Making Equations Speak: Communicating Mathematical Models Across Engineering Disciplines

In engineering programmes, mathematical modelling is usually introduced as a bridge between theory and the real physical world. In practice, however, many undergraduates still treat equations as something to be solved rather than something to be understood. They are often able to follow the algebraic steps, but they struggle to explain what those equations are actually saying about motion, energy, current, or force. This paper looks at that problem from a communication point of view. The discussion in this paper is based on the teaching experience of three instructors who have each taught mathematical modelling in both mechanical and electrical engineering courses at Universiti Teknikal Malaysia Melaka. Over several years of working with undergraduate engineering students, similar patterns kept appearing: students could “do the maths”, but they could not confidently describe what the terms in the model meant in physical terms. We reflected on these recurring situations using informal classroom observations, short student feedback, and adjustments made during live teaching. From that reflection, we identified typical barriers that block understanding, such as students’ habit of seeing equations only as calculation procedures, or lecturers’ habit of delivering explanations in one direction. We also describe three teaching moves that repeatedly helped: (i) using analogy and short narrative to make an equation feel like a story of cause and effect, (ii) showing behaviour visually in real time, and (iii) encouraging students to talk through meaning, not just provide answers. These three moves are then organised into a simple communication framework with three stages: translation, visualisation, and dialogue. The aim of the framework is to help students link symbols to physical behaviour in a way that feels concrete to them, regardless of whether the system is mechanical or electrical. The paper argues that mathematical modelling is not only a technical skill but also a language that needs to be spoken, shown, and discussed. Clearer communication can help students read equations with understanding, not only manipulate them. The work ends by suggesting that engineering educators and curriculum planners should treat communication as part of core modelling instruction, not as something optional.

mathematical modelling, engineering education, conceptual understanding

1. Lyon, J. A., & Magana, A. J. (2020). A review of mathematical modeling in engineering education. International Journal of Engineering Education, 36(1A), 101–116. [Google Scholar] [Crossref]

2. Wankat, P. C., & Oreovicz, F. S. (2015). Teaching engineering (2nd ed.). Purdue University Press. [Google Scholar] [Crossref]

3. Felder, R. M., & Brent, R. (2024). Teaching and learning STEM: A practical guide (2nd ed.). John Wiley & Sons. [Google Scholar] [Crossref]

4. Magana, A. J., Falk, M. L., Vieira, C., Reese, M. J., Alabi, O., & Patinet, S. (2017). Affordances and challenges of computational tools for supporting modeling and simulation practices. Computer Applications in Engineering Education, 25(3), 352–375. [Google Scholar] [Crossref]

5. Dori, Y. J., & Belcher, J. (2005). How does technology-enabled active learning affect undergraduate students’ understanding of electromagnetism? Journal of the Learning Sciences, 14(2), 243–279. [Google Scholar] [Crossref]

6. Trevelyan, J. (2014). The making of an expert engineer. CRC Press (Taylor & Francis). [Google Scholar] [Crossref]

7. Chi, M. T. H., & Wylie, R. (2014). The ICAP framework: Linking cognitive engagement to active learning outcomes. Educational Psychologist, 49(4), 219–243. [Google Scholar] [Crossref]

8. Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., & Wenderoth, M. P. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences, 111(23), 8410–8415. [Google Scholar] [Crossref]

9. Kheir, N. A., Åström, K. J., Auslander, D., Cheok, K. C., Franklin, G. F., Masten, M., & Rabins, M. (1996). Control systems engineering education. Automatica, 32(2), 147–166. [Google Scholar] [Crossref]

10. Kolb, D. A. (2015). Experiential learning: Experience as the source of learning and development (2nd ed.). Pearson Education. [Google Scholar] [Crossref]

11. Biggs, J., & Tang, C. (2011). Teaching for quality learning at university (4th ed.). McGraw-Hill / Open University Press. [Google Scholar] [Crossref]

12. Gibbs, G. (1998). Learning by doing: A guide to teaching and learning methods. Oxford Brookes University. [Google Scholar] [Crossref]

13. Prince, M. J., & Felder, R. M. (2006). Inductive teaching and learning methods: Definitions, comparisons, and research bases. Journal of Engineering Education, 95(2), 123–138. [Google Scholar] [Crossref]

14. Jalili, N., & Candelino, N. W. (2023). Dynamic systems and control engineering. Cambridge University Press. [Google Scholar] [Crossref]

15. Whitcomb, K. M., Kalender, Z. Y., Nokes-Malach, T. J., Schunn, C. D., & Singh, C. (2020). Engineering students’ performance in foundational courses as a predictor of future academic success. International Journal of Engineering Education, 36(4), 1340–1355. [Google Scholar] [Crossref]

16. Litzinger, T., Lattuca, L. R., Hadgraft, R., & Newstetter, W. (2011). Engineering education and the development of expertise. Journal of Engineering Education, 100(1), 123–150. [Google Scholar] [Crossref]

17. Mayer, R. E. (Ed.). (2014). The Cambridge handbook of multimedia learning (2nd ed.). Cambridge University Press. [Google Scholar] [Crossref]

18. Normey-Rico, J. E., & Morato, M. M. (2024). Teaching control with basic maths: Introduction to process control course as a novel educational approach for undergraduate engineering programs. Journal of Control, Automation and Electrical Systems, 35(1), 41–63. [Google Scholar] [Crossref]

19. Adams, R. S., Turns, J., & Atman, C. J. (2003). Educating effective engineering designers: The role of reflective practice. Design Studies, 24(3), 275–294. [Google Scholar] [Crossref]

20. Winsor, D. A. (1996). Writing like an engineer: A rhetorical education. Lawrence Erlbaum Associates. [Google Scholar] [Crossref]

21. Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge University Press. [Google Scholar] [Crossref]

22. Bunyamin, M. A. H., Abdul Rahman, N. F., Osman, S., Ahmad Alhassora, N. S., Hanri, C., Nawi, N. D., & W. Azelee, N. I. (2022). Graduate success attributes for engineering students: Major learning outcomes and significance of the course. AIP Conference Proceedings, 2433(1), 020009. AIP Publishing. [Google Scholar] [Crossref]

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