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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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## Connecting Quadratics, Line Segments, Continued Fractions, and Matrices

One of the many benefits of teaching mathematics is having the opportunity to encounter unexpected mathematical connections while planning lessons or exploring ideas with students and colleagues. Consider the two problems in figure 1.

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## Letters to the editor

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## May 2019 Calendar and Solutions

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## Table Techniques

There is a distinction between using technology as a tool for doing mathematical tasks and using it to develop conceptual understanding (Dick and Hollebrands 2011). In this article, the table feature of the TI-84 Plus graphing calculator is used in the second role, enabling students to participate in the reasoning and sense-making process. This article showcases four classroom activities that use tables as a dynamic tool for inquiry, applying numerical representations to algebraic, graphical, and geometric phenomena. Although these activities are presented using the TI-84 Plus CE graphing calculator, other calculator and computer platforms can be employed; see the Teacher Guide in more4U for details.

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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.