Students' understanding of ɛ-statements involving equality and limit

Imène Ghedamsi (1) , Thomas Lecorre (2)

1 IPEIT - Institut Préparatoire aux Etudes d'Ingénieur de Tunis
2 BONHEURS - Bien-être, Organisations, Numérique, Habitabilité, Education, Universalité, Relation, Savoirs

The purpose of this paper is to explore how students may understand the link between the formalisations through ɛ-statements of infinite processes in the Archimedean continuum. These processes illustrate either equality or limit. In particular, we focus on the extent to which students perceive the formalisation of the infinite closeness notion in the two processes. The data is collected from an extensive design research carried out at the transition between Calculus course and Analysis course. TDS construct of milieu is deployed to build and to analyse exploratory teaching-experiments. The results put forward how ɛ-statements may assist students to reconsider their informal understanding of limit.

Mots clés: equality; limit; process; statement; ɛ; milieu.; milieu; ɛ-statement

Domaines: Education; Histoire et perspectives sur les mathématiques [math.HO]

Imène Ghedamsi, Thomas Lecorre. Students' understanding of ɛ-statements involving equality and limit. Proceedings of the Second Conference of the International Network for Didactic Research in University Mathematics, V. Durand-Guerrier, R. Hochmuth, S. Goodchild & N.M Hogstad, Apr 2018, Kristiansand, Norway. pp.34-44. ⟨hal-01849943⟩