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Agida G. Manizade and Marguerite M. Mason

When calculating the area of a trapezoid, students use a range of problem-solving strategies and measurement concepts.

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Karin E. Lange, Julie L. Booth, and Kristie J. Newton

Presenting examples of both correctly and incorrectly worked solutions is a practical classroom strategy that helps students counter misconceptions about algebra.

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Erik Jacobson

Table representations of functions allow students to compare rows as well as values in the same row.

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Ann E. West

The use of mnemonic devices, or “tricks,” in the mathematics classroom has been criticized by some authors. However, when used in the proper context, such “tricks” can be extraordinarily helpful in motivating students and helping them remember procedures while understanding concepts and mastering appropriate mathematical vocabulary.

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Amy F. Hillen and Tad Watanabe

Conjecturing is central to the work of reasoning and proving. This task gives fourth and fifth graders a chance to make conjectures and prove (or disprove) them.

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Allison B. Hintz

Teachers can foster strategy sharing by attending to the cognitive demands that students experience while talking, listening, and making mistakes.

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Marcy B. Wood

Identity is an important tool for understanding students' participation in mathematics lessons. Researchers usually examine identity at a macro-scale: across typical classroom activity and in students' self-reports. However, learning occurs on a micro-scale: in moments during a lesson. To capture identity in these moments, I used positioning theory to develop a framework of micro-identity and then to examine the identities and learning of 1 fourth-grade student during 1 mathematics lesson. This study demonstrates how mathematical identities can shift in dramatic ways in response to minor changes in context so that a student might be, in one moment, engaged in an identity that undermines learning and then later engaged in an academically productive identity. These shifting micro-identities have important implications for mathematical learning, classroom contexts, and macro-identities.

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A cartoon highlighting growth of a retirement fund is coupled with a full-page activity sheet.

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Wendy B. Sanchez

Educating students—for life, not for tests—implies incorporating open-ended questions in your teaching to develop higher-order thinking.

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Gabriel T. Matney and Brooke N. Daugherty

Cans on a grocery store shelf and Hirst's Capric Acid Amide can illustrate dot arrays, thus helping students understand the distributive property, partial products, and the standard algorithm for multiplication.