Making it explicit?

Zum Lehren und Lernen von mathematischen Leitideen und „nature of science“ als Aspekte mathematischer bzw. naturwissenschaftlicher Grundbildung

Abstract

This article deals with the question of how to teach conceptual didactical constructs underlying actual core curricula, „nature of science“ (NOS) and „fundamental mathematical ideas“ in pre-service teachers education. Contemporary NOS teaching, especiallyin pre-service teacher education, is explicit, highly instructive, problem- and context oriented,and emphasizes reflective and meta-cognitive aspects. The question is posed inhow far a closer look onto such teaching concepts can be fruitful for teaching on fundamental mathematical ideas, with a focus on pre-service teacher education. In a first step, NOS and fundamental mathematical ideas are concretized and compared on a meta-conceptual level. In a second step, this concretized understanding of fundamental mathematical ideas isconfronted with highly instructive ways of making NOS an explicit object of consideration in pre-service teachers’ didactical seminars. The conclusion is to refrain from the instructive character of explicitly teaching conceptual constructs for the case of fundamental mathematical ideas in teachers’ education. In the last part of this paper, a short description of a preservice teachers’ course on fundamental mathematical ideas is given which follows a different explicit-reflective paradigm, keeping the orientation to problems and contexts, and the consideration of meta-cognitive aspects.