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

## Reconsidering Mathematical Authority

### Michael D. Hicks, Jessica Pierson Bishop, Christina Koehne, and Mai Bui

Who has mathematical authority in your classroom, and what does authority look like? Find out different ways you can help students gain authority.

## Translanguaging Pedagogy in Elementary Mathematics

### Tara M. Willging and Luciana C. de Oliveira

A monolingual English-speaking teacher reflects on her experiences practicing a translanguaging stance in first grade with two multilingual learners and provides a set of guiding principles.

## Building Equitable Math Talk Classrooms

### Karen C. Fuson and Steve Leinwand

The power of Number Talks and extensions that can build to an equitable Math Talk Classroom

## 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.

## Subtraction, Decomposition, and Argumentation

### Chepina Rumsey, Jody Guarino, and Michelle Sperling

We describe how mathematical argumentation supports curiosity and exploration by sharing a first-grade lesson in which students explored decomposition with subtraction. We also reflect on the conditions that supported the inclusion of mathematical argumentation.

## Same Task but Different Learning Goals

### Stephanie D. Sigmon, Kelly Q. Halpin, Damien J. Ettere, and Jennifer Suh

This article models how to plan and facilitate implementing the same task in two sixth-grade classrooms with two different learning goals using the Five Practices structure.

## Mathematical Discussions: Revealing Biases

### Ashley Schmidt, Treshonda Rutledge, Tandrea Fulton, and Sarah B. Bush

Do you use mathematical discussions to increase engagement in your classroom? In this Front and Center article, authors provide a discourse tool that can be used to reveal potential biases found in the implementation of the Five Practices.

## A New Twist on Fraction Equations

### Victoria R. Jacobs, Susan B. Empson, Joan M. Case, Amy Dunning, Naomi A. Jessup, Gladys Krause, and D’Anna Pynes

The authors introduce an activity involving “follow-up equations” to connect with ideas children have already expressed during fraction problem solving.

## Using Number Talks to Compare Fractions

### George J. Roy, Kristin E. Harbour, Christie Martin, and Matthew Cunningham

Using this strategy, a teacher facilitates a short conversation during which students verbally explain and justify reasoning. We have found that a coordinated series of number talks supports students’ reasoning when comparing fractions.