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

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### 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.

### 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.

### 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.

### Courtney K. Baker, Terrie M. Galanti, Kimberly Morrow-Leong, and Tammy Kraft

The Teaching for Robust Understanding framework facilitates online collaborative problem solving with digital interactive notebooks that position all students as doers of 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.

### 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.

### Amanda K. Riske, Catherine E. Cullicott, Amanda Mohammad Mirzaei, Amanda Jansen, and James Middleton

We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.

Excerpts from discussion threads on the online MyNCTM community.