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Barbara M. Kinach

More emphasis on spatial reasoning is a way to increase meaning when students study geometry.

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Charles F. Marion

Anyone who is looking for insights into the problem-solving process in mathematics is well advised to start with two books that have been in print for more than seven and three decades, respectively: How to Solve It (Pólya), first published in 1945; and The Art of Problem Posing (Brown and Walter) in 1983.

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Martin V. Bonsangue

In the absence of a decimal number system and representations for square roots, Archimedes estimated the value of pi using inscribed and circumscribed polygons to a circle.

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Bobson Wong and Larisa Bukalov

Parallel geometry tasks with four levels of complexity involve students in writing and understanding proof.

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Readers comment on published articles and share their mathematical interests.

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Kara Suzuka and Linda Venenciano

Use the Reversibility, Flexibility, Generalization (RFG) questioning framework to develop robust, multifaceted, interconnected, and lasting mathematical comprehension.

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Karen D. Campe

Mathematics teachers can use a broad range of technologies—calculators, computers, display systems, and others—as teaching and learning tools. Although actual access is influenced by budgets and demand, the important thing is to make the best use of the technology available. Whether you have one computer station for demonstration, a classroom set of graphing calculators, or a fully wired classroom, you can take steps to make your technology implementation most effective and successful.

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Rachael Eriksen Brown and Kimberly Masloski

This article shares the authors' use of written teaching replays as part of a professional development experience for beginning secondary mathematics teachers. This form of narrative writing is inspired by Horn's (2010) descriptions of teachers sharing their practice in professional learning communities. In this study, written teaching replays are used to gain insights about what beginning teachers noticed about their teaching practice and whether these noticings highlighted dilemmas or successes in their teaching practice. The analysis of teaching replays indicated that, despite being in their _ rst years of teaching, these beginning teachers' narrative writings focused least on management issues. Instead, the writings had a strong focus on mathematics or teaching mathematics as well as on social issues within their classrooms. These _ ndings counter the research literature that suggests beginning teachers are overwhelmingly concerned with classroom management. The authors conclude with their re_ ections on the potential of this form of narrative writing for beginning teachers and how it could be used by other mathematics educators.

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Wayne Nirode

What I wish I had known about implementing DG tasks when I began by teaching career!

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A set of problems of many types