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Christopher E. Smith

Considering circles in taxicab geometry helps students with Euclidean concepts.

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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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Dick J. Smith and Eric F. Errthum

Many mathematics instructors attempt to insert guided exploration into their courses. However, exploration tasks frequently come across to students as contrived, pertinent only to the most recently covered section of the textbook. In addition, students usually assume that the teacher already knows the answers to these explorations.

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John M. Livermore

The study of the history of mathematics can be an important approach to engaging students in learning mathematics. At the same time, mathematics history provides a context that will help students understand how and why certain types of mathematics were developed and used. The study of p has as rich a history as any mathematical topic.

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Readers comment on published articles and share their mathematical interests.

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Courtney R. Nagle and Deborah Moore-Russo

Students must be able to relate many representations of slope to form an integrated understanding of the concept.

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Students analyze a photograph to solve mathematical questions related to the images captured in the photograph. This month, photographs of the Al Bahr Towers in Abu Dhabi generate questions on area, the Pythagorean theorem and special right triangles, and trigonometric regression.

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Lee Melvin M. Peralta

One of the many benefits of teaching mathematics is having the opportunity to encounter unexpected mathematical connections while planning lessons or exploring ideas with students and colleagues. Consider the two problems in figure 1.

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A set of problems of many types.