'Defining the problem: mathematical errors and misconceptions exhibited by first-year bioscience undergraduates

摘要

This study extends the debate concerning the mathematical skills deficit of bioscience undergraduates towards a deeper understanding of their mathematics learning, since only through the latter can appropriate and effective explicit teaching be implemented. Three hundred and twenty-six first-year bioscience undergraduates, from three pre- and four post-1992 UK universities completed a basic mathematics test, comprising 10 pure abstract mathematical calculations and 10 brief word problems set within biological contexts. In addition to participants' overall performance in the test, the students' performances on individual test items were analysed and students' test scripts examined for the methods of calculation adopted as well as the types of errors and misconceptions students exhibited. The test proved challenging for many participants, with 60% of students achieving scores of <40% and only 6% of students scoring 70-90%; the mean score was 38.5%. Although students' scores on the abstract items correlated positively with their scores on the word problems, scores were significantly higher on the pure abstract mathematics questions (mean score 55%) than on the contextualized word problems (mean score 23%). A high proportion (52-95%) of students encountered difficulties with individual questions involving the calculation of volume or surface area, the conversion of units of measurement, working with ratios, proportions and powers of 10, and determining magnification or magnitude. Students also exhibited a greater reluctance to attempt the contextualized word problems (11-75% did not attempt individual items) than the pure abstract mathematics calculations (2-12% did not attempt individual questions). Many of the errors and misconceptions students exhibited were similar to those reported previously as made commonly by 13-14-year-old children. Factors potentially influencing the students' performance and the educational implications of the findings are discussed, with particular reference to contextualized mathematics learning and learning transfer in bioscience.