Different types of open tasks can be used as a tool to promote rigorous student mathematical discourse and considerations for facilitation.

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## Let’s Give Them Something to Talk About

### Nicola M. Hodkowski and Carolyn Carhart-Quezada

## Reconsidering Mathematical Authority

### Michael D. Hicks, Jessica Pierson Bishop, Christina Koehne, and Mai Bui

Who has mathematical authority in your classroom, and what does authority look like? Find out different ways you can help students gain authority.

## Using Public Records to Scaffold Joint Sense Making

### Keith R. Leatham, Blake E. Peterson, Ben Freeburn, Sini W. Graff, Laura R. Van Zoest, Shari L. Stockero, and Nitchada Kamlue

Teachers can more productively use board work to scaffold joint sense making.

## Ways to Help Students Become Powerful Mathematical Thinkers

### Alan H. Schoenfeld

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

## Discuss It! Collaborating on the Tortoise and Hare Task

### K. Ann Renninger, Maria Consuelo De Dios, Annie Fetter, Maeve R. Hogan, Moe Htet Kyaw, Ana G. Michels, Marina Nakayama, Richard Tchen, Stephen A. Weimar, Helena Werneck de Souza Dias, and Feven Yared

The authors share an online collaborative problem-solving activity that integrates support for students’ developing conceptual understanding, focused engagement, and positive feelings of agency and identity.

## Prove It! Graph Theory and Induction: The Next Big Thing

### Jeffrey P. Smith

Eighth-grade students participated in a two-day lab exploring graph theory. In addition to learning about a completely new topic, they experienced a subtle introduction to proof by induction.

## Filling Vases and Making Tanks

### Jana Dean

Two classic hands-on tasks address conceptual understanding of functions. The tasks center student discourse and rough draft mathematics as students grapple with the relationship between input and output.

## Poetic Equations

### Helena Soares

## GPS: Teaching Shapes Inclusively

### Samuel Otten, Tiffany J. LaCroix, Faustina Baah, and Rebekah Hanak

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

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Revisiting How to Foster and Improve S^{3}D

### Sarah Quebec Fuentes

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