The purpose of this miniproject was to conduct research to investigate whether study of an e-Proof results in better proof comprehension than an equal amount of time studying an ordinary written proof, and whether students can transfer the skills of inferring warrants and breaking down structure to other proofs for themselves. The analysis revealed that while e-Proofs are seen by students as an effective learning resource, studying an e-Proof as a first exposure to a proof appears to result in poorer retention over time than attending a standard lecture or reading the proof in a standard format. This unexpected result led to the consideration of possible hypotheses involving, primarily, the degree to self-explanation prompted by the various formats, and possible variations in the ways in which more expert and more novice readers approach the task of proof comprehension.
This miniproject followed the design and construction of e-Proofs with the support of an Academic Practice Award from Loughborough University, where they have now been used in the analysis module. This module was taken by approximately 140 students, and delivered via two 50-minute lectures per week for an 11-week term. The students were then split into three groups for tutorials, in which they worked in groups on problems related to recent and forthcoming material. The course covered standard material on continuity, differentiability and Riemann integrability. The e-Proofs were made available to the students via the university’s virtual learning environment (VLE).
Each e-Proof was presented as a sequence of screens and accompanying audio files, and each comes in three versions:
1. A basic version in which the proof appears one line at a time and the audio commentary reads that line;
2. A line-by-line version in which the whole proof is visible but greyed out, with each screen showing one line (or part of a line) fully visible, arrows and boxes indicating why that line is valid and its relationships to the other parts of the proof, and the audio providing explanation; and,
3. A chunk version, in which the whole proof is visible but greyed out, with each screen showing several lines fully visible, a box indicating what that section achieves, and the audio describing this in a little more detail.
In the majority of cases, students were given a printed copy of the whole proof, invited to spend a few minutes trying to understand it, and then shown the line-by-line and chunk versions. After this, the e-Proof was made available via the VLE.
Following the unexpected results of the miniproject, an eyetracker study was conducted to investigate possible expert-novice differences.