This lesson uses the pH scale to build students’ understanding of the additive identity and inverse. It also gives suggestions for how to extend the lesson to multiplication.

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### Susanne Prediger, Kirstin Erath, Henrike Weinert, and Kim Quabeck

Empirical evidence exists that enhancing students’ language can promote the mathematics learning of multilingual students at risk, whereas other target groups (e.g., monolingual students, successful students, both with diverse academic language proficiency) have hardly been considered. This cluster-randomized controlled trial (*N* = 589) investigates differential effects for these extended target groups, comparing two language-responsive interventions (with or without vocabulary work) and a control group. The regression analysis reveals that all students significantly deepened their conceptual understanding in both interventions. Unlike what was anticipated, multilingual students’ growth of conceptual understanding had no significant additional benefit from integrated vocabulary work. These findings call for promoting language-responsive mathematics instruction for all students and for using a discursive rather than a vocabulary focus.

### Dorothy Y. White

Use this activity to support students in working together, recognizing one another’s contributions, and leveraging their mathematical strengths to solve challenging problems.

### S. Asli Özgün-Koca, Kelly Hagan, Rebecca Robichaux-Davis, and Jennifer M. Bay-Williams

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

### Min Wang, Candace Walkington, and Koshi Dhingra

An example of an after-school club activity gives educators some tools and suggestions to implement such an approach in their schools.

### Jonathan D. Bostic, Brooks Vostal, and Timothy Folger

All students have strengths that can be leveraged through universally designed instruction.

### Christine Taylor and Jean S. Lee

We implemented a STEM task that highlights the engineering cycle and engages students in productive struggle. Students problem solved in productive ways and saw tangible benefits of revising their work to achieve mathematical goals.

### Caroline Byrd Hornburg, Heather Brletic-Shipley, Julia M. Matthews, and Nicole M. McNeil

Modify arithmetic problem formats to make the relational equation structure more transparent. We describe this practice and three additional evidence-based practices: (1) introducing the equal sign outside of arithmetic, (2) concreteness fading activities, and (3) comparing and explaining different problem formats and problem-solving strategies.

### Angela Just and Jennifer D. Cribbs

The authors outline the importance of using variety when teaching mathematics.

### Deborah M. Thompson and A. Susan Gay

This article provides actionable steps and tools for teachers to use to promote student discourse while teaching multiplication fact strategies.