Upper secondary school students' difficulties with mathematical modelling

This article reports on a combined quantitative and in-depth qualitative study of 315 Danish upper secondary (grades 10–12) mathematics students’ answers to six modelling tasks that place emphasis on the early phases of the so-called modelling cycle. In order to focus attention on the extra-mathematical aspects of modelling, the technical mathematical requirements of the tasks designed were reduced as much as possible. The article analytically and empirically identifies the most significant ‘stumbling blocks’ in modelling with particular regard to the learning difficulties that the population considered experienced and displayed in getting started on relatively idealised mathematical modelling tasks. The results show that a significant number of students have difficulty in accepting or understanding modelling tasks that seem to breach the standard didactical contract in Danish upper secondary mathematics education, and that – more than acknowledged in previous research – pre-mathematisation is a significant stumbling block in modelling, which is also co-responsible for the better known fact that mathematisation, too, is a crucial stumbling block in mathematical modelling. The study further shows that insufficient or missing so-called implemented anticipation is a major factor in these difficulties. It is finally concluded that since there was no evidence of students having severe problems with the technical mathematical knowledge base (e.g. pure mathematical concepts and formulae) in dealing with the six tasks, the stumbling blocks reside in the fundamentals of subjecting extra-mathematical situations to mathematical modelling.