### Karen C. Fuson and Steve Leinwand

The power of Number Talks and extensions that can build to an equitable Math Talk Classroom

### Kelly Overby Byrd, Kayla Cooper, Raegan Bolger, and Heather Treece

We share two examples of student engagement in visible, mathematical thinking through a Chalk Talk within the four walls of the classroom, as well as the connected spaces of online learning. Five steps for facilitating the Chalk Talk are outlined, with descriptions of teacher moves for each step.

### Yael Luz and Michal Yerushalmy

We report on an innovative design of algorithmic analysis that supports automatic online assessment of students’ exploration of geometry propositions in a dynamic geometry environment. We hypothesized that difficulties with and misuse of terms or logic in conjectures are rooted in the early exploration stages of inquiry. We developed a generic activity format for if–then propositions and implemented the activity on a platform that collects and analyzes students’ work. Finally, we searched for ways to use variation theory to analyze ninth-grade students’ recorded work. We scored and classified data and found correlation between patterns in exploration stages and the conjectures students generated. We demonstrate how automatic identification of mistakes in the early stages is later reflected in the quality of conjectures.

### Karen Zwanch and Bridget Broome

This game teaches algebraic generalizations through differentiated play in pairs, small groups, or as a whole class and uses manipulatives to bridge numerical and algebraic thinking.

### T. Royce Olarte and Sarah A. Roberts

Teachers can implement a mathematics language routine within in-person/hybrid and remote instructional contexts.

### Lara K. Dick, Amanda G. Sawyer, Margaret MacNeille, Emily Shapiro, and Tabitha A. Wismer

We investigate resources on TeachersPayTeachers and discuss how what is available affects our teaching practices.

### Katherine Ariemma Marin and Natasha E. Gerstenschlager

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.

### Patricio Herbst

My academic family lost our patriarch, Jeremy Kilpatrick, on September 17, 2022. As I write this in October, reflecting on his legacy to our field feels timely. After a brief biographical sketch, I explore how Jeremy's influence, particularly in his role as Editor in Chief of JRME, shaped our field—and my own work as editor.