Mathematics for future engineers : a study of teaching and learning mathematics in an engineering curriculum.

Abstract

This is a study of teaching and learning in the first mathematics module for engineering students at a South African university. The theoretical framing of the study is derived from multiple analytical tools: Bernstein’s theory of the Pedagogic Device; the construct of beliefs and Bloom’s revised taxonomy. As such this study draws on Bernstein’s concepts of recontextualisation, singulars and regions and classification and framing to describe the three message systems (content, pedagogy and assessments). The beliefs framework identifies the teaching styles used by lecturers while Bloom’s revised taxonomy provides the analytical tool to evaluate the quality of the final examination questions. This study took a pragmatist stance which privileged a mixed methods approach to data collection. The first research question sought to determine the role of mathematics in engineering. To fully understand the role of mathematics in engineering, document analysis was used to analyse the international (Washington Accord) and national (ECSA) professional body documents and the institutional requirements and interviews were conducted with academic staff in the department of mathematics and the school of engineering. The literature showed that mathematics is a key component in engineering education and in engineering practice. It also foregrounded the ongoing debate about whether it is sufficient for engineers to know the practical application of mathematics or whether knowledge of mathematics in all its abstraction is required. The second and third research questions looked at how teaching and learning is approached and reasons why it is approached in those ways. Data were generated from the documents stated above, observation of lectures as well as tutorials and interviews with relevant

academic staff and students. An analysis of the Washington Accord and ECSA documents fell within the Official Recontextualising Field and showed the influence of the external bodies on the recontextualisation of the ME curriculum. The textbook and head of school (MSC), constituted the Pedagogic Recontextualising Field (PRF), and were found to influence the framing over selection, sequencing, pacing and evaluative criteria. It was also established that there was further recontextualisation at the level of the classroom (by lecturers). In effect, the recontextualisation resulted in the exclusion of proofs and theoretical underpinning of the mathematics taught. The module showed strong classification of content on the interdisciplinary, intradisciplinary and interdiscursive level while framing over selection, sequencing, pacing and evaluative criteria were strong. The regionalization of the ME module resulted in it being a site of conflict and struggle over ownership of the pedagogic device. Despite differences in beliefs about mathematics, the teaching styles of lecturers were similar in that they demonstrated an algorithmic, assessment-oriented approach to teaching. The analysis revealed that lecturers viewed mathematics in terms of application and as a tool to solve engineering problems. Analysis of the final examination questions showed that it fell within the cognitive domain of Apply in Blooms’ revised taxonomy. A closer inspection of the final examination questions and those of the mock examination showed a close correlation between the two indicating that the conceptual demand was not as high as initially established. Despite the strong alignment between lectures, tutorials and assessments, many students were unsuccessful in passing the module. The thesis concludes with a discussion of the implications of the findings and suggests recommendations for the improvement of teaching and learning mathematics to future engineers and for further research.