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Varying the Intensity of Scaffolding for English Learners

Haiwen Chu, Jill Neumayer DePiper, and Leslie Hamburger

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

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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.

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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.

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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.

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Supporting Probability Understanding through Area Models

LouAnn H. Lovin

Moving beyond memorization of probability rules, the area model can be useful in making some significant ideas in probability more apparent to students. In particular, area models can help students understand when and why they multiply probabilities and when and why they add probabilities.

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What's in a Name? Language Use as a Mirror into Your Teaching Practice

Tracy E. Dobie and Miriam Gamoran Sherin

Language is key to how we understand and describe mathematics teaching and learning. Learning new terms can help us reflect on our practice and grow as teachers, yet may require us to be intentional about where and how we look for opportunities to expand our lexicons.

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Noticing before Responding

Julie M. Amador, David Glassmeyer, and Aaron Brakoniecki

This article provides a framework for integrating professional noticing into teachers' practice as a means to support instructional decisions. An illustrative example is included based on actual use with secondary students.

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Mathematical Explorations: A New Twist on Collaborative Learning

classroom-ready activities

Stephanie M. Butman

Research on students' learning has made it clear that learning happens through an interaction with others and through communication. In the classroom, the more students talk and discuss their ideas, the more they learn. However, within a one-hour period, it is hard to give everyone an equal opportunity to talk and share their ideas. Organizing students in groups distributes classroom talk more widely and equitably (Cohen and Lotan 1997).

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What's the Big Deal about Vocabulary?

Pamela J. Dunston and Andrew M. Tyminski

Techniques for teaching mathematics terminology allow adolescents to expand their abstract reasoning ability and move beyond operations into problem solving.

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Capturing Thinking on the Talk Frame

Tutita M. Casa

This instructional tool helps students engage in discussions that foster student reasoning, then settle on correct mathematics.