An investigation of what knowledge in valued and how it is communicated in a mathematics support course for first-year engineering students

Abstract

There is longstanding and widespread concern that students find the transition from school to university mathematics difficult. There have been various practical responses to supporting students in this transition. Research conducted on these responses tends to focus on student perceptions and the impact on academic performance. However, research which explores the pedagogy implemented in support courses is lacking. Yet such research is needed if we are to understand what knowledge is valued and how it is communicated in support courses, which is an important first step in establishing whether these courses are replicable and whether they might indeed provide access to the knowledge valued in mainstream mathematics courses. My study investigates the implemented pedagogy of one particular mathematics support course for first-year engineering students. The pedagogy intended for the course is similar to the problem-centred approach (PCA), which is a competence pedagogy popular in selected white primary schools in South Africa in the 1990s. Critiques of school-level PCA - such as that it affords students insufficient "guidance" and that it is difficult to replicate – highlight the importance of understanding this support course's pedagogy. I made video records of one activity of the course in order to explore what knowledge the course values and how that knowledge is communicated to students. My theoretical framework is founded on Bernstein's (1996) theory of the pedagogic device, since it affords a language for speaking about the transformation of knowledge into pedagogic communication. I adopted theoretical tools from Davis's (2001; 2005) investigation of PCA at the primary school level. My study demonstrates the generalisability of these theoretical tools. Regarding what knowledge is valued in the course, I found that the central notion is problem solving. Problem solving serves as a vehicle for developing "sense-making". However, the notion of problem solving remains implicit since it is not discussed with students and students do not have an opportunity to solve the given problem independently. Regarding how knowledge is communicated, I found the implemented pedagogy to be a hybrid of Bernstein's competence and performance models. The former emerges in that much of the privileged knowledge remains implicit and the hierarchy between teacher and student is apparently flattened. The performance model is seen in teachers guiding students, both explicitly and implicitly. For example, they explicitly tell students to draw a diagram and how to check their answers. They implicitly guide students by modelling the problem-solving process and subtly positioning the students in complex ways. My results raise questions about whether students acquire the notion of problem solving in the course. Furthermore, the pedagogy identified may mitigate against students acquiring the sense-making disposition that the course intends to develop. My results bring into question the replicability of the course and how it may support students in their transition to university mathematics.