Proof With a Purpose
Students in Janet Drake’s Advanced Geometry class recently completed a holiday-themed triangle proof project. In the assignment, students drafted a “prove” statement and demonstrated that at least one pair of triangles is congruent by constructing a two-column proof with at least six logical steps.
Students had to be precise when drafting their proofs, including just the right amount of given information. The project required them to think backward from the conclusion, carefully determining which hints and statements were necessary to support the proof logically. “Proof writing is really tricky,” says Janet, “These are our highest level math students. They can memorize math skills and apply them very well, but the leap in geometry is moving beyond the skill itself to focus on the logic behind why something is true.”
Students had a week to design a poster board that was complex enough to make their proof interesting and challenging. While proof writing may not seem like an inherently creative pursuit, students clearly enjoyed developing designs, with the corresponding statement and reason columns, inspired by Hanukkah, Christmas, and Chinese New Year. “It's fun because they've had the
aha moment,” says Janet. “Instead of just being given information, they now know how to create it and provide just enough information to lead someone to what they want to prove. It’s tricky, but they have made that leap.”
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