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

## 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.

## 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.

## Improving Our Criticism of Technology in Mathematics Education

### Craig J. Cullen and Joshua T. Hertel

Rather than centering technology, we need to view tools as raw materials that students can use strategically to build mathematical knowledge.

## 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.

## Enacting Co-Craft Questions Using Flexible Teaching Platforms

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

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

## 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.

## Math, Culture, Language, and Identity for Emergent Bilinguals

### Ricardo Martinez and Ji Yeong I

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

## 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.