<p>A significant gap exists between the way mathematical knowledge is taught in service mathematics courses and how it is applied in discipline-specific contexts such as engineering. This gap often leads to fragmented learning experiences for non-mathematics majors, who struggle to transfer and apply mathematical knowledge like the Laplace transform (LT) in real-world contexts. To address this issue, this study proposes the development of a structured reference model—an archeorganisation—for teaching mathematical knowledge in service mathematics courses. Drawing on the anthropological theory of the didactic (ATD), particularly praxeological analysis, didactic transposition, and the six didactic moments, the study outlines a methodological framework for constructing such an archeorganisation. Using the LT as a case study, data were collected from textbooks, classroom observations, and interviews with lecturers and students in both mathematics and engineering contexts. Findings reveal significant epistemological and institutional fragmentation in how LT is defined, taught, and applied across disciplines. The proposed methodological approach aims to integrate the theoretical and practical dimensions of the knowledge at stake, fostering greater instructional coherence and disciplinary relevance. This study contributes both to the theoretical development of archeorganisations within the ATD and to practical strategies for teaching and learning mathematics to non-mathematics majors in STEM fields.</p>