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Eric.ed.gov – Can Classification Criteria Constitute a Correct Mathematical Definition? Preservice and In-Service Teachers’ Perspectives

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The study reported here addresses pre-service and in-service teachers’ attitudes toward mathematical-geometrical definitions. The goal of the study is to investigate whether understanding the role of definitions as classification and identification criteria will guarantee that participants: (1) accept that there may be more than one equivalent definition for particular concept; and (2) accept the minimal definitions which include necessary and sufficient attributes to be legal definitions. Fifty-three math educators participated the study, including 22 preservice junior teachers, 19 pre-service senior teachers and 12 in-service senior teachers. The findings indicate that considering (an) attribute/s as sufficient in order to classify examples and non-examples of the concept did not guarantee considering this/ese attributes as concept definition. 56% of the participants did not accept equivalent definitions as legal definitions, 36% of them (the participants) did not accept the minimal definitions, which include necessary, and sufficient attributes to be a legal definition. For many participants, the essence of the mathematical concept is more important than the essence of the mathematical definition.

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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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