2020 Volume 13 Pages 11-29
Concrete didactical means for learning mathematics, as for instance chips for the number concept, or everyday activities in situations of application as the balance for understanding the algebraic equation, are often seen as an immediate and an effective basis for abstract mathematical knowledge in school mathematics. In this article the specific role of concrete didactical means is analyzed from an epistemological perspective. They are distinguished by two major positions: on the one side they are considered as elements of a real world of things and on the other side they are conceived as elements within a systemic world of mathematical relations. A major consequence of the following epistemological reflections is that the concrete didactical material in the world of things cannot explain per se mathematical knowledge, especially, when the pedagogical tool (i.e. the concrete material) assists in understanding mathematical knowledge, those elements no longer belong to the physical world, but they belong to the world of mathematical relations.
