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

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

### Rachel H. Orgel

Returning to in-person learning after COVID-19, our goal was to use our district’s framework along with the CASEL 5 to help us address the social and emotional learning needs of our students without losing the integrity of the mathematics.

### Kathryn Lavin Brave and Jillian Miller

Two teachers describe how to use Fermi Questions to illuminate the connections between the Standards for Mathematical Practice and the social and emotional learning competencies.

### 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.

### Luz A. Maldonado Rodríguez, Naomi Jessup, Marrielle Myers, Nicole Louie, and Theodore Chao

Elementary mathematics teacher education often draws on research-based frameworks that center children as mathematical thinkers, grounding teaching in children’s mathematical strategies and ideas and as a means to attend to equity in mathematics teaching and learning. In this conceptual article, a group of critical mathematics teacher educators of color reflect on the boundaries of Cognitively Guided Instruction (CGI) as a research-based mathematical instructional framework advancing equity through a sociopolitical perspective of mathematics instruction connected to race, power, and identity. We specifically discuss CGI along the dominant and critical approaches to equity outlined by , ) framework. We present strategies used to extend our work with CGI and call for the field to continue critical conversations of examining mathematical instructional frameworks as we center equity and criticality.

### Madelyn W. Colonnese

A teacher implements this type of personal prose in the classroom to help students make sense of fractions and communicate ideas.

### 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.

### 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.

### Heidi Fee

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

### Corinne Thatcher Day

This hands-on task, featuring differentiation and open-ended learning, sets up students to discover area models for themselves. Organized around NCTM’s eight teaching practices from *Principles to Actions*, this article describes the task’s setup and implementation.