PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
Logical implication as an object and proficiency in proof by mathematical induction
Page: 1191
Proof by mathematical induction is known to be conceptually difficult for undergraduate students. We present a model that may simulate the impact of logical implication on students mastering proof by induction. We combine Piaget’s action-object theory of mathematical development with a psychological model of working memory and Harel and Sowder’s proof schemes. We analyzed three sets of written assessments from two Introduction to Proofs classes: after students learned about logical implication; before and after instruction on proof by induction. We examine the relationship between proficiency with mathematical induction and treating logical implication as an object within these two classes.