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

Abstract

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