Proof by induction in calculus - investigating first-year students’ examination scripts

Abstract

Students’ transition from secondary to university mathematics and the difficulties they face are at the forefront of mathematics education research. This study explores one of the areas that students have difficulties with, namely proof by induction. The presentation focuses on first-year undergraduate mathematics students’ difficulties when solving a proof by induction task. This task comes from a final-year Calculus examination paper and combines proof by induction and differentiation. Our data consist of 197 students’ Calculus solutions to this task and the corresponding module materials, specifically lecture notes and coursework exercises. Using coding and theming, we explore what solution processes arise when solving the task. In the presentation, we present and discuss the relevant teaching materials and then focus on students’ difficulties when engaging with the examination task. The findings illustrate that students have difficulties with the proof by induction process, differentiation processes, and issues related to both. We present student work from all three categories and conclude that combining both induction and differentiation principles in one task, poses additional challenges for students. We also discuss the implications of our work.

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Identifiers

ORCID for Athina Thoma: orcid.org/0000-0002-5985-3820

ORCID for Christian Bokhove: orcid.org/0000-0002-4860-8723

ORCID for David Gammack: orcid.org/0000-0003-1214-1057

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