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Blake Peterson

Examining the covariation of triangle dimensions and area offers a geometric context that makes analyzing a piecewise function easier for students.

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Deanna Pecaski McLennan

For the Love of Mathematics

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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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Lindsay Vanoli and Jennifer Luebeck

Engaging mathematics students with peers in analyzing errors and formulating feedback improves disposition, increases understanding, and helps students uncover and correct misconceptions while informing opportunities for targeted instruction.

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Kelly Curtis, Katrina Lindo, and Amanda Jansen

When a ninth-grade teacher used discourse moves aligned with responding to students’ thinking and explicitly promoting productive dispositions, her students reported having positive experiences.

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Micah S. Stohlmann

An escape room can be a great way for students to apply and practice mathematics they have learned. This article describes the development and implementation of a mathematical escape room with important principles to incorporate in escape rooms to help students persevere in problem solving.

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Tim Erickson

We modify a traditional bouncing ball activity for introducing exponential functions by modeling the time between bounces instead of the bounce heights. As a consequence, we can also model the total time of bouncing using an infinite geometric series.

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Erin E. Baldinger, Matthew P. Campbell, and Foster Graif

Students need opportunities to construct definitions in mathematics. We describe a sorting activity that can help students construct and refine definitions through discussion and argumentation. We include examples from our own work of planning and implementing this sorting activity to support constructing a definition of linear function.

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Rebecca Vinsonhaler and Alison G. Lynch

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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Patrick Sullivan

Is the “Last Banana” game fair? Engaging in this exploration provides students with the mathematical power to answer the question and the mathematical opportunity to explore important statistical ideas. Students engage in simulations to calculate experimental probabilities and confirm those results by examining theoretical probabilities