Are Students Able to Transfer Mathematical Knowledge?

The ability to use mathematics in other disciplines is generally expected of all science and engineering students. Anecdotal evidence suggests that many students lack this ability. While there is a substantial body of research dealing with the transfer of training, and the transfer of mathematical skills to problem solving in everyday life, there is very little relating to the transfer of mathematics to other scientific disciplines. This paper reports on the development and trialing of an instrument which can be used to research the ability of students to transfer mathematical skills and knowledge to other disciplines. The instrument consists of mathematical problems set in various contexts. All the problems involve exponential and logarithmic functions, and are based on scenarios from physics, microbiology and computer science. In each case, any discipline-specific knowledge required to solve the problem is given, so that all the problems can be solved with mathematical knowledge only. The problems were initially written by a physicist, a microbiologist and a computer scientist. The instrument has been trialed with 47 first year science students at the University of Sydney. Performance on the instrument has been correlated against final high school marks, first year university results, and subjects studied. These results are presented. The paper also discusses some of the interesting issues which arose from the collaboration of a mathematician with academics from three other scientific disciplines. For example, differences in the ways the physicist, the microbiologist and the computer scientist used mathematics were apparent. Also, their use of mathematics was often quite imprecise. Such issues have important implications for the teaching and learning of mathematics, both as a subject in its own right and within other disciplines.