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Julie M. Amador, David Glassmeyer and Aaron Brakoniecki

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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Susan Baker Empson, Victoria R. Jacobs, Naomi A. Jessup, Amy Hewitt, D'Anna Pynes and Gladys Krause

The complexity of understanding unit fractions is often underappreciated in instruction. We introduce a continuum of children's understanding of unit fractions to explore this complexity and to help teachers make sense of children's strategies and recognize milestones in the development of unit-fraction understanding. Suggestions for developing this understanding are provided.

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JoAnne Growney

Sophia Kovalevsky's story

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Alyson E. Lischka and D. Christopher Stephens

The area model for multiplication can be used as a tool to help learners make connections between mathematical concepts that are included in mathematics curriculum across grade levels. We present ways the area model might be used in teaching about various concepts and explain how those ideas are connected.

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George J. Roy, Jessica S. Allen and Kelly Thacker

In this paper we illustrate how a task has the potential to provide students rich explorations in algebraic reasoning by thoughtfully connecting number concepts to corresponding conceptual underpinnings.

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Krista L. Strand and Katie Bailey

K-5 teachers deepen their understanding of the Common Core content standards by engaging in collaborative drawing activities during professional development workshops.

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Nicholas H. Wasserman, Keith Weber, Timothy Fukawa-Connelly and Juan Pablo Mejía-Ramos

A 2D version of Cavalieri's Principle is productive for the teaching of area. In this manuscript, we consider an area-preserving transformation, “segment-skewing,” which provides alternative justification methods for area formulas, conceptual insights into statements about area, and foreshadows transitions about area in calculus via the Riemann integral.

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Alyson E. Lischka, Kyle M. Prince and Samuel D. Reed

Encouraging students to persevere in problem solving can be accomplished using extended tasks where students solve a problem over an extended time. This article presents a structure for use of extended tasks and examples of student thinking that can emerge through such tasks. Considerations for implementation are provided.

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Ed Dickey

A personal reflection by Ed Dickey on the influence and legacy of NCTM's journals.

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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