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.

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

### Surani Joshua, James Drimalla, Dru Horne, Heather Lavender, Alexandra Yon, Cameron Byerley, Hyunkyoung Yoon, and Kevin Moore

The Relative Risk Tool web app allows students to compare risks relating to COVID-19 with other more familiar risks, to make multiplicative comparisons, and to interpret them.

### Jere Confrey, Meetal Shah, and Alan Maloney

Three learning trajectories and their connections show how to promote vertical coherence in PK–12 mathematics education.

### Rachel Lambert

In this article, I propose a mathematical version of Universal Design for Learning called UDL Math. I describe three classrooms that include students with disabilities in meaningful mathematics and explore how the teachers create access through multiple means of engagement, representation, and strategic action.

### 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.

### Crystal Kalinec-Craig, Emily P. Bonner, and Traci Kelley

This article describes an innovation in an elementary mathematics education course called SEE Math (Support and Enrichment Experiences in Mathematics), which aims to support teacher candidates (TCs) as they learn to teach mathematics through problem solving while promoting equity during multiple experiences with a child. During this 8-week program, TCs craft and implement tasks that promote problem solving in the context of a case study of a child’s thinking while collecting and analyzing student data to support future instructional decisions. The program culminates in a mock parent–teacher conference. Data samples show how SEE Math offers TCs an opportunity to focus on the nuances of children’s strengths rather than traditional measures of achievement and skill.

### Zachary Champagne

Providing students the autonomy and choice to learn when productive struggle becomes unproductive is a core teaching belief in the author’s classroom. This article tells the story of one student’s ability to know and express when his frustration was too great and how he chose to walk away from his work and return the next day.

### Theresa J. MacVicar, Amy R. Brodesky, and Emily R. Fagan

A teacher uses formative assessment interviews to uncover evidence of students’ understandings and to plan targeted instruction in a mathematics intervention class. We present an example of a student interview, a discussion of the benefits and challenges of conducting interviews, and actionable suggestions for implementing them.

### Hyunyi Jung and Sarah Brand

Five approaches led to multiple valid solutions, considered students’ real-world knowledge, and increased students’ interest.