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Barbara J. Dougherty

With changes in mathematical content and instructional techniques in first-year algebra, we are forced to change the tasks we give students as a means of expressing their understandings. Homework papers consisting of endless drill with no thrill cannot give a good indication of what students are learning. Test questions that focus on applying an algorithm cannot assess how students connect mathematical ideas. Neither traditional measure gives adequate information about how students have constructed generalizations or about attitudinal changes. Thus, traditional tasks do not give a clear picture of what students understand or believe.

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Dung Tran and Barbara J. Dougherty

The choice and context of authentic problems—such as designing a staircase or a soda can—illustrate the modeling process in several stages.

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J. Matt Switzer, Kelley Buchheister, and Barbara Dougherty

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.

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Barbara J. Dougherty and Terry Crites

NCTM's Commission on Standards for School Mathematics (1987) has identified problem solving and number sense as important components of an effective mathematics program. This emphasis is generating attempts to understand the problem-solving process better and to incorporate the results into classroom practice. In keeping with the thrust, this article discusses the interrelationships between problem solving and number sense in light of difficulties experienced by students participating in the problem-solving process.

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Karen S. Karp, Sarah B. Bush, and Barbara J. Dougherty

Turn away from overgeneralizations and consider alternative terminology and notation to support student understanding.

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Karen S. Karp, Sarah B. Bush, and Barbara J. Dougherty

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. The Whole-school Agreement strategy proposes that all educators in a school community agree that mathematics is better taught when everyone shares in consistent language, symbols and notation, models and schema, and rules that support the developing learner.

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Karen S. Karp, Sarah B. Bush, and Barbara J. Dougherty

Try these meaningful alternative approaches to helping students make sense of word problems.

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Barbara J. Dougherty, Sarah B. Bush, and Karen S. Karp

Many times what is taught in one grade can “expire” when students face topics and situations that are more sophisticated in the grades that follow.

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Karen S. Karp, Sarah B. Bush, and Barbara J. Dougherty

Overgeneralizing commonly accepted practices, using imprecise vocabulary, and relying on tips and tricks that do not promote conceptual mathematical understanding can lead to misunderstanding later in students' math careers.

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Ji Yeong I, Barbara J. Dougherty, and Zaur Berkaliev

The meat and potatoes of multiplication is the change of units.