This approach to determining measures of angles fosters stronger understanding of formal proof.
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Michael Todd Edwards, James Quinlan, Suzanne R. Harper, Dana C. Cox, and Steve Phelps
Natalya Vinogradova
Investigating the sum of the medians of a triangle leads to inequalities related to the perimeter.
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).
Nicholas J. Gilbertson and Kimberly Cervello Rogers
Can you find a triangle in which the three bases and three heights are integer values?
Jennifer Earles Szydlik, Amy Parrott, and Jason Knight Belnap
Share practice and culture through three explicit discussions about the nature of mathematics.
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?
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.
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.
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.
