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.

# Browse

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

### Daniel Frischemeier

Bar graphs are fundamental to display distributions of categorical variables in primary school. Here is an approach using TinkerPlots™ to create bar graphs on different representation levels in small and large data sets.

### Mindy Kalchman

Process-oriented, question-asking techniques provide a framework for approaching modern challenges, including modality pivots and student agency.

### 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.

### Jenna R. O’Dell, Cynthia W. Langrall, and Amanda L. Cullen

An unsolved problem gets elementary and middle school students thinking and doing mathematics like mathematicians.

### 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.

### Stacy R. Jones and Carlos Nicolas Gomez Marchant

Through a composite counter-story from the perspective of fifth-grade Raza learners, the authors show how race and language play a role in the mathematics classroom.

### 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.