Learning trajectories help teachers challenge children at just the right level for their best learning.

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### Douglas H. Clements, Shannon S. Guss, and Julie Sarama

### Carybeth Hobbs

This article describes how fortuitous mathematical moments should be noticed, encouraged, embraced, and capitalized upon.

### Alice Aspinall

This article describes how fortuitous mathematical moments should be noticed, encouraged, embraced, and capitalized upon.

### 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.

### Johnnie Wilson

This department provides a space for current and past PK–12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.

### 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.

### 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.

### 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.

### Elizabeth P. Cunningham

Teachers can use short periods in their classroom to build children’s experiences with and understanding of mathematics, outside of mathematics time.