Adult science learners’ mathematical mistakes: an analysis of responses to computer-marked questions

Abstract

Inspection of thousands of student responses to computer-marked assessment questions has brought insight into the errors made by adult distance learners of science. Most of the questions analysed were in summative use and required students to construct their own response. Both of these things increased confidence in the reliability of the findings, as did the fact that similar errors were seen in different variants and in different questions. Questions on logarithms, graphs and gradient, differentiation and standard deviation were poorly answered. However, the most persistent errors, seen in questions designed to assess a range of different skills, were in rounding numerical values to an appropriate number of decimal places or significant figures and in working out the units of an answer. Other errors included incorrect precedence in calculations, giving symbols in an incorrect case, and problems with reciprocation, adding fractions, handling powers, performing unit conversions, and simplifying algebraic expressions. Possible reasons for the errors include careless slips, poor understanding of a method, and deeper conceptual misunderstandings. Many of the errors were similar to those reported by others, both at university and school level, and it appears that there are some very basic stumbling blocks that affect a wide range of students. It is suggested that increased use of discussion with students might bring further insight into the reasons for errors as well as increasing student understanding.