Factors Influencing Students’ Propensity for Semantic and Syntactic Reasoning in Proof Writing: a Case Study

In this paper we present a case study of an individual student who consistently used semantic reasoning to construct proofs in calculus but infrequently used semantic reasoning to produce proofs in linear algebra. We hypothesize that the differences in these reasoning styles can be partially attributed to this student’s familiarity with the content, the teaching styles of the professors who taught him, and the amount of time he was given to complete the tasks. We suggest that there are factors that have been ignored in previous research, including domain, instruction, and methodological constraints, that researchers should consider when ascribing to students a proving style.