In this article, we report on the findings of an exploratory study into the experience of students as they learn first year engineering mathematics. Here we define engineering as the application of mathematics and sciences to the building and design of projects for the use of society [M. Kirschenman and B. Brenner, Education for Civil Engineering: A Profession of Practice, Leader. Manag. Eng. 10 (2010), p. 54]. Qualitative and quantitative data on students' views of the relevance of their mathematics study to their engineering studies and future careers in engineering was collected. The students described using a range of mathematics techniques (mathematics skills developed, mathematics concepts applied to engineering and skills developed relevant for engineering) for various usages (as a subject of study, a tool for other subjects or a tool for real world problems). We found a number of themes relating to the design of engineering mathematics curriculum emerged from the data. These included the relevance of mathematics within different engineering majors, the relevance of mathematics to future studies, the relevance of learning mathematical rigour and the effectiveness of problem-solving tasks in conveying the relevance of mathematics more effectively than other forms of assessment. We make recommendations for the design of engineering mathematics curriculum based on our findings.