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

# Browse

## Varying the Intensity of Scaffolding for English Learners

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

## 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.

## Using Number Talks to Compare Fractions

### George J. Roy, Kristin E. Harbour, Christie Martin, and Matthew Cunningham

Using this strategy, a teacher facilitates a short conversation during which students verbally explain and justify reasoning. We have found that a coordinated series of number talks supports students’ reasoning when comparing fractions.

## “Constructing Complexity for Differentiated Learning”

### Catherine A. Little, Sherryl Hauser, Jeffrey Corbishley, and Introduction by: Denise M. Walston

From the Archives highlights articles from NCTM’s legacy journals, as chosen by leaders in mathematics education.

## The Importance of Play in Middle School Mathematics

### Kate Degner

Using question 28 from the May Problems to Ponder in volume 114, the author and her seventh- and eighth-grade students launched into a discussion of creativity, linearity, piecewise, and recursive definitions of functions. This pattern to ponder provided rich mathematical opportunities for all students in my middle school classroom.

## Student Engagement with the “Into Math Graph" Tool

### 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.

## Developing Spatial Skills through Mental Rotation Activities

### Atara Shriki and Dorit Patkin

Success in STEM fields depends largely on robust spatial skills, in particular on the ability to perform a mental rotation. Given that this ability can be nurtured, this article includes examples of diverse relevant tasks appropriate for grades 6–8 students.

## Launching a Mathematical Modeling Lesson

### Sarah Brand, Hyunyi Jung, Ashley Dorlack, and Samuel Gailliot

Five teacher discussion strategies and outcomes of students’ responses to each are illustrated with examples.

## 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.