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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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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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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 Annette N. Matsumoto

“We're ready!” students shout. Each group has just spent about eight minutes preparing a presentation about a homework problem. Agatha is randomly selected from her group to present their ideas. She puts up the transparency. See figure 1.

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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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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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Jessica T. Ivy, Sarah B. Bush and Barbara J. Dougherty

To promote reversibility and strengthen number sense, we created an engaging and novel rational number exploration, which promoted flexible and reflective thinking. A class of fifth-grade students took an active role in a collaborative learning task, discussed their strategies, revisited the task, and reflected on their self-constructed generalizations.

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Barbara J. Dougherty and Linda C. H. Venenciano

How first graders' sense of number can be developed through the perspective of measurement. Includes a Reflect and Discuss component to use with colleagues. Measure Up is a research project for grades 1-5, and there is a summary of impact on math learning in later years.

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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.