Undergraduate students' difficulties and convictions with mathematical induction

Abstract

The study reported in this thesis has the purpose to gain insight into students’ difficulties and self-described difficulties with mathematical induction and their convictions in their produced proofs. Participants were 78 undergraduate students from a four-year university. Three written tasks were administered, and interviews were conducted with eight of the participants. Two of the tasks asked the participants to prove two identities by mathematical induction and probed their conviction in their proofs. The third task asked the participants to describe their difficulties with proving said identities using mathematical induction. During the interviews, the participants were given an identity to prove using mathematical induction. Data analysis showed that students experienced difficulties at every step of mathematical induction, but mainly with stating P(k + 1), algebraic manipulations needed to prove P(k) → P(k + 1), and writing the proof in the correct form. Students’ self-described difficulties focused on the algebraic manipulations to prove P(k) → P(k + 1). With respect to their convictions in their proofs, students often derived conviction from one source – the proof or empirical evidence. Shifting the source of conviction from empirical evidence to the proof was uncommon.