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…

In a recent paper, Alcock and Inglis (in press) noted a distinction between the way that Weber (in press) and they defined syntactic and semantic proof productions. Weber argued that "a syntactic proof production occurs when one works predominantly within the representation system of proof [...] Alternatively, a semantic proof production occurs…

In this paper, we distinguish between two ways that an individual can construct a formal proof. We define a syntactic proof production to occur when the prover draws inferences by manipulating symbolic formulae in a logically permissible way. We define a semantic proof production to occur when the prover uses instantiations of mathematical…