasoning when comparing fractions.
Using Number Talks to Compare Fractions
George J. Roy, Kristin E. Harbour, Christie Martin, and Matthew Cunningham
The Opportunities of No-Solution Problems
Nicholas J. Gilbertson
When students encounter unusual situations or exceptions to rules, they can become frustrated and can question their understanding of particular topics. In this article, I share some practical tips.
Mathematical Explorations: A New Twist on Collaborative Learning
Stephanie M. Butman
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).
Algebra Homework: A Sandwich!
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.
Changing the Rules to Increase Discourse
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.
Bird Boxes Build Content Area Knowledge
Sherri Ann Cianca
Communicating reasoning and constructing models fold nicely into a geometry activity involving the building of nesting boxes.
Develop Reasoning through Pictorial Representations
Wendy P. Ruchti and Cory A. Bennett
Solutions coupled with drawings can illustrate students' understandings or misunderstandings, particularly in the area of proportional reasoning.
Capturing Thinking on the Talk Frame
Tutita M. Casa
This instructional tool helps students engage in discussions that foster student reasoning, then settle on correct mathematics.
Becoming a Mathematical Problem Solver
Nicole R. Rigelman
Take a page from the humanities and have your students investigate mathematics in writing.