Vary the intensity of pedagogical scaffolding along three dimensions—grouping, structure, and language—with the same rigorous prompt.

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## Varying the Intensity of Scaffolding for English Learners

### Haiwen Chu, Jill Neumayer DePiper, and Leslie Hamburger

## Student Engagement with the “Into Math Graph" Tool

### 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.

## Supporting Probability Understanding through Area Models

### LouAnn H. Lovin

Moving beyond memorization of probability rules, the area model can be useful in making some significant ideas in probability more apparent to students. In particular, area models can help students understand when and why they multiply probabilities and when and why they add probabilities.

## What's in a Name? Language Use as a Mirror into Your Teaching Practice

### Tracy E. Dobie and Miriam Gamoran Sherin

Language is key to how we understand and describe mathematics teaching and learning. Learning new terms can help us reflect on our practice and grow as teachers, yet may require us to be intentional about where and how we look for opportunities to expand our lexicons.

## Noticing before Responding

### Julie M. Amador, David Glassmeyer, and Aaron Brakoniecki

This article provides a framework for integrating professional noticing into teachers' practice as a means to support instructional decisions. An illustrative example is included based on actual use with secondary students.

## What's the Big Deal about Vocabulary?

### Pamela J. Dunston and Andrew M. Tyminski

Techniques for teaching mathematics terminology allow adolescents to expand their abstract reasoning ability and move beyond operations into problem solving.

## 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.

## 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.