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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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Eric L. McDowell

Enhance students' number sense and illustrate some surprising properties of this alternative operation.

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Robin S. Kalder

Teachers who have been in the classroom for a while know that year after year we see students make the same mistakes that previous students made. To prevent these errors, we try a variety of techniques, but it seems that no matter what we do, they reappear in students' work time and time again. Are we, despite our best efforts, contributing to these mistakes? I believe that we do, indeed, use some practices that inadvertently undermine our best intentions.

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Sherry L. Bair and Edward S. Mooney

Mathematical precision means more than accuracy in computation or procedures; it also means precision in language. The Common Core State Standards for Mathematics states, “Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning” (CCSSI 2010, p. 7). In our recent experience in working with teachers and students, we have noticed a trend toward teachers using informal, and often creative, language and terminology in an effort to connect with students and make mathematical procedures easier to remember.

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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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Readers comment on published articles or offer their own ideas.

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Isaac Frank

A critique of FOIL provides an alternate method of multiplying polynomials.

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Readers react to published articles or submit their own mathematical explorations.

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A set of problems of many types.