Vary the intensity of pedagogical scaffolding along three dimensions—grouping, structure, and language—with the same rigorous prompt.

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## Varying the Intensity of Scaffolding for English Learners

### Haiwen Chu, Jill Neumayer DePiper, and Leslie Hamburger

## Let’s Give Them Something to Talk About

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

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

## 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.

## 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.

## 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.

## Translanguaging Pedagogy in Elementary Mathematics

### Tara M. Willging and Luciana C. de Oliveira

A monolingual English-speaking teacher reflects on her experiences practicing a translanguaging stance in first grade with two multilingual learners and provides a set of guiding principles.

## Teaching Is a Journey: Vulnerability in Our Work as Educators

### Taylee Nelson

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.