Ständige Restrukturierung – ein Erfordernis des Lernens von Mathematik

Abstract

Mathematical descriptions are central to teaching this discipline. Achieving competence in dealing with these descriptions is a dynamic process. New notation forms are continuously introduced, essentials of various descriptions are modified, descriptions are placed in new contexts, and new ways of seeing these descriptions are assumed. Processes of restructuring encompass all these changes. Restructuring processes concern not only the one learning but the development of mathematical knowledge in general. Applying these restructuring methods within particular representational systems as well as on the interaction between varying systems, apparent contradictions are removed, and their application and explanatory power are broadened. Some of the herein described restructuring processes have epistemic meaning. This exploration employs instruments of the semiotics of Charles S. Peirce.