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Beyond the Sign Rules

Are your students negative about integers? Help them experience positivity and joy doing integer arithmetic!

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“Measurement and Fair-Sharing Models for Dividing Fractions”

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

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Student Engagement with the “Into Math Graph" Tool

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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Support and Enrichment Experiences in Mathematics (SEE Math): Using Case Studies to Improve Mathematics Teacher Education

This article describes an innovation in an elementary mathematics education course called SEE Math (Support and Enrichment Experiences in Mathematics), which aims to support teacher candidates (TCs) as they learn to teach mathematics through problem solving while promoting equity during multiple experiences with a child. During this 8-week program, TCs craft and implement tasks that promote problem solving in the context of a case study of a child’s thinking while collecting and analyzing student data to support future instructional decisions. The program culminates in a mock parent–teacher conference. Data samples show how SEE Math offers TCs an opportunity to focus on the nuances of children’s strengths rather than traditional measures of achievement and skill.

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One Task, Multiple Proportional Reasoning Strategies

Tasks and materials that allow for different approaches can help teachers incorporate student reasoning and can promote connections across different mathematical ideas.

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Supporting Probability Understanding through Area Models

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

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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GPS: Spring Frogs

April 2020's GPS department provides tasks for each grade band that invite students to reason with age-appropriate number theoretic concepts.

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Noticing before Responding

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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Now: The Metamorphosis of the Educational World

“It's a YouTube World” (Schaffhauser, 2017), and educators are using digital tools to enhance student learning now more than ever before. The research question scholars need to explore is “what makes an effective instructional video?”.