Undergraduate students’ mathematical proof skills: Examining the impact of six cognitive resources

Proof is essential for mathematics as a science. However, previous studies have indicated that students often struggle with handling mathematical proof. This has been suspected to be due to a lack of different (meta-)cognitive resources, in particular conceptual and procedural knowledge, problem-solving abilities, mathematical strategic knowledge, conditional reasoning abilities, and metacognitive awareness. Yet, sound empirical evidence for this assumption is only available for a few resources. Therefore, this study quantitatively investigates the relation between these six resources and students’ performance in constructing and validating proofs. Data on the resources and proof construction and validation performance was gathered from 64 first-year undergraduate students. Generalized linear mixed model analyses confirm that domain-specific resources, particularly conceptual knowledge, are crucial for constructing and validating proofs successfully. Additionally, data indicates that the importance of mathematical strategic knowledge for handling mathematical proof has previously been underestimated. Unlike domain-specific resources, the domain-general resources showed no significant prediction when controlling for domain-specific resources. The study’s results partially confirm prior research but also raise new questions regarding the mechanisms behind the joint effects of the resources. Finally, they suggest that domain-specific resources are a plausible first choice when searching for instructional levers to support mathematical proof skills.