Making Equations Speak: Communicating Mathematical Models Across Engineering Disciplines

Abstract

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.