Productive struggle is an essential part of mathematics instruction that promotes learning with deep understanding. A video scenario is used to provide a glimpse of productive struggle in action and to showcase its characteristics for both students and teachers. Suggestions for supporting productive struggle are provided.

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### Katherine Baker, Naomi A. Jessup, Victoria R. Jacobs, Susan B. Empson, and Joan Case

### Amanda Milewski and Daniel Frohardt

Few high school students associate mathematics with playfulness. In this paper, we offer a series of lessons focused on the underlying algebraic structures of the Rubik's Cube. The Rubik's Cube offers students an interesting space to enjoy the playful side of mathematics, while appreciating mathematics otherwise lost in routine experiences.

### Amber G. Candela, Melissa D. Boston, and Juli K. Dixon

We discuss how discourse actions can provide students greater access to high quality mathematics. We define discourse actions as what teachers or students say or do to elicit student contributions about a mathematical idea and generate ongoing discussion around student contributions. We provide rubrics and checklists for readers to use.

### Sandra M. Linder and Amanda Bennett

This article presents examples of how early childhood educators (prek-2nd grade) might use their daily read alouds as a vehicle for increasing mathematical talk and mathematical connections for their students.

### 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.

### J. Michael Shaughnessy

In celebration of NCTM's 100th birthday I'm very pleased to have this opportunity to share this retrospective on two early career events that had a big impact on mathematics education nationally and internationally, and turned out to be surprisingly instrumental in my own professional development.

### 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.

### Jessica T. Ivy, Sarah B. Bush, and Barbara J. Dougherty

To promote reversibility and strengthen number sense, we created an engaging and novel rational number exploration, which promoted flexible and reflective thinking. A class of fifth-grade students took an active role in a collaborative learning task, discussed their strategies, revisited the task, and reflected on their self-constructed generalizations.

### Aaron Trocki

The advent of dynamic geometry software has changed the way students draw, construct, and measure by using virtual tools instead of or along with physical tools. Use of technology in general and of dynamic geometry in particular has gained traction in mathematics education, as evidenced in the Common Core State Standards for Mathematics (CCSSI 2010).

### Corey Webel

Do you use group work in your mathematics class? What does it look like? What do you expect your students to do when they work together? Have you ever wondered what your students think they are supposed to do?