## Abstract

In the opening session of a course for first-year secondary (lower track secondary school) pre-service teachers, the participants were asked to rate the conviction , verification and explanatory power of four different kinds of proofs (a generic proof with numbers, a generic proof in the context of figurate numbers , a proof in the context of figurate numbers using “geometric variables” and the formal proof). In this study, students’ ratings express their preference for the formal proof concerning the aspects conviction, verification, and explanatory power. The other proofs achieve significantly lower ratings, especially in the case of conviction . The results may open the discussion about the use of generic proofs, the use of figurate numbers and the concept of proofs that explain.

### Keywords

- Transition to university
- Generic proof
- Figurate numbers
- Function of proof

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Kempen, L. (2018). How Do Pre-service Teachers Rate the Conviction, Verification and Explanatory Power of Different Kinds of Proofs?. In: Stylianides, A., Harel, G. (eds) Advances in Mathematics Education Research on Proof and Proving. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-70996-3_16

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