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".