After a particularly interesting masterthesis on logic in mathematics education, I was given the opportunity to complete a four-year research project with Flemish funding (1S35225N) starting in November 2024.
The 200-word abstract (for researchers) can be found here.
The 5-page summary and previous participation call (for teachers) can be found here.
Underneath I provide a more concrete abstract for both researchers and teachers.
Project Summary
Mathematical proof is central to secondary mathematics education, yet students consistently struggle with it. A natural hypothesis is that students make logical errors in proofs because they lack formal logical reasoning skills — but is explicit logic instruction actually the solution, as the Flemish curriculum posits? This PhD project investigates that question across four objectives.
- What logical difficulties arise specifically in proof comprehension? A large-scale proof validation test is administered to 9th–10th grade students, whose responses are qualitatively analyzed. The outcome is an empirical inventory of logical difficulties in proof, with an indication of how frequently each type of error occurs.
- Does logical reasoning ability actually predict proof comprehension? Students complete several short multiple-choice reasoning tests alongside the proof validation measure. Statistical regression models are then built, controlling for confounding variables . The outcome is a quantitative estimate of how strongly logical reasoning ability predicts proof validation.
- How can instruction on proof validation be designed effectively — with or without explicit logic? An extensive literature review of existing proof didactics informs the design of two classroom learning modules: one integrating explicit logic instruction, one without it. Both are piloted iteratively in real classrooms. The outcome is two evidence-informed, ready-to-use instructional modules aligned with current curriculum goals.
- Which instructional approach works better, and for whom? Parallel classes follow either the logic or the non-logic module simultaneously, with proof validation measured before and after. Statistical analysis of the pre/post results identifies which approach is more effective and for which student profiles. The outcome is concrete, evidence-based guidance teachers can use to make the best choice for their own classroom.
Registering Interest
Click on the QR-code image below to register your interest or scan the QR-code.
This PhD is dedicated to Gilles Castel (✝2022)
