Pre-service teachers' perceptions of generic proofs in elementary number theory

Leander Kempen (1) , Rolf Biehler (1)

1 University of Paderborn

In this paper, we present our concept of the usage of four different types of proofs to engage students in the proving process: the generic proof (with numbers), the generic proof in the context of figurate numbers, the so-called "formal proof" , and the proof in the context of figurate numbers using "geometric variables". Further, we report from our case study, where 12 pre-service teachers were interviewed after attending our bridging-course, which had a focus on argumentation and proof. We investigated students' perceptions of the generic proof with numbers. Our findings suggest the classification of perceptions in three categories: "Logical acceptance and psychological conviction", "general acceptance of the concept and psychological uncertainty", and "inappropriate understanding of the concept".

Mots clés: Generic proof; conviction; transition; figurate numbers

Domaines: Education; Histoire et perspectives sur les mathématiques [math.HO]

Leander Kempen, Rolf Biehler. Pre-service teachers' perceptions of generic proofs in elementary number theory. CERME 9 - Ninth Congress of the European Society for Research in Mathematics Education, Charles University in Prague, Faculty of Education; ERME, Feb 2015, Prague, Czech Republic. pp.135-141. ⟨hal-01281024⟩