A Mathematician's Influence on Students’ Perceptions – The Case of Mathematical Induction

In this study, we report on a professor of mathematics who also teaches mathematics in a secondary school. We checked
the influence of the professor’s presenting the mathematical induction (MI) principle on his students’ perceptions of the
principle. Extensive observations on the MI content were performed to determine the professor's conception the MI
principle. Moreover, seventy four students answered a questionnaire which was built to examine the students'
perceptions of the MI principle. Finally, both data analysis were triangulated and crosschecked. It was concluded that
the students’ main perception of MI was: mathematical induction identifies the natural number set, including
formulation; following four representations of the MI that were exposed by the teacher. This means that the learners
mainly, perceived MI by reflecting on the properties of the set of natural numbers, in addition to the usual perception
which is as “a method of proof”. Consequently, it can be argued that this representation has pedagogical advantages.