Learn about strategies and tools to examine and improve your practice with respect to fostering equitable small-group, student-to-student discourse.

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### Alice Aspinall

This article describes how fortuitous mathematical moments should be noticed, encouraged, embraced, and capitalized upon.

### Madeline Corrigan

This manuscript describes my attitude and disposition toward mathematics at an early part in my educational career.

### Amanda K. Riske, Catherine E. Cullicott, Amanda Mohammad Mirzaei, Amanda Jansen, and James Middleton

We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.

Excerpts from discussion threads on the online MyNCTM community

### Cory A. Bennett and Mick J. Morgan

Chalk Talks, a silent discussion protocol, can be used to begin developing cocreated norms. The insights gained shaped the support provided by both the teacher and students throughout the year.

### Amber G. Candela, Melissa D. Boston, and Juli K. Dixon

We discuss how discourse actions can provide students greater access to high quality mathematics. We define discourse actions as what teachers or students say or do to elicit student contributions about a mathematical idea and generate ongoing discussion around student contributions. We provide rubrics and checklists for readers to use.

## Mathematical Explorations: A New Twist on Collaborative Learning

### classroom-ready activities

### 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).

### Corey Webel

Do you use group work in your mathematics class? What does it look like? What do you expect your students to do when they work together? Have you ever wondered what your students think they are supposed to do?

## Informing Practice: Examples as Tools for Constructing Justifications

### 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.