The influence of an educational intervention involving mathematical modelling on the visualisation of engineering students

Ph.D. (Mathematics Education)Abstract: Many engineering subjects rely on the interpretation of symbolic, numeric and graphic representations. Engineering students have difficulties with the interpretation of representations generated with a computer algebra system (CAS). For professional engineers, the interpretation of multiple representations is a daily activity and inherent to problem solving. The ability to reason visually and to fluently interpret multiple representations is a cognitive process referred to as visualisation. The use of CAS such as Mathematica has stimulated new mathematical tools desirable for work-place engineers; these include programming, mathematical modelling and visualisation. Step-by-step processes that are automated by CAS create a pragmatic-epistemic gap, an underlying principle of visualisation not yet sufficiently researched in mathematics education. This study assesses the influence of mathematical modelling on the visualisation of engineering diploma students at the University of Johannesburg (UJ), South Africa (SA). The aim is to contribute to research on visualisation within the vocational field, both nationally and internationally. The research is driven by the question: What is the influence of an educational intervention involving mathematical modelling on the visualisation of engineering students? An explanatory sequential mixed methods design was used in three phases. In the first phase, a preliminary pilot study involved two mathematical modelling tasks and an open-ended questionnaire. For the second phase, a pilot study involved a quasi-experiment with a pre-test, mathematical modelling intervention – using the same modelling tasks as in phase one – and a post-test. The quasi-experiment was augmented by two semi-structured reflective group interviews. Phase two was repeated in its entirety for the main study, which was phase three. In each phase, the sample was a different cohort of engineering diploma students in their second year of study at UJ. Quantitative data were analysed with descriptive and inferential statistics, using the Statistical Package for the Social Sciences (SPSS). All qualitative data were analysed with content analysis. Four visualisation dimensions were identified namely translation, visual reasoning, new insights and intuition. While both the experimental and control group could smoothly translate from one representation to another, the experimental group benefited mostly..