The Summary Task and its Potential for Proof Comprehension
摘要
In this chapter, I use comparative judgement to evaluate a series of proof summaries written by students from an undergraduate class on Proofs and Problem Solving. Twenty students summarized (a subset of) nine proofs each, assessed via pairwise comparisons performed by expert judges. The first section of analysis focuses on the reliability and validity of the resulting scores using standard measures from the comparative judgement literature. The second analysis section addresses questions of dimensionality in proof comprehension by comparing students’ performance in different context domains. The findings add to the growing body of literature reporting the reliability of evaluating proof summaries using comparative judgement, and the validity of the resulting scores as proxies for understanding of proof more generally. Moreover, these findings are consistent, even when judging summaries of multiple proofs in the same session. The latter analyses support conjectures in the literature on variations of the difficulty of proof comprehension in different settings, and the dimensionality of proof comprehension as a singular construct to be understood by undergraduate students.