Structuralist praxeologies in the perspective of Klein

the case of connectedness in analysis

authored by

Thomas Hausberger, Reinhard Hochmuth

Abstract

This article is a continuation of our previous work on structuralist aspects of analysis at university in the framework of the Anthropological Theory of the Didactic. We now examine how the teaching of abstract structures (in particular metric spaces and topology) may contribute to Klein's perspective of “Elementary Mathematics from a higher standpoint”. Precisely, on the basis of a real and abstract analysis textbook used in the transition between Bachelor and Master degree programs in mathematics and in the light of the notion of structuralist praxeology and its dialectics, we discuss whether we can defend teaching the notion of connectedness to teacher students as a means to link real and abstract analyses in the spirit of Klein.

Organisation(s)

Institute of the Teaching of Mathematics and Physics
Abteilung Mathematikdidaktik

External Organisation(s)

Institut Montpelliérain Alexander Grothendieck (IMAG)

Type

Conference contribution

Pages

135 - 144

Publication date

10.06.2024

Publication status

Published

Peer reviewed

Yes