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Csaba Csíkos: Proofs in school mathematics and the ability to construct proofs This study reviews some theories and empirical data concerning proofs in school mathematics and proving ability. After some theoretical considerations about the importance of cognitive abilities the paper focuses on the role of proofs in mathematics and in the school. It is hypothesized that there is a general proving ability that makes determining the truth-status of a statement possible by means of using other (formerly proven) statements and inference rules. Our basic assumption is that proofs in school mathematics can be the 'leaven' to foster the development of proving ability. Therefore special attention is paid to the principles of teaching proofs in school mathematics and to the difficulties the evaluation of students' proofs calls forth. Different approaches are discussed contrasting the 'old' DTP- (definition, theory, proof) model with the 'new' exploration-explanation-formalization models. From the point of view of educational evaluation there is an emphasis on arguing for the use of a hierarchical proof-categorization developed by Harel and Sowder. MAGYAR PEDAGÓGIA 99. Number 1. 3-21. (1999) An English version of the paper can be obtained from the author. Levelezési cím / Address for correspondence: Csaba Csíkos, Department of Education, Attila József University, H-6722 Szeged, Petőfi sgt. 30-34. |
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