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Michael Todd Edwards, James Quinlan, Suzanne R. Harper, Dana C. Cox, and Steve Phelps

This approach to determining measures of angles fosters stronger understanding of formal proof.

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Natalya Vinogradova

Investigating the sum of the medians of a triangle leads to inequalities related to the perimeter.

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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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Jennifer Earles Szydlik, Amy Parrott, and Jason Knight Belnap

Share practice and culture through three explicit discussions about the nature of mathematics.

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Nicholas J. Gilbertson and Kimberly Cervello Rogers

Can you find a triangle in which the three bases and three heights are integer values?

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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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Patrick Harless

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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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Michael S. Meagher, Michael Todd Edwards, and S. Asli Özgün-Koca

The Geoboard Triangle Quest yields many results. The challenge for students is to verify which—if any—are correct.

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Zhonghong Jiang and George E. O'Brien

Using technology to explore the Three Altitudes of a Triangle problem, students devise many proofs for their conjectures.