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.

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## GPS: Making Meaningful Use of Structure in PK–12

### Katherine Ariemma Marin and Natasha E. Gerstenschlager

## A New Twist on Fraction Equations

### Victoria R. Jacobs, Susan B. Empson, Joan M. Case, Amy Dunning, Naomi A. Jessup, Gladys Krause, and D’Anna Pynes

The authors introduce an activity involving “follow-up equations” to connect with ideas children have already expressed during fraction problem solving.

## Using Number Talks to Compare Fractions

### George J. Roy, Kristin E. Harbour, Christie Martin, and Matthew Cunningham

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.

## Developing Preservice Teachers’ Understanding of Area Through a Units Intervention

### Megan H. Wickstrom

Preservice elementary teachers (PSTs) often enter their teacher preparation programs with procedural and underdeveloped understandings of area measurement and its applications. This is problematic given that area and the area model are used throughout K–Grade 12 to develop flexibility in students’ mathematical understanding and to provide them with a visual interpretation of numerical ideas. This study describes an intervention aimed at bolstering PSTs’ understanding of area and area units with respect to measurement and number and operations. Following the intervention, results indicate that PSTs had both an improved ability to solve area tiling tasks as well as increased flexibility in the strategies they implemented. The results indicate that PSTs, similar to elementary students, develop a conceptual understanding of area from the use of tangible tools and are able to leverage visualizations to make sense of multiplicative structure across different strategies.

## Students as Teachers

### Heidi Fee

This article shows how to empower students in their own learning by their own creation of instructional videos and assessment.

## “Measurement and Fair-Sharing Models for Dividing Fractions”

### Jeff Gregg, Diana Underwood Gregg, and Introduction by: Melissa Boston

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

## Developing Skills for Exploring Children’s Thinking From Extensive One-on-One Work With Students

### Corey Webel and Sheunghyun Yeo

In this article, we share results from a field experience model in which junior-year methods classes were held in an elementary school and preservice teachers (PSTs) worked with a single student (a “Math Buddy") on mathematics for 30 minutes per day. We focus on the development of PSTs’ skills for exploring children’s thinking and the structures and tools that we used to support this development. Data sources include screencast recordings of interactions with Math Buddies and written reflections completed by PSTs. Although the responsiveness of interactions varied across individuals and interactions, in general, PSTs showed improvements in exploring children’s thinking. We share implications of these findings for similar field experience models and for practice-based approaches to teacher education generally.

## Formative Assessment through Think Alouds

### Tiara Hicks and Jonathan D. Bostic

We describe a formative assessment approach called whole-class think alouds, which foster evidence-based instructional practices and promote the goal of assessment to promote learning. They allow students to collaborate and orally communicate their problem solving.

## Keep Calm and Press for Reasoning

### Nancy Anderson

The questions that teachers ask to elicit student reasoning—often referred to as *press for reasoning*—help students explicate the concepts and principles that undergird their strategies. This article describes the term, addresses its benefits and challenges, and offers three routines.

## Playing with Fractions

### Juli K. Dixon, Treshonda Rutledge, Jennifer C. Caton, and Edward C. Nolan

Constraints for social distancing require teachers to find creative ways to engage students. Consider this fun strategy for exploring fraction equivalence, addition, and subtraction in a game environment where students use self-made or digital manipulatives.