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Charles F. Marion

The simplest of prekindergarten equations, 1 + 2 = 3, is the basis for an investigation involving much of high school mathematics, including triangular numbers, arithmetic sequences, and algebraic proofs.

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Taea Fonkert

This department provides a space for current and past PK-12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.

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George J. Roy, Kristin E. Harbour, Christie Martin, and Matthew Cunningham

Using this strategy, a teacher facilitates a short conversation during which students verbally explain and justify reasoning. We have found that a coordinated series of number talks supports students’ reasoning when comparing fractions.

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Jen Munson, Geetha Lakshminarayanan, and Thomas J. Rodney

Off You Go is a PK–12 mathematical routine that leverages children’s home resources and assets to support them in developing conceptual precision. We provide a guide for how to adapt this routine to engage students at any grade in argumentation and attending to precision.

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Ruthmae Sears

This article describes how visual representations can help develop students’ reasoning and proof skills.

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Alexandra Martinez

This department provides a space for current and past PK–12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.

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José N. Contreras

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Jennifer M. Bay-Williams

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Molly Rawding and Steve Ingrassia

Problems to Ponder provides 28 varying, classroom-ready mathematics problems that collectively span PK–12, arranged in the order of the grade level. Answers to the problems are available online. Individuals are encouraged to submit a problem or a collection of problems directly to mtlt@nctm.org. If published, the authors of problems will be acknowledged.

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Rick Anderson and Peter Wiles

Recognizing the complex nature of students’ geometric reasoning, we present guidelines and suggestions for implementing a Guess My Shape minilesson that focuses students’ attention on properties and attributes of geometric shapes.