541 © Springer International Publishing AG 2017 G.A. Stillman et al. (eds.), Mathematical Modelling and Applications, International Perspectives on the Teaching and Learning of Mathematical Modelling, https://doi.org/10.1007/978-3-319-62968-1_45 Chapter 45 Mathematical Modelling for Engineering Diploma Students: Perspectives on Visualisation Hanti Kotze, Gerrie J. Jacobs, and Erica D. Spangenberg Abstract This inquiry aims to determine the infuence of mathematical modelling on engineering diploma students’ visualisation when solving differential equations (DE) with a computer algebra system (CAS). In CAS environments, students usu- ally struggle to interpret numerical tables and computer graphs derived from sym- bolic DEs and often leave interpretative questions unanswered. Participants comprised 80 second year vocational engineering diploma students at a comprehen- sive university. Students’ abilities to make contextual connections between different representations through a model-eliciting task were assessed using content analysis. By reversing the curricular approach, most participants constructed a meaningful DE that deepened understandings of the world in which they modelled. The model- ling environment stimulated development of adequate schema through experimen- tation with paper-and-pen and CAS technologies. Keywords Computer algebra system • Differential equations • Engineering diploma students • Visualisation • Mathematical modelling • Multiple representations H. Kotze (*) Department of Applied Physics and Engineering Mathematics, Faculty of Science, University of Johannesburg, Doornfontein Campus, C/o Beit and Nind Streets, Doornfontein, Johannesburg 2092, South Africa e-mail: hantik@uj.ac.za G.J. Jacobs • E.D. Spangenberg Department of Science and Technology Education, Faculty of Education, University of Johannesburg, Auckland Park Kingsway Campus, C/o University and Kingsway Roads, Auckland Park, Johannesburg 2092, South Africa e-mail: gjacobs@uj.ac.za; ericas@uj.ac.za