Spannungen zwischen Referenzkontexten und Konstrukten am Beispiel der negativen Zahlen

Abstract

Steinbring’s view upon the construction of negative numbers on the basis of concrete contexts is restricted to the perspective of idealisation. Thus he comes to the conclusion of a tension or even a contradiction between concept and context. In my comments I want to complete this one-sided view, using the concepts of mathematisation and abstraction. Abstraction and idealisation are narrowly interwoven and often confluent. Therefore abstraction and idealisation can hardly be separated. Furthermore, it has to be asked carefully whether the process of learning is regarded from the learners or the teachers perspective. In my opinion idealisation and abstraction, in reference to cognition, can not grow up unless former experience is linked to (real) contexts.