Recall and substantiation routines in exam scripts: injective and surjective functions
Résumé
In this paper, we focus on first-year university students’ engagement with university mathematics discourse in the context of a final examination question on injective and surjective functions. The data consists of twenty-two responses as well as excerpts from an interview with the exam-setting lecturer. Our commognitive analysis focuses on student engagement with recall and substantiation routines: how they recall and provide relevant definitions, and how they substantiate whether a function is injective or surjective. We identify three issues that are exemplified with samples from the data: ambivalent word use, and visual mediation, relating to equivalence; partial justifications regarding the injectivity of h(n) = 3n; and, conflation of justifications for a function’s surjectivity in Z with those used for functions in R. We conclude by discussing the notion of precedent events as evident in students’ engagement with routines in a range of mathematical topics.
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