Deriving Basic Ideas as Prescriptive Guidelines-Description of a Theory-Based Framework

Abstract

Basic ideas (Grundvorstellungen) are guidelines for the conception of learning processes. They also structure empirical research aiming at analyzing individual mental representations. However, it is often not exactly described how content-specific formulations of basic ideas are carried out. In this paper, we propose a framework for deriving basic ideas as prescriptive guidelines. It comprises five steps: (1) selection of the central mathematical concepts for which basic ideas should be formulated and a preliminary determination of further guidelines, (2) class formation based on subject-matter analyses of relevant definitions, their phenomenology and empirical findings, (3) formulation of basic ideas based on the previously formed classes and analyses of the relationships between the formulated basic ideas (4) specification of the relevant basic knowledge and analyses of further basic ideas, (5) assessment of the didactical relevance. The derivation of basic ideas with the proposed framework is carried out exemplarily for the concepts of sine and fractional numbers.