Making Sense of Mathematical Discourse: Implications for Success in the Learning of Differentiation in a University Classroom

Abstract

This article reports part of a case study which investigated errors that occurred in a Mathematics classroom owing to poor conceptualisation of mathematical concepts and a lack of the required mathematical register among a group of thirty first year university students. The study focused on the critical issue of making sense of mathematical concepts and examined this issue by exploring students’ interpretations and misinterpretations in their learning of mathematical differentiation. The students were registered for Mathematics 1 in Chemical Engineering. Data was derived from the students’ written work, along with video-recorded material of their ‘live’ learning interactions. This data was then analysed within the framework of Sfard’s (2007) Commognitive approach as a means of attempting to address errors that are displayed by students when learning differentiation. The students demonstrated different types of difficulties, namely, conceptual, interpretation, procedural, linear extrapolation and arbitrary errors. The application of the Commognitive approach to the identification and addressing of students’ errors to advance their understanding of differentiation has proven to be positive in enhancing student learning and success.