Different types of open tasks can be used as a tool to promote rigorous student mathematical discourse and considerations for facilitation.

# Browse

## Let’s Give Them Something to Talk About

### Nicola M. Hodkowski and Carolyn Carhart-Quezada

## Adapt It! Adapting Stories and Technology for Engagement in Geometry

### Karen L. Terrell, Dennis J. DeBay, and Valerie J. Spencer

A task to develop and provide access to mathematics for all.

## Construct It! What’s in a Name? Collecting, Organizing, and Representing Data

### Eva Thanheiser, Courtney Koestler, Amanda T. Sugimoto, and Mathew D. Felton-Koestler

Build a classroom community by building representations and visualizations of data related to students’ names.

## Exploring Prospective Teachers’ Development of the Cartesian Form of Complex Numbers

### Gülseren Karagöz Akar, Merve Saraç, and Mervenur Belin

In this study, we investigated prospective secondary mathematics teachers’ development of a meaning for the Cartesian form of complex numbers by examining the roots of quadratic equations through quantitative reasoning. Data included transcripts of the two sessions of classroom teaching experiments prospective teachers participated in, written artifacts from these teaching sessions, and their answers to pre-and-post written assessment questions. Results point toward prospective teachers’ improved meanings regarding the definition of complex numbers and the algebraic and geometrical meanings of the Cartesian form of complex numbers. Implications for mathematics teacher education include providing specific tasks and strategies for strengthening the knowledge of prospective and in-service teachers.

## “Mathematics: The Universal Language?”

### Sharon B. Hoffert and Introduction by: Candies Cook

From the Archives highlights articles from NCTM’s legacy journals, previously discussed by the *MTLT* Journal Club.

## Experience First, Formalize Later

### Sarah Stecher, Luke Wilcox, and Lindsey Gallas

The EFFL model empowers students to build strong conceptual understanding of mathematics through carefully designed, equity-minded activities that disrupt the traditional lecture-based classroom.

## “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.

## Teaching Is a Journey: Math Talks for Agency, Identity, and Ownership

### Timothy L. Weekes

This department provides a space for current and past PK-12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.

## A Local Instruction Theory for Emergent Graphical Shape Thinking: A Middle School Case Study

### Teo Paoletti, Allison L. Gantt, and Julien Corven

Emergent graphical shape thinking (EGST) involves interpreting or constructing a graph as dynamically generated, which is useful across science, technology, engineering, and mathematics fields. Although evidence suggests that students as young as middle school can engage in EGST with support, other research indicates most college students and U.S. teachers do not spontaneously engage in such reasoning when potentially productive. We describe a local instruction theory (LIT) to support middle school students developing EGST as part of their graphing meanings. We then present a case study to show how two students engaged with a task sequence designed with the LIT in mind to develop meanings for EGST. This article illustrates general principles researchers and educators could use to promote students’ graphing meanings.

## Turning Trucks Into a Meaningful Geometry Exploration

### Kate Roscioli and Jennifer Suh

Learn how to engage students in geometry concepts through a real-world task that leverages GeoGebra to provide students with generalization and authorship opportunities.