Fostering first-year pre-service teachers’ proof competencies

In the study presented, as we report in this paper, we describe our theoretical and practical consideration to engage first-year pre-service teachers in proving activities in the context of a transition-to-proof course. We investigated how students argued to verify a claim of elementary number theory on entering university and compared the results to their performance in the final examination of the course. Subsequently, we elaborate on the following results: On entering university, students do not seem to be capable of using algebraic variables as a heuristic to engage in reasoning. However, after learning about different kinds of proofs and the symbolic language of mathematics, students give evidence of starting to value mathematical language and of enhancing their proof competencies.