Chains of inferences in proof by induction: a cognitive analysis

In this paper, we investigate the students’ knowledge of proof by induction. We will focus on cognitive processes that appear fundamental in learning proof by induction, that are the construction of chains of inferences from the base case, and the transition from the actual construction of inferences to imagining that construction, without carrying it out. The empirical study and its theoretical analysis we conducted with university students will show that imagining the construction of chains of inferences is more problematic when the distance from the inductive base increases, and when the inferences involved are modus tollens. The result will show, in general, the complexity, even for university students, related to the process of development of a formal knowledge and intuitive acceptance of proof by mathematical induction, blended in a unique form of understanding,