Efficiency of Learning from Proof Blocks Versus Writing Proofs

TL;DR

This study compares the effectiveness of Proof Blocks, a scaffolded proof tool, with traditional proof writing, finding similar learning gains but with less time required for students learning proof by induction.

Contribution

The paper provides empirical evidence that Proof Blocks can facilitate proof learning efficiently, reducing time without sacrificing learning outcomes.

Findings

Proof Blocks are as effective as writing proofs for learning proof by induction.

Students using Proof Blocks spend less time on proof exercises.

Proof Blocks are positively received by students and useful for assessments.

Abstract

Proof Blocks is a software tool that provides students with a scaffolded proof-writing experience, allowing them to drag and drop prewritten proof lines into the correct order instead of starting from scratch. In this paper we describe a randomized controlled trial designed to measure the learning gains of using Proof Blocks for students learning proof by induction. The study participants were 332 students recruited after completing the first month of their discrete mathematics course. Students in the study took a pretest and read lecture notes on proof by induction, completed a brief (less than 1 hour) learning activity, and then returned one week later to complete the posttest. Depending on the experimental condition that each student was assigned to, they either completed only Proof Blocks problems, completed some Proof Blocks problems and some written proofs, or completed only written proofs for their learning activity. We find that students in the early phases of learning about proof by induction are able to learn just as much from reading lecture notes and using Proof Blocks as by reading lecture notes and writing proofs from scratch, but in far less time on task. This finding complements previous findings that Proof Blocks are useful exam questions and are viewed positively by students.