Centre for Research in Mathematics Education, University of Nottingham, Jubilee Campus, Nottingham, NG1 4BU, UK
Geoff Wake is a Professor of Mathematics Education at the University of Nottingham, UK. His research focuses on applications of mathematics and modelling. Most recently his work has focused on the professional learning of teachers in lessons for mathematical problem solving.
This article is based on data from two major research projects that investigated students involved in mathematically demanding courses during their transition through college and into university. It explores the nature of modelling as a mathematical practice in this important transition phase for students. Theoretical considerations are informed by illustrative accounts of a college mathematical modelling lesson and engineering lecture exemplifying the complex nature of mathematical modelling in these two phases of post-compulsory education. This raises important issues concerning the teaching and learning of mathematical practices in relation to modelling and applications. The discussion presented here is seen through the lens of Cultural Historical Activity Theory that informed the project team’s analysis of the case studies developed of both institutions and individuals. In this article, data and earlier findings are reinterpreted to better understand how we might support students as they move from learning mathematics to learning to use mathematics effectively in pursuit of their other studies. The accounts of classroom and lecture activity illustrate how ‘doing mathematics’ is mediated in different ways ensuring that students experience modelling and applications as mathematical practices very differently in each. This leads me to explain why, but also infer that students are likely to experience difficulties in transition both ‘vertically’ in progression from one activity system to another over time (college to higher education) and ‘horizontally’ between activity systems in which they participate concurrently (maths and engineering classes in university).