Reflected acting in mathematical learning processes. Zentralblatt für Didaktik der Mathematik

Abstract: Acting and thinking are strongly inter-connected activities. This paper proposes an approach to mathematical concepts from the angle of hands-on acting. In the process of learning, special emphasis is put on the reflec-tion of the own actions, enabling learners to act consciously. An illustration is presented in the area number representation and extensions of number fields. Using didactical materials, processes of mathematical acting are stimulated and reflected. Mathematical concepts are jointly developed with the learners, trying to address shortcomings from own experiences. This is accompanied by reflection processes that make conscious to learners the rationale of mathe-matical approaches and the creation of mathe-matical concepts. Teaching mathematics follow-ing this approach does intent to contribute to the development of decision-making and responsi-bility capabilities of learners