Transition from School to University Mathematics: Manifestations of Unresolved Commognitive Conflict in First Year Students’ Examination Scripts

Abstract

We explore the transition from school to university through a commognitive (Sfard 2008) analysis of twenty-two students’ examination scripts from the end of year examination of a first year, year-long module on Sets, Numbers, Proofs and Probability in a UK mathematics department. Our analysis of the scripts relies on a preliminary analysis of the tasks and the lecturers’ (also exam setters’) assessment practices, and focuses on manifestations of unresolved commognitive conflict in students’ engagement with the tasks. Here we note four such manifestations concerning the students’ identification of and consistent work with: the appropriate numerical context of the examination tasks; the visual mediators and the rules of school algebra and Set Theory discourses; the visual mediators of the Probability and Set Theory discourses; and, with the visual mediators and rules of the Probability Theory discourse. Our analysis suggests that, despite lecturers’ attempts to assist students towards a smooth transition to the different discourses of university mathematics, students’ errors at the final examination reveal unresolved commognitive conflicts. A pedagogical implication of our analysis is that a more explicit and systematic presentation of the distinctive differences between these discourses, along with facilitation of the flexible moves between them, is needed.