### Amber G. Candela and Melissa Boston

In this article we detail a research study using the Instructional Quality Assessment (IQA) Rubrics () as the frame for a professional development with mathematics teachers in grades 3-8. We wanted to create a professional development around a tool that was typically used in research as a way to observe teachers, as a tool to use with teachers on their reflection of instruction. In this study we share both the researchers’ and teachers’ perspectives of affordances and constraints of the professional development and observational rubrics.

### Carybeth Hobbs

This article describes how fortuitous mathematical moments should be noticed, encouraged, embraced, and capitalized upon.

### 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.

### Christopher C. Jett, Cathery Yeh, and Maria del Rosario Zavala

Critical Race Theory (CRT) has entered into public discourse at an accelerated rate. Instead of using CRT as a basis to produce a more racially conscious populace, the latest hysteria, unfortunately, has centered on banning CRT. Governmental actions have been instituted to establish executive orders to forbid CRT training. Administrators and educators have been written up, suspended, and even terminated for teaching about race. The current landscape around CRT is about censoring race-related discussions and obstructing any advancements in service to racial equity and justice. In the educational arena, more than 20 states have banned CRT from being taught in

### Farshid Safi, Sarah B. Bush, Siddhi Desai, and Introduction by: Kevin J. Dykema

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

### Chunlian Jiang and Eunmi Joung

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.

### 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.

### Amanda T. Sugimoto

Mathematics standards and practices highlight the vital role that language plays in mathematics education. However, there remains a common misconception that mathematics is somehow language-free or less linguistically demanding than other content areas. This qualitative study describes an intervention implemented in six elementary mathematics methods courses. The intervention was designed to attune prospective teachers’ noticing to the language modalities and supports in mathematics teaching and learning. The intervention began with an observation tool that prospective teachers completed in their field placement classrooms. This article classifies prospective teachers’ noticings and explicates how these noticing became a pedagogical catalyst for further learning and discussion in subsequent mathematics methods classes.