# Representational flexibility and mathematical expertise

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## Flexibility in mathematics

It is more or less taken for granted that the efficacy of mathematical acts is highly dependent on the quality of relevant representational acts (though there is considerable debate about the ontology of representation). In this commentary, I react to the preceding five papers, in which, as with all experimental work that addresses this topic, we can observe the struggle of the experimenters to devise experimental tasks and aligned interpretative tools to approach the difficult task of making inferences about internal processes from external behavior.

By way of introduction, I offer some comments on the importance of flexibility in doing and learning/teaching mathematics, related aspects of expertise and structural awareness, and the centrality of representations as culturally and historically embedded cognitive tools.

One of my mathematics teachers once said that a good mathematician is lazy. He explained that what he meant is that a good mathematician looks...

## Keywords

Good Mathematician Didactical Contract Test Constructor Adaptive Expertise Sociomathematical Norm## References

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