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

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## Advancing Agency Through Conjecturing

### Kristin Doherty

## Making Sense of Algebraic Expressions in Context

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

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

## Balloons and Weights: Integer Subtraction in Context

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

Support students in developing contextual reasoning about integer subtraction.

## Exploring Young Children’s Math Thinking in Sandcastle Building

### Hannah Tan and Cynthia Lim

Children explore concepts of capacity and height measurement through sand play in nursery class.

## Math, Will You Be My Valentine?

### Jennifer M. Bay-Williams

## Non-Euclidean Geometry Lesson Promotes Mathematical Reasoning

### 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.

## Puddle Play!

### Deanna Pecaski McLennan

## Examining Errors and Framing Feedback

### 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.

## Promoting Discourse: Fractions on Number Lines

### 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.

## The Opportunities of No-Solution Problems

### 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.