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Robert Powers and Michelle Chamberlin

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

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Ethan P. Smith, Jennifer Kelly, Susan Sappington, Kareemah Warren, and Amanda Jansen

Language is a conduit for communicating and understanding mathematical ideas. This article explores how we can use judicious telling to attend to students’ written and spoken literacy in mathematics.

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Maria Franshaw

Mathematics abounds in the beauty of the seasons. Where you live, work, or travel, how do you engage with and explore the wonders of math in our natural world?

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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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Eric Cordero-Siy and Hala Ghousseini

Three deliberate teaching practices can help students strengthen multiple connections to a unifying concept.

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F. Paul Wonsavage

Three approaches to the Doughnut task highlight how representing functions in multiple ways can support student understanding in interpreting key features of functions within a context.

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José N. Contreras

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Megan H. Wickstrom

Preservice elementary teachers (PSTs) often enter their teacher preparation programs with procedural and underdeveloped understandings of area measurement and its applications. This is problematic given that area and the area model are used throughout K–Grade 12 to develop flexibility in students’ mathematical understanding and to provide them with a visual interpretation of numerical ideas. This study describes an intervention aimed at bolstering PSTs’ understanding of area and area units with respect to measurement and number and operations. Following the intervention, results indicate that PSTs had both an improved ability to solve area tiling tasks as well as increased flexibility in the strategies they implemented. The results indicate that PSTs, similar to elementary students, develop a conceptual understanding of area from the use of tangible tools and are able to leverage visualizations to make sense of multiplicative structure across different strategies.

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Nicole Garcia, Meghan Shaughnessy, and D’Anna Pynes

Representing and recording student thinking in public spaces during mathematics discussions is challenging work. We share principles for recording student thinking in the moment and share an activity for improving your recording practice.

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Emiliano Gómez, Risa A. Wolfson, and Introduction by: Trena L. Wilkerson