Eine Untersuchung zur Diskussion über Schwierigkeiten im Umgang mit dem Konvergenzbegriff

Abstract

Primarily the controverse discussions in didactical research concerning the foundations of analysis — especially the different approaches to the limit concept — are considered. In the recent years many suggestions have been made to overcome the difficulties of the “usual” limit concept (Epsilon-n_o, Epsilon-Delta Definition). The didactical analysis of these difficulties and the suggestions to overcome them led to the development of some new curricula. Hence it is now necessary to examine if the analysis of these difficulties exactly reflects the difficulties which pupils really have. In a first step the consequences of the above mentioned didactical analysis are transformed into questions which the authors — in a second step — tried to answer in the last three years by different tests which were presented to pupils and students. The results of these tests are reported and the consequences of these results are compared with different observations of other authors.