The teaching of mathematics in Singapore continues, in most cases, to follow a traditional model. While this traditional approach has many advantages, it does not always adequately prepare students for University-level mathematics, especially applied mathematics. In particular, it does not cultivate the ability to deal with "non-routine problems," which is an essential virtue for any practitioner of "mathematical modelling" (MM). Here, we argue that this inability to handle non-routine problems is the principal reason for the serious difficulties experienced by Singaporean students who encounter MM at the tertiary level in Singapore universities. A survey was conducted, primarily to understand the difficulties facing the preliminary batch of first-year undergraduate engineering students doing a course in MM using differential equations (DEs) and linear algebra. Our work is motivated by concerns that the novelty of this course in the Singaporean context could lead to difficulties for these students. Students' abilities in attempting novel modelling-type problems, the techniques they employ in solving such problems, their comments on the course and expectations of their lecturers and tutors are being probed. We present our analyses of the survey results and discuss the implications for future work. (Contains 2 notes.)