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Janet B. Andreasen and Erhan S. Haciomeroglu

Dynamic software is used to teach geometry, tying into the Common Core's Standard 5, “Use appropriate tools strategically.”

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Priya V. Prasad

Assess the robustness of students’ understanding of polygons and move students beyond drawing to constructing geometric shapes.

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Darin Beigie

Although technology places a premium on quick and efficient ways to answer questions, the author discusses extended-time, or “slow-cooker,” questions, as illustrated by a task on the Triangle Inequality theorem.

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Sherri Ann Cianca

Communicating reasoning and constructing models fold nicely into a geometry activity involving the building of nesting boxes.

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Solve It! Student Thinking: Shaded Rectangles

big solutions to little problems

Students' thinking is discussed, and the procedures used with problem solving are explored.

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Hyewon Chang and Barbara J. Reys

Using Clairaut's historic-dynamic approach and dynamic geometry tools in middle school can develop students' conceptual understanding before they encounter formal proof in geometry.

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Joe Champion and Ann Wheeler

A classic manipulative, used since the 1960s, continues to offer opportunities for intriguing problem solving involving proportions.

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Dongjo Shin, Ryan C. Smith, and Somin Kim

Use a framework to evaluate a tool: Is it mathematically sound? Does it offer opportunities for student engagement with little distraction? Will it afford students the chance to develop their own ideas?

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Arthur N. DiVito

Mathematics has been taught throughout history without much more than a straightedge, a compass, and an abacus. So there is little question that all the major concepts of mathematics can be delivered without the aid of modern technology. But clearly, just the time-saving aspect of using technology can greatly enhance the art of teaching. Here we will identify some of the ways the use of technology can prove helpful in the classroom.

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Christopher W. Parrish, Ruby L. Ellis, and W. Gary Martin

NCTM identified eight Mathematics Teaching Practices within its reform-oriented text, Principles to Actions: Ensuring Mathematical Success for All (2014). These practices include research-informed, high-leverage processes that support the in-depth learning of mathematics by all students. Discourse within the mathematics classroom is a central element in these practices. The goal of implementing the practice facilitate meaningful discourse is to give students the opportunity to “share ideas and clarify understandings, construct convincing arguments regarding why and how things work, develop a language for expressing mathematical ideas, and learn to see things from other perspectives” (NCTM 2014, p. 29). To further support implementing meaningful discourse, mathematics educators must become adept at posing questions that require student explanation and reflection, hence, pose purposeful questions, which is another of the eight practices. Posing purposeful questions allows “teachers to discern what students know and adapt lessons to meet varied levels of understanding, help students make important mathematical connections, and support students in posing their own questions” (NCTM 2014, pp. 35-36).