Using online randomised quizzes to boost student performance in mathematics and operations research

The use and development of online tools for learning in mathematically based disciplines is flourishing. This has occurred in reponse to the need to provide flexible learning choices for cohorts of students having a wide range of mathematical backgrounds, often insufficient for their chosen fields of study. Many students have difficulty with detailed written assignments which contain substantial amounts of mathematics, and need to be given extra incentive to spend time doing the necessary preparatory exercises. Furthermore, it is necessary that students revise previously learned concepts, preferably without using up valuable lecture time. Students need encouragement to do this, rather than trusting that they will magically remember what is needed along the way. To make such preparatory and revision work compulsory means assessing it in some way, which is an insurmountable task to do manually, but well suited to a computer. The importance of providing timely and accurate feedback to students regarding their progress cannot be underestimated. However it is impractical to provide this feedback to large classes unless either plenty of staff, or an automated system, is available. With appropriate feedback, students are more likely to do more than the minimum requirements, and so their achievement and interest in the subject will be enhanced. The MacQTEX online quiz project ([1], [2], [3], [4], [5]) was developed in the Department of Mathematics, Macquarie University, Sydney, and for the past three years has been used for formative assessment in undergraduate mathematics units. Following its success in improving students' learning outcomes, in 2005 the Department of Statistics introduced it in an elementary Operations Research unit. Quizzes are presented online as interactive PDF documents. Students may repeat a quiz as many times as is necessary to achieve a passing score, thereby getting valuable practice. Randomisation of numerical parameters and other aspects of the questions means that each instance of a quiz is different. A quiz is marked on submission to the server and students receive immediate feedback. At this time detailed solutions are revealed, which, rather than being general solutions, use the actual random parameters of each question instance. Question types include the usual multiple choice, multiple response (the correct answer is comprised of several choices), and fill-in-the-answer style. The latter may take a numerical answer, or a mathematical expression. Equivalence of mathematical expressions is recognised, so answers such as √x and x^1/2, for example, are both acceptable. With the use of a system such as MacQTEX, it is possible to begin to overcome some of the difficulties of teaching large classes. In such classes it is easy for students having marginal interest or ability to fall behind, or to feel anonymous and isolated. It is an interesting contradiction that the introduction of an automated system can encourage student contact with a real live staff member, particularly in the case of students who would not normally approach a lecturer or request help with their learning. In this paper we describe the MacQTEX quiz project itself, and the positive effects it has had on student performance and behaviour. We describe the ways in which quiz system makes it possible to identify struggling students early in the semester, and the action that can then be taken, giving these students the sense that their lecturers care that they succeed. Additionally we discuss how the system provides teaching staff with an immediate indication of the level of understanding the students have reached. If necessary, more time can then be spent on topics that have been more challenging for the students than expected.