An unsolved problem gets elementary and middle school students thinking and doing mathematics like mathematicians.

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### Jenna R. O’Dell, Cynthia W. Langrall, and Amanda L. Cullen

### 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.

### Lara K. Dick, Mollie H. Appelgate, Dittika Gupta, and Melissa M. Soto

A group of mathematics teacher educators (MTEs) began a lesson study to develop a research-based lesson to engage elementary preservice teachers with professional teacher noticing within the context of multidigit multiplication. Afterward, MTEs continued teaching and revising the lesson, developing an integrated process that combined lesson study with the continuous improvement model. This article introduces the continuous improvement lesson study process, shares an example of how the process was used, and discusses how the process serves as a collaborative professional development model for MTEs across institutions.

### Hyunyi Jung, Ji-Won Son, and Ji-Yeong I

Use a COVID-19 lesson as an example of how to apply a framework aligned with research recommendations to support students as they apply mathematics to real life.

### S. Leigh Nataro

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

### Lindsay Vanoli and Jennifer Luebeck

Engaging mathematics students with peers in analyzing errors and formulating feedback improves disposition, increases understanding, and helps students uncover and correct misconceptions while informing opportunities for targeted instruction.

### Tiara Hicks and Jonathan D. Bostic

We describe a formative assessment approach called whole-class think alouds, which foster evidence-based instructional practices and promote the goal of assessment to promote learning. They allow students to collaborate and orally communicate their problem solving.

### Matt B. Roscoe

Symmetric dot patterns are a particularly powerful object for investigation, providing opportunities for foundational learning across PK–5. We found that second-grade students naturally used repeated addends to count symmetric dot patterns created using the new software TileFarm.

### Lucy A. Watson, Christopher T. Bonnesen, and Jeremy F. Strayer

Teachers can offer opportunities for K–12 students to reflect on the nature of mathematics (NOM) as they learn.