# Studying mathematical practices: the dilemma of case studies

## Abstract

In this paper we argue that the choice of research methods reflects the theoretical framework even before these methods have been put to use in case studies. We understand the term ‘case study’ broadly in this paper and argue that neither thinking of them as cherry-picked cases to support preconceived ideas about mathematical practices nor thinking of them as inductive leaps from (too) few cases to general features is suitable. By realising the deep entanglement of our case studies with our theoretical framework we propose to view case studies as an invitation for critical reflection upon one’s own assumptions. We discuss an example taken from the philosophy of mathematical practices. The upshot is threefold: (1) we provide an argument that case study based research strategies can be successful; (2) we delineate how an awareness of the methodological difficulties of case study based research strategies can positively influence the way case studies are conducted; (3) we suggest that case studies are not dispassionate examinations that deliver cold facts.

## Keywords

Philosophy of mathematical practices Case studies Methodology Set theory## Notes

### Acknowledgements

We would like to thank Karen François for helpful discussions, three anonymous referees for valuable comments, the participants of the “Mathematical Evidence and Argument” symposium (Bremen 2017) for their insightful remarks, and the reading group of the *Centre for Logic and Philosophy of Science* at the Vrije Universiteit Brussel for their critical minds. Furthermore we thank Henrik Kragh Sørensen for his consent to present here the list of methods that have been used to study mathematical practices philosophically plus associated exemplar publications, which was created by him in joint work with the first author. Research for this paper by the first author has been funded by the Research Foundation—Flanders (FWO), project G056716N.

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