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## Students' Understanding of Counterexamples

This article focuses on students use and understanding of counterexamples and is part of a research project on the role of examples in proving. We share student interviews and offer suggestions for how teachers can support student reasoning and thinking and promote productive struggle by incorporating counterexamples into the classroom.

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## Capturing Mathematical Curiosity with Notice and Wonder

Capturing students' own observations before solving a problem propelled a culture of sense making by meeting needs typical of middle school learners.

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## Letters to the editor

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## May 2019 Calendar and Solutions

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## Transforming Middle School Geometry Instruction

Students move from slides, flips, and turns into reasoning about the characteristics of rigid transformations.

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## April 2019 Calendar and Solutions

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## Building Sets, Video Games, and Scatterplots

Explore the creation of a unique problem-based learning (PBL) experience.

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## Life in A-town

Welcome to A-town! All the residents of A-town have names that start with the letter A! Could you live here? Join these students as they solve problems around their neighborhood. Remember, math is everywhere.

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## The Sound of Thunder

You may have heard that if you are outside and see a flash of lightning, you can estimate the distance between you and the lightning strike fairly well by counting the number of seconds that pass between the lightning flash and the clap of thunder. The rule of thumb is that for every 5 seconds that pass before you hear the thunder, the lightning strike is 1 mile away.

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## The ABCs of Covariance

While filling three-dimensional letters, students analyzed the relationship between the height of water level and elapsed time.