Experimental approaches to theoretical thinking the mathematics classroom: artefacts and proofs

In this chapter we have discussed some strands of experimental mathematics both from an epistemological and from a didactical point of view. Precisely, we have introduced some past and recent historical examples in western and eastern cultures in order to illustrate how the use of tools has driven the genesis of many abstract mathematical concepts. We have shown how the intertwining between concrete tools and abstract ideas introduces an “experimental” dimension in mathematics, and a dynamic tension between the empirical nature of the activities with the tools –which encompass perceptual and operational components– and the deductive nature of the discipline –which entails a rigorous and sophisticated formalization.