The Building Painted Cubes Task is a groupworthy algebraic task. Students build cubes using linking unit cubes, search for algebraic patterns, and report findings on posters. This task can create spaces for students to see themselves as doers of mathematics.

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## Construct It! Building Painted Cubes Task: Serena’s Case

### Elizabeth Suazo-Flores and Lisa Roetker

## Digital Learning Routes: An Example of Mathematical Modeling

### Salomé Martínez, Flavio Guiñez, and Darío González

An online activity provides instructional strategies that can help students engage in mathematical modeling and autonomous learning.

## Ways to Help Students Become Powerful Mathematical Thinkers

### Alan H. Schoenfeld

Ear to the Ground features voices from several corners of the mathematics education world.

## “Rahul is a Math Nerd” and “Mia Can Be a Drama Queen”: How Mixed-Reality Simulations Can Perpetuate Racist and Sexist Stereotypes

### Liza Bondurant and Daniel Reinholz

This article focuses on using simulations of practice in teacher education. We studied preservice teachers’ engagement with a popular simulations platform, which creates *mixed-reality simulations* of five digital avatars controlled by a single live interactor. Because simulations are only an approximation of real practice, our overarching goal was to understand how mathematical stereotypes might arise in simulated spaces. We used Discourse analysis to classify the stereotypes present and the EQUIP observation tool to understand how PTs made participation opportunities available. We found that the simulations might have perpetuated overtly racist and sexist stereotypes and that negatively stereotyped students were afforded lower-quality opportunities to participate. We discuss how to mitigate potential harm caused and offer guidance for redesigning more equitable and antiracist simulations. Our goal is to raise critical questions for our field around the use of simulations of practice.

## Conceiving Phase Shift as Time Travel

### Jeffrey Connelly and Pablo Garcia

Two teachers use homemade pendulums for their students to explore phase shift in sine curves. The use of Desmos’s Activity Builder enabled students to become mathematical explorers and supported their sense of mathematical agency.

## The Hidden Beauty of Complex Numbers

### Juan Carlos Ponce Campuzano

## Rethinking Wait Time: What Can 3 Seconds Do?

### Kathryn Early, K. Elizabeth Hammonds, Brea Ratliff, Mariya Rosenhammer, and W. Gary Martin

A high-leverage strategy first discussed more than 50 years ago, wait time has many benefits for both teachers and students yet is not used to its full potential. See how it can enhance your students’ mathematical discourse.

## Using Judicious Telling to Strengthen Literacy in Mathematics

### Ethan P. Smith, Jennifer Kelly, Susan Sappington, Kareemah Warren, and Amanda Jansen

Language is a conduit for communicating and understanding mathematical ideas. This article explores how we can use judicious telling to attend to students’ written and spoken literacy in mathematics.

## Approximating Pi

### Lidia Gonzalez

This method using the area of regular polygons inscribed in circles to approximate a value for pi is similar to the method used by Archimedes using circumferences.

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Variations on a Theme of Fibonacci^{
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### Sheldon P. Gordon and Michael B. Burns

We introduce variations on the Fibonacci sequence such as the sequences where each term is the sum of the previous three terms, the difference of the previous two, or the product of the previous two. We consider the issue of the ratio of the successive terms in ways that reinforce key behavioral concepts of polynomials.