TY - JOUR
TI - Méthodes de raisonnement et leurs modélisations logiques. Spécificité de l’analyse. Quelles implications didactiques ?
AU - Durand-Guerrier, Viviane
AU - Arsac, Gilbert
T2 - Recherches En Didactique Des Mathématiques
AB - We explore the question of rigour in the field of calculus along two dimensions: How can students avoid invalid proofs in the absence of explicit logical rules for mathematical reasoning, on the one hand, and what replaces the missing logical references, on the other?
To that end, we study the practise of demonstration in calculus at the beginning of university studies. This practise is based on reasoning with a generic element, for which natural deduction in predicate calculus provides an analytic frame. In the teacher’s discourse, this mode of reasoning appears in the form of rules for manipulating variables, and we show why this is specific to calculus in contrast to geometry and algebra. Our study of teachers’ commentaries on a student’s error shows the prevalence of one such rule, historically explainable and existing in textbooks. The study also shows that these rules, highly contextualised, are strongly dependent on the mathematical knowledge of the field in question, which might explain why beginners have such difficulty understanding them. Modelling these rules for manipulating variables within a logical frame makes it possible to refer to coherent knowledge and to situate our inquiry with respect to previous work on deductive reasoning.
DA - 2003///
PY - 2003
VL - 23
IS - 3
SP - 295
EP - 342
J2 - RDM
LA - FR
SN - 0246–9367
UR - https://revue-rdm.com/2003/methodes-de-raisonnement-et-leurs/
ER -