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Mastaneh Davis, Gordon J A Hunter
Department of Mathematics, Kingston University, KT1 2EE U.K., United Kingdom
Development of proficiency in mathematics is an essential aspect of many higher education programmes of study. This applies both to specialist mathematics students, and students of many other disciplines, including engineering, most natural sciences and some social/human sciences, business and commercial subjects. Students’ knowledge of and expertise in mathematics (or lack thereof), at least at an elementary level, can have a major impact on many other areas of their studies and their subsequent career prospects. However, mathematics is an area which many students find difficult, particularly those from “non-traditional” academic backgrounds, including disabled and mature students, and they often do not realise its relevance and importance to their other courses, nor do they (or can they) devote as much time or effort as they perhaps ideally should, and face to face tutorial support is often limited. Although there have been previous attempts to develop on-line tutorial exercises, with automated marking and feedback, to assist students with their mathematical studies, most of these have either been restricted to multiple choice or numerical answer questions, or have only addressed the most elementary of topics – notably simple algebra, functions & graphs and trigonometry.
In this paper, we describe our efforts to remedy this situation. We have produced a set of resources, called CalculEng, including a variety of exercises, on single variable differential and integral calculus, with applications, which can be delivered on-line or using a Virtual Learning Environment such as Blackboard or Moodle. These exercises, in the form of structured questions developed using the QTI framework, allow algebraic input from the student, which is checked for consistency with the “correct” solution, and with the outcomes of anticipated “common errors”, using the MAXIMA computer algebra engine. The students’ responses are automatically marked, with the aid of the Computer Algebra System, and intelligent, relevant feedback - based on the mistakes made by the student - provided. We discuss the design and implementation of resources we have produced, their relevance to various degree curricula, and their evaluation when used on a number of first year mathematical modules within undergraduate engineering degrees. We also describe the reflections and opinions of the students participating in the evaluation, both with respect to their experiences of using CalculEng, and regarding their attitudes and preferences towards studying mathematical topics. Analysis of these comments and feedback should facilitate improving CalculEng to make it better-suited to students needs and study styles.