From the Archives highlights articles from NCTM’s legacy journals, previously discussed by the *MTLT* Journal Club.

# Browse

### Blake E. Peterson, Douglas L. Corey, Benjamin M. Lewis, Jared Bukarau, and Introduction by: Wendy Cleaves

### Charles F. Marion

The simplest of prekindergarten equations, 1 + 2 = 3, is the basis for an investigation involving much of high school mathematics, including triangular numbers, arithmetic sequences, and algebraic proofs.

### Sandra J. Miles

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.

### 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.

### Jody Guarino, Shelbi Cole, and Michelle Sperling

In a humanized approach to assessment, the design of the instrument itself is only a small part of the overall process.

### Kaycie Maddox

This department provides a space for current and past PK–12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.

### Catherine A. Little, Sherryl Hauser, Jeffrey Corbishley, and Introduction by: Denise M. Walston

From the Archives highlights articles from NCTM’s legacy journals, as chosen by leaders in mathematics education.

### Sandra Vorensky

Design projects to encourage your students’ self-efficacy and motivate mathematics learning by helping them apply their prior knowledge from real-world experiences.

### Xiaobo She and Timothy Harrington

Get familiar with this visual instructional tool to help students make sense of mathematical relationships and select suitable operations for word problems at varied grade levels.

### 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.