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Csaba Csíkos: 10-17 year-old students' judgments on proving strategies

The focus of this study is the nature and development of reasoning processes (so-called proving ability) that allow for verifying logical statements. Students' judgments on different proofs of a given statement can be considered as important indicators of proving ability. In order to categorize different proof types, in this investigation proof concepts of philosophy, mathematics and jurisprudence are reviewed. Two tests of proving ability were administered to 1944 students from grades 5, 7, 9 and 11. The tests contained statements five different proofs that were categorized - based on Harel and Sowder's taxonomy - as authoritarian, ritual, symbolic, empirical and analytic. The proof types were constructed on the basis of a pilot study that set as an aim to let students allow writing many types of proofs to open-ended tasks. Students scored the different proofs on a five-point Likert-scale. From the aspect of educational practice, the main results of this study are: (1) Fifth-graders accept authoritarian arguments more often than older children do. (2) In each age group, meaningless symbol-manipulation is over-valued. Even in case of non-mathematical content there is a tendency to give higher scores to meaningless symbol-manipulations. (3) In each age group, empirical proofs are relatively under-valued. Since students' judgments can largely be traced back to math teachers' bias towards symbolic proofs, mathematics can play an important role in fostering the development of proving ability. Practical considerations about the results of the present investigation may involve emphasizing the importance of 'exploring the territory' before proving a statement. Developmental tendencies revealed by cross-sectional comparisons may be relevant for teacher educators and also for textbook writers and curriculum.

MAGYAR PEDAGÓGIA 101. Number 3. 319-345. (2001)

Address for correspondence: Csíkos Csaba, Szegedi Tudományegyetem Pedagógiai Tanszék, H-6722 Szeged, Petőfi S. sgt. 30-34.

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Magyar Tudományos Akadémia