PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
Coordinating two meanings of variables in proofs that apply definitions repeatedly
Page: 87
In this paper we use data from a recent teaching experiment to characterize a particular challenge in proof comprehension that arises when a proof uses the same definition multiple times in related ways. This difficulty involves coordinating the role and value of a quantified variable in the definition, a distinction we explicate in the paper. We do so by providing two proofs that exemplify the key difficulty and presenting an episode in which two students who were reading a proof together adopted alternate interpretations of a variable (one as value and the other as role), but were for a time unable to coordinate the two meanings. The primary contribution of the paper is to sensitize the research community to this challenge in a way that will help future research on students’ reading of mathematical proof.