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Jon R. Star, Soobin Jeon, Rebecca Comeford, Patricia Clark, Bethany Rittle-Johnson, and Kelley Durkin

CDMS is a routine that allows teachers to organize instruction around students’ mathematical discussions and multiple problem-solving methods.

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Deanna Pecaski McLennan

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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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Sarah Brand, Hyunyi Jung, Ashley Dorlack, and Samuel Gailliot

Five teacher discussion strategies and outcomes of students’ responses to each are illustrated with examples.

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Sean P. Yee, George J. Roy, and LuAnn Graul

As mathematical patterns become more complex, students' conditional reasoning skills need to be nurtured so that students continue to critique, construct, and persevere in making sense of these complexities. This article describes a mathematical task designed around the online version of the game Mastermind to safely foster conditional reasoning.

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Matt Enlow and S. Asli Özgün-Koca

Equality is one of the main concepts in K–12 mathematics. Students should develop the understanding that equality is a relationship between two mathematical expressions. In this month's GPS, we share tasks asking students one main question: how do they know whether or not two mathematical expressions are equivalent?

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Scott Corwin, Michelle Cascio, Katherine Emerson, Laura Henn, and Catherine Lewis

Our middle school mathematics department used lesson study to investigate how to introduce fractions division to our sixth-grade students. We highlight our learnings during the Study and Plan phases, describe our observations during the lesson, and provide tips for educators interested in using lesson study to study their own content.

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Aline Abassian and Farshid Safi

This article dives into the importance of engaging students in investigating the mathematics of businesses that pressure their members to recruit new members as a basis for success, also referred to as multi-level marketing (MLM). The mathematics behind these businesses are discussed, and a sample student task is given.

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Angela T. Barlow

Editor Comments for May 2020 issue

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

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.