This paper reports on the results of an observational parallel study conducted simultaneously at 2 universities -one each in New Zealand and Germany. It deals with university engineering students' difficulties in the formulation step of solving a typical application problem from a first-year calculus course. Two groups of students (54 in New Zealand and 50 in Germany) completed a questionnaire about their difficulties in solving the problem which was set as part of a mid-semester test. The research endeavoured to find reasons most of the students could not use their knowledge to construct a simple function in a familiar context. It was neither lack of mathematics knowledge nor an issue with the context. The students' difficulties are analysed and presented along with their suggestions on how to improve their skills in solving application problems.

This paper presents the results of two studies on using an innovative pedagogical strategy in teaching mathematical modelling and applications to engineering students. Both studies are dealing with introducing non-traditional for engineering students contexts in teaching/learning of mathematical modelling and applications: environment and ecology. The aims of using these contexts were: to introduce students to some of the techniques, methodologies and principles of mathematical modelling for ecological and environmental systems; to involve the students in solving real-life problems adjusted to their region emphasising the aspects of both survival (short term) and sustainability (long term); to encourage students to pay attention to environmental issues. On one hand, the contexts are not directly related to engineering. On the other hand, chances are that most of the graduates in engineering will be dealing with mathematical modelling of environmental systems in one way or another in their future work because nearly every engineering activity has an impact on the environment. The first study is a parallel study conducted in New Zealand and Germany simultaneously with first-year students studying engineering mathematics. The second study is a case study based the experimental course Mathematical Modelling of Survival and Sustainability taught to a mixture of year 2-5 engineering students in Germany by a visiting lecturer from New Zealand. The models used with the students from both studies had several special features. Analysis of students' responses to questionnaires, their comments and attitudes towards the innovative approach in teaching are presented in the paper.

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