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

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## Let’s Give Them Something to Talk About

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

## Build It! The Rectangle Game

### Theresa Wills, Jennifer Suh, Kate Roscioli, Amanda Guzman, Jennifer Everdale, and Sandra Lee

Discover technology-enhanced, game-based tasks and student generalizations.

## Using Mathematics to Design a Droid

### George J. Roy, Matthew Cunningham, and Kenneth Rafanan

Teachers have the opportunity to make mathematics relevant. We leveraged the popularity of *Star Wars* to engage students in exploring and connecting two dimensions and three dimensions to careers in toy design.

## Exploring Grades 3–5 Mathematics Activities Found Online

### 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.

## Promoting Equitable PST Participation in Mathematical Discourse: Rough Drafts on an Asynchronous Discussion Board

### Margaret Rathouz, Nesrin Cengiz-Phillips, and Angela S. Krebs

Issues of equity in mathematics classrooms existed prior to COVID-19. For many students, however, meaningful participation in mathematical discussions became nearly impossible in online settings during the pandemic. In this study, we note the diversity in and nature of participation in mathematical discourse in an online course for preservice teachers (PSTs). We investigate the influence of implementing two support strategies for discussion: (a) establishing a “rough-draft/revision” orientation to mathematical tasks; and (b) providing time and structure (tasks and prompts) in an online discussion board for PSTs to post their initial thoughts, react to peers’ solutions, and collectively revise their ideas. In this article, we highlight several benefits of these support strategies to equitable PST participation in a unit on number theory. For example, as compared with oral discussions where only a few PSTs offered their ideas, the written discussion format encouraged every PST to post their ideas. Using a rough-draft/revision stance in the prompts fostered sharing and revealed diverse mathematical approaches, perspectives, and ideas. We argue that giving students opportunities to interact with one another and the mathematics in a variety of ways promotes equitable participation.

## Three-Act Tasks and Online Teaching

### Amanda T. Sugimoto and Heidi Meister

The authors draw on collaboration with a group of teachers to describe how three-act tasks could be (re)designed and implemented for online synchronous and asynchronous learning, identifying technological factors that teachers might consider.

## Empowering Latinx Families to Help Children with Mathematics

### Sabrina De Los Santos Rodríguez, Audrey Martínez-Gudapakkam, and Judy Storeygard

An innovative program addresses the digital divide with short, engaging videos modeling mathematic activities sent to families through a free mobile app.

## Exploring Matrices with Spreadsheets

### Marina Goodman

Bridge the digital divide by teaching students a useful technological skill while enhancing mathematics instruction focused on real-life matrix applications.

## Positioning Students to Explore Math with Technology

### Allison W. McCulloch, Jennifer N. Lovett, Lara K. Dick, and Charity Cayton

The authors discuss digital equity from the perspective of using math action technologies to position all students as mathematics explorers.