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When visitors enter the High Museum in Atlanta, one of the first pieces of art they encounter is Physic Garden, by Molly Hatch (details in photographs 1 and 2). Physic Garden consists of 456 handpainted dinner plates arranged to form a rectangle with 24 horizontal rows and 19 vertical columns and extends from the floor to the ceiling of the first floor. The design of the “plate painting” was inspired by two mid-18th-century English ceramic plates from the museum's collection (photograph 3).

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Wayne Nirode

Using technology to solve triangle construction problems, students apply their knowledge of points of concurrency, coordinate geometry, and transformational geometry.

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Chris Harrow and Lillian Chin

Exploration, innovation, proof: For students, teachers, and others who are curious, keeping your mind open and ready to investigate unusual or unexpected properties will always lead to learning something new. Technology can further this process, allowing various behaviors to be analyzed that were previously memorized or poorly understood. This article shares the adventure of one such discovery of exploration, innovation, and proof that was uncovered when a teacher tried to find a smoother way to model conic sections using dynamic technology. When an unexpected pattern regarding the locus of an ellipse's or hyperbola's foci emerged, he pitched the problem to a ninth grader as a challenge, resulting in a marvelous adventure for both teacher and student. Beginning with the evolution of the ideas that led to the discovery of the focal locus and ending with the significant student-written proof and conclusion, we hope to inspire further classroom use of technology to enhance student learning and discovery.

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Kevin C. Moore and Kevin R. LaForest

A connected introduction of angle measure and the sine function entails quantitative reasoning.

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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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Lorraine A. Jacques

Teachers have what they need-students, a data projector or an interactive whiteboard, and connection to the Internet. Teachers know what they want-students observing mathematics in action, making conjectures, and supporting their conjectures with solid reasoning. However, when using applets, teachers quickly encounter two difficulties: how to choose them and how to use them.

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Harold B. Reiter, John Thornton and G. Patrick Vennebush

Through KenKen puzzles, students can explore parity, counting, subsets, and various problem-solving strategies.

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Jeffrey J. Wanko and Jennifer V. Nickell

Shapedoku puzzles combine logic and spatial reasoning with an understanding of basic geometric concepts.

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Nicholas J. Gilbertson, Samuel Otten, Lorraine M. Males and D. Lee Clark

For many American students, high school geometry provides their only focused experience in writing proofs (Herbst 2002), and proof is often viewed as the application of recently learned theorems rather than a means of establishing and understanding the truth of general results (Soucy McCrone and Martin 2009).

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Margaret Rathouz, Christopher Novak and John Clifford

Constructing formulas “from scratch” for calculating geometric measurements of shapes—for example, the area of a triangle—involves reasoning deductively and drawing connections between different methods (Usnick, Lamphere, and Bright 1992). Visual and manipulative models also play a role in helping students understand the underlying mathematics implicit in measurement and make sense of the numbers and operations in formulas.