Teaching "Foundations of Mathematics" with the Lean Theorem Prover

TL;DR

This study investigates whether integrating the Lean theorem prover into a mathematics course enhances students' understanding of proofs, based on performance data and statistical analysis from a pilot at the University of Zurich.

Contribution

It provides empirical evidence on the impact of using Lean in teaching foundational mathematics to freshmen, which is a novel application in education research.

Findings

Lean students showed improved proof understanding.

Statistical tests indicated significant differences.

Lean integration positively affected exam performance.

Abstract

This study aims to observe if the theorem prover Lean positively influences students' understanding of mathematical proving. To this end, we perform a pilot study concerning freshmen students at the University of Zurich (UZH). While doing so, we apply certain teaching methods and gather data from the volunteer students enrolled in the ``Foundations of Mathematics'' course. After eleven weeks of study covering some exercise questions implemented with Lean, we measure Lean students' performances in proving mathematical statements, compared to other students who are not engaged with Lean. For this measurement, we interview five Lean and four Non-Lean students and we analyze the scores of all students in the final exam. Finally, we check significance by performing a $t$-test for independent samples and the Mann-Whitney $U$-test.