Verallgemeinem als zentrale mathematische Fähigkeit

Abstract

It is commonly accepted that mathematical concepts are the results of processes of generalization. But there are differing opinions about the structure and the means of these processes and therefore about how concepts are to be taught. A schema for the process of generalization is presented which is based on the view that mathematical concepts like other theoretical conepts represent schematizations and generalizations of human actions (operations) and of relations established and/or intended by these actions. This schema is not descriptive but prescriptive in the sense of the hypothesis that concept acquisition can and should be organized according to the schema. Further it is asserted that the schema itself can be acquired as a cognitive schema or frame which then guides generalization and concept acquisition.