This paper describes the development of a procedure for investigating the ability of university students to employ their mathematical skills in a range of scientific contexts. This ability is called transfer. An instrument (consisting of a set of questions) to test transfer was designed jointly by three scientists and a mathematician and attempted by 47 students studying first-year science subjects at the University of Sydney. The instrument is described, and some of its strengths and weaknesses are discussed. The performances of the students on the instrument are analysed and interpreted, and a method by which each student's overall transfer ability may be quantified is suggested. Methods for determining a student's ability to transfer specific skills or items of mathematical knowledge are also described.