Proceedings of the International Group for the Psychology of Mathematics Education · Volume 1
Mela Aziza, Chris Sangwin
The University of Edinburgh
⬇ Download PDFRobust algebraic reasoning depends on recognising when expressions or equations are equivalent and justifying that judgement. This study investigates students' definitions and their actual justification strategies, and the alignment between them. Open written responses from 13 first-year undergraduate mathematics students were analysed thematically, both in a traditional manner and using an LLM. The tasks required definitions, examples of equivalent or non-equivalent pairs, and justification for equivalence in expressions and equations. For equivalence of expressions, students primarily provided normative definitions, the same value for every x, whereas in practice, students often relied on transformations or numerical-value checks. Meanwhile, students showed greater alignment in equivalent equations.
Equivalencenormative definitionLLM