CalMaeth: an interactive learning system focussing on the diagnosis of mathematical misconceptions

This article describes the operation of CalMaeth, a Webbased tutorial system, which is being used in teaching mathematics. The unique feature of CalMaeth is that it can provide detailed computer-generated diagnostic feedback for answers consisting of mathematical expressions. We give some examples of the system’s diagnostics in Calculus, described how they were generated and assess the range of student misconceptions that it is able to detect. Finally, data is presented illustrating some of the effects the diagnostics had on learning outcomes. This article describes and discusses a Web-based tutorial system, called CalMaeth, that is being used in teaching mathematics at the University of Western Australia. CalMaeth has been used with intermediate calculus, statistics, and linear algebra, but in this article only calculus examples are discussed. The CalMaeth system performs a variety of functions. It poses students individual randomised questions, which may require mathematical expressions as answers. Questions are labelled either “practice” or “assessed”: the assessed questions are marked in detail, whereas for practice questions, the students receive detailed computer-generated diagnostics for their incorrect answers. CalMaeth also maintains records of students’ answers, marks, and activity.