The Laplace transform is often introduced in STEM curricula through procedurally focused methods, relying heavily on predefined formulas and transformation tables. While effective for basic problem-solving, this approach tends to obscure the conceptual underpinnings of the transform, reducing it to a mechanical tool and limiting students’ ability to transfer their knowledge to complex or novel contexts.

This paper presents a case study rooted in undergraduate engineering mathematics instruction, where the Laplace transform is introduced not as a formal definition, but as a natural consequence of modelling physical systems—specifically, electrical circuits governed by Kirchhoff’s laws. The approach is implemented in the Engineering Mathematics course for electrical engineering students at the Faculty of Engineering, University of Rijeka (Croatia).

Students first derive differential equations in the time domain and then confront limitations of classical solution methods when input signals lack differentiability. This moment becomes the pedagogical pivot: the Laplace transform is proposed as an entry point into an algebraic world that bypasses these obstacles.

The teaching strategy combines mathematical rigor—through full derivation of transform properties—with conceptual dialogue on the existence conditions of the transform and its epistemological role in engineering. The approach invites students to critically reflect on whether the transform is merely a computational convenience or a modelling necessity.

The paper concludes by outlining design principles that can inform similar interventions across STEM disciplines, where proceduralism remains a persistent barrier to deep understanding. Implications for course design, curriculum integration, and interdisciplinary collaboration will also be discussed.

Keywords: Conceptual learning, Laplace transform, engineering mathematics, proceduralism, case study, STEM education.