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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.

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S. Asli Özgün-Koca, Michael Todd Edwards, and Michael Meagher

The Spaghetti Sine Curves activity, which uses GeoGebra applets to enhance student learning, illustrates how technology supports effective use of physical materials.

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Lisa A. Brooks and Juli K. Dixon

A second-grade teacher challenges the raise-your-hand-to-speak tradition and enables a classroom community of student-driven conversations that share both mathematical understandings and misunderstandings.

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This department publishes brief news articles, announcements and guest editorials on current mathematics education issues that stimulate the interest of TCM readers and cause them to think about an issue or consider a specific viewpoint about some aspect of mathematics education. This month in the Coaches' Corner, take a closer look at CCSS Standard 3 for Mathematical Practice, Explain and Justify. Coaches may want to demonstrate the integration of math and writing with Speak, Write, Reflect, Revise, a five-step approach for integrating problem solving and the writing process.

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Jennifer M. Bay-Williams

Being mindful of language used during discussions of fractions can promote greater understanding and retention.