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4 février 2015
- handle: 10670/1.l6or5i
- hal: hal-01280542
info:eu-repo/semantics/OpenAccess
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Infinitesimal calculus Analysis (Mathematics) Fluxions (Mathematics) Limits (Mathematics)Citer ce document
Paolo Boero, « Analyzing the transition to epsilon-delta Calculus: A case study », HAL-SHS : sciences de l'éducation, ID : 10670/1.l6or5i
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The purpose of this paper is to analyze and discuss a think-aloud production of a first year university student trying to prove an elementary theorem, concerning continuous functions, within the frame of the epsilon-delta Calculus. I will shortly consider current studies on the relationships between a visual justification, based on the graphical representation of a continuous function, and such epsilon-delta proving. Then I will try to show how a comprehensive theoretical framework (integrating different tools) based on Habermas' construct of ration-ality may account for the complexity of the whole process, for the difficulties met by the student in the transition from the visual-graphical to the epsilon-delta proving, and for the relevance of the visual-graphical reasoning to overcome them.