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Eric.ed.gov – Common Errors and Misconceptions in Mathematical Proving by Education Undergraduates

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Ninety-seven education students majoring or minoring in mathematics had their math homework examined in a Number Theory or Abstract Algebra course. Each student’s homework was observed for the purpose of identifying common errors and misconceptions when writing mathematical proofs. The results showed that students collectively made four recurring errors: assuming the conclusion in order to prove the conclusion, proving general statements using specific examples, not proving both conditions in a biconditional statement, and misusing definitions. In the same courses taken subsequently by 91 new students, we informed them about these common errors prior to assigning their homework to see how the students’ proving processes would differ. The results showed that more exercises were left blank with comments such as “I’m not sure how to start the proof”, and that many students provided unnecessary examples to supplement their valid proofs.

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Troels Gannerup Christensen

Jeg er ansat som adjunkt hos Læreruddannelsen i Jelling, hvor jeg underviser i matematik, specialiseringsmodulet teknologiforståelse, praktik m.m. Jeg har tidligere været ansat som pædagogisk konsulent i matematik og tysk hos UCL ved Center for Undervisningsmidler (CFU) i Vejle og lærer i udskolingen (7.-9. klasse) på Lyshøjskolen i Kolding. Jeg er ejer af og driver bl.a. hjemmesiderne www.lærklokken.dk og www.iundervisning.dk, ggbkursus.dk og er tidligere fagredaktør på matematik på emu.dk. Jeg går ind for, at læring skal være let tilgængelig og i størst mulig omfang gratis at benytte.

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