Support students in conjecturing in ways that can promote their agency in the learning process.

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### Isabel White, Michael Foster, and Joanne Lobato

Explore three challenges that students faced and how they made progress.

### Christine Andrews-Larson, Jonee Wilson, Matthew Mauntel, Jessica Smith, and Thomeca Hawthorne-Glover

Support students in developing contextual reasoning about integer subtraction.

### Derek A. Williams, Kelly Fulton, Travis Silver, and Alec Nehring

A two-day lesson on taxicab geometry introduces high school students to a unit on proof.

### 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.

### Susan Ahrendt, Debra Monson, and Kathleen Cramer

Examine fourth graders’ thinking about the unit, partitioning, order, and equivalence on the number line and consider ways to orchestrate mathematical discussions through the Five Practices.

### Nicholas J. Gilbertson

When students encounter unusual situations or exceptions to rules, they can become frustrated and can question their understanding of particular topics. In this article, I share some practical tips.

### Anne Quinn

The paper discusses technology that can help students master four triangle centers -- circumcenter, incenter, orthocenter, and centroid. The technologies are a collection of web-based apps and dynamic geometry software. Through use of these technologies, multiple examples can be considered, which can lead students to generalizations about triangle centers.