Analyzing the transition to epsilon-delta Calculus: A case study

Paolo Boero (1)

1 Dipartimento di Mathematica

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.

Keywords: Calculus proof; visual-graphical rationality; epsilon-delta rationality

Domains: Education; History and Overview [math.HO]

Paolo Boero. Analyzing the transition to epsilon-delta Calculus: A case study. CERME 9 - Ninth Congress of the European Society for Research in Mathematics Education, Charles University in Prague, Faculty of Education; ERME, Feb 2015, Prague, Czech Republic. pp.93-99. ⟨hal-01280542⟩