By P. Boero

Over the past decade, a revaluation of evidence and proving inside arithmetic curricula used to be steered; nice emphasis used to be wear the necessity of constructing proof-related talents because the starting of basic tuition. This ebook, addressing arithmetic educators, teacher-trainers and lecturers, is released as a contribution to the endeavour of renewing the educating of facts (and theorems) at the foundation of historical-epistemological, cognitive and didactical concerns. Authors come from 8 international locations and various study traditions: this truth bargains a vast medical and cultural point of view. during this booklet, the old and epistemological dimensions are handled by way of authors who examine particular examine ends up in the historical past and epistemology of arithmetic with an eye fixed to an important matters with regards to academic offerings. papers care for the relationships among curriculum offerings bearing on facts (and the comparable implicit or specific epistemological assumptions and historic traditions) in diverse college structures, and the instructing and studying of evidence there. The cognitive measurement is critical as a way to stay away from that the didactical offerings don't healthy the desires and the possibilities of beginners. Our selection used to be to to start with care for the gains of reasoning relating to facts, almost always about the relationships among argumentation and facts. the second one a part of this e-book concentrates on a few an important cognitive and didactical facets of the advance of evidence from the early technique in basic college, to school and college. we'll convey how compatible didactical proposals inside of acceptable academic contexts can fit the good (yet, underestimated!) younger scholars' possibilities in imminent theorems and theories.

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Additional resources for Theorems in School: From History, Epistemology and Cognition to Classroom Practice (New Directions in Mathematics and Science Education)

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1980). Le sens pratique, Paris: Ed. de Minuit. Chevallard, Y. (1985). La transposition didactique, Grenoble: La Pensée Sauvage. Caveing, M. (1977). La constitution du type mathématique de l’idéalité dans la pensée grecque, thèse, Université Paris 10, Atelier national de reproduction des thèses, Université Lille 3 (1982). Caveing, M. (1979). A propos des débuts des mathématiques grecques. Réflexions sur l’ouvrage de A. Szabo. Revue d’histoire des sciences, XXXII(2), 163–168. Caveing, M. (1982).

1981). Mythe et pensée chez les Grecs, tome 1, Paris: Maspero. Vernant, J. P. (1982). Mythe et pensée chez les Grecs, tome 2, Paris: Maspero. Vitrac, B. (1990). Euclide, les éléments, Paris: PUF. Von Fritz, K. (1945). , 2ème série, 46, 242–264. Zafiropoulo, J. (1950). L’Ecole éléate, Paris: Belles Lettres. Gilbert Arsac, IREM et LIRDHIST, Université Lyon 1, France. 42 FERDINANDO ARZARELLO 2. THE PROOF IN THE 20TH CENTURY From Hilbert to Automatic Theorem Proving Introduction In this chapter the notion of proof is investigated from an epistemological point of view.

We will restrict our study to the western tradition whose origin takes place in Greece, and which is continuing in Arabic science then in western countries, and this for several reasons: it is the origin of all contemporary mathematics, and it is the first that makes systematic use of proof in a fixed and even stereotyped way. Actually, Greece is the place of a radical transformation of mathematics which simultaneously characterised the objects of this science by defining them axiomatically as idealities, ideal objects, and rules of their handling, particularly mathematical proof which allows true statements to be distinguished.

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