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Lindsay Reiten

Guiding questions and a task-analysis framework support teachers in using virtual manipulatives to enhance student understanding.

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Teri N. Johnson and Stephen I. Tucker

During the past thirty years, various forms of technology have facilitated teaching and learning. Recently, touchscreen tablets are among the devices growing in popularity. Many mathematics apps are available; however, they vary in their usefulness for different users. Monitoring students' interactions with selected apps is important for teachers to do to ensure that earners are benefiting from technology integration. The Modification of Attributes, Affordances, Abilities, and Distance (MAAAD) for Learning Framework (see fig. 1) emerged from evaluations of students' interactions with educational technology (Tucker 2016). Teachers can use this framework to select apps for use in the classroom, formatively assess student understanding, and evaluate the appropriateness of tasks presented by apps.

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Adam Clinch

Justifications, methods, and results compare two classes of students who used a new technique that ties together procedural fluency and conceptual understanding in a manner unlike other current strategies.

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Redeem Reasoning

readers speak out

Kuo-Liang Chang

This opinion piece discusses how simplicity, ease, and efficiency—in the guise of shortcuts, tips, and packed procedures—kill mathematical reasoning.

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Frieda Parker and Vida Treviño

This activity engages students in a lesson about algebraic relationships concerning groupings of hamburgers and French fries, coupled with full-page activity sheets.

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Joanna B. Stegall and Jacquelynn A. Malloy

An algebra 1 teacher collaborated with two university researchers to develop vocabulary minilessons and peer discussions to support students in understanding and using algebraic language.

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Cherie Lynn Ichinose and Armando M. Martinez-Cruz

A Diophantine equation engages mathematics students as they problem solve.

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Jerilynn Lepak and Taren Going

In an eighth-grade classroom, the authors used the Connected Math Project curriculum and three essential components of an argument implied by Driscoll (1999) to adapt mathematical tasks to elicit written arguments that go beyond recounting steps.

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Susan F. Zielinski and Michael Glazner

Help students stop making typical, persistent errors related to misconceptions about exponents, distribution, fraction simplification, and more.

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Orly Buchbinder, Daniel I. Chazan, and Michelle Capozzoli

Many research studies have sought to explain why NCTM's vision for mathematics classrooms has not had greater impact on everyday instruction, with teacher beliefs often identified as an explanatory variable. Using instructional exchanges as a theoretical construct, this study explores the influence of teachers' institutional positions on the solving of equations in algebra classrooms. The experimental design uses surveys with embedded rich-media representations of classroom interaction to surface how teachers appraise correct solutions to linear equations where some solutions follow suggested textbook procedures for solving linear equations and others do not. This paper illustrates the feasibility of studying teaching with rich-media surveys and suggests new ways to support changes in everyday mathematics teaching.