Undergraduate student difficulties, convictions, and self-efficacy with strong and weak mathematical induction

The purpose of this study is to describe and compare undergraduate students’ difficulties with proofs by strong and weak mathematical induction and to investigate their convictions in their proofs. Further, the study looks at self-efficacy for mathematical proofs using the two forms of mathematical induction, weak and strong induction. Participants were five undergraduate mathematics major students from a four-year university. Students completed a demographic questionnaire, a self-efficacy questionnaire for proofs by mathematical induction, and three tasks asking them to prove a statement P(n) using strong and weak mathematical induction and to state their convictions in the value of truth of the statement P(n) for different values of n. Two of the five students participated in an interview to probe for difficulties with proofs by induction. The results showed that students had more difficulties with strong induction. Students from the study also had the most difficulties with the inductive step itself for both weak and strong induction. Students’ convictions regarding the validity of a statement P(n) seemed to be the same overall for weak and strong induction. Students had proof conviction when asked if P(n) was true for a value n within the domain of validity. They had mixed answers when they were asked for convictions referring to a value n outside of the domain. Scores for self-efficacy and performance for strong induction tasks were lower than the self-efficacy and performance scores for weak induction tasks.