Assessment-driven learning of mathematics for engineering students

International Journal of Electrical Engineering Education, Jan 2005 by Davis, L E, Harrison, M C, Palipana, A S, Ward, J P

Abstract

HELM (Helping Engineers Learn Mathematics) is a three-year curriculum development project undertaken by a consortium of five universities (Loughborough, Hull, Reading, Sunderland and UMIST) which aims to enhance the mathematical education of engineering undergraduates by the provision of flexible learning resources. HELM makes extensive use of a computer aided assessment (CAA) regime, available in web- and CD-based versions, to drive student learning.

This paper first describes the HELM learning resources and outlines the project's assessment philosophy; the HELM assessment regime and how it can be successfully used for both formative and summative assessment are then described. Finally, the viability of the HELM assessment regime across the higher education sector is examined.

Keywords assessment; e-learning; engineering undergraduates; HELM project; mathematics

Numerous recent reports testify to the severity of the 'mathematics problem' now faced by higher education. In 1995, the report Mathematics Matters in Engineering1 was published on behalf of various institutions of engineers and mathematicians. It concluded that 'too many graduate engineers are perceived to be deficient in mathematical concepts and fluency'. The report also highlighted the many pressures to reduce and simplify mathematical content. In the same year, the Engineering Council published The Changing Mathematical Background of Undergraduate Engineers,2 containing the results of a detailed study into the difficulties which undergraduate engineers face with mathematics. It concluded that 'students are now accepted on engineering degree courses with relatively low mathematics qualifications', which many lecturers believed was undermining the quality of their degrees. The 2000 Engineering Council report Measuring the Mathematics Problem3 confirmed the decline in basic mathematics skills between 1990 and 2000, quantified by Lawson4 and echoed in the Roberts Report5.

QAA External Subject Review reports (1996-2000) have repeatedly linked high failure and withdrawal rates with the 'mathematics problem'.6

Given the above, there is a clear need for a more accessible and flexible mathematics curriculum for engineering students, which the HELM project aims to provide.

HELM is a major three-year curriculum development project undertaken by a consortium of five universities, Loughborough, Hull, Reading, Sunderland and UMIST, funded by a �250,000 FDTL4 grant. HELM aims to enhance the mathematical education of engineering undergraduates by the provision of a range of flexible learning resources in the form of workbooks and web-delivered computer-aided learning (CAL) segments. These incorporate engineering exercises and case studies closely related to the mathematics presented. Significantly however, HELM makes extensive use of a computer-aided assessment (CAA) regime to drive student learning of engineering mathematics and provides both an integrated web-delivered CAA implementation and an alternative stand-alone CD based version. This CAA regime is essential to gain the full potential of the other HELM learning resources.

This paper first describes the HELM learning resources and outlines the project's assessment philosophy. It then describes the HELM computer-aided assessment regime and how it can be successfully used for formative assessment of students learning engineering mathematics. It discusses some of the concerns raised by students and staff using CAA. Finally it outlines the evaluation and trialling strategies proposed by the HELM team to evaluate these learning resources and to assess the viability of 'rolling out' the HELM assessment regime across the HE sector.

Learning resources

The HELM learning resources consist of workbooks, CAL courseware and computer-aided assessments (CAA).

High-quality printed workbooks cover basic engineering mathematics. Eventually 50 workbooks will cater for syllabus requirements in calculus, algebra, Fourier analysis, Laplace and z-transform methods, ordinary and partial differential equations, complex analysis, numerical methods, probability and statistics and modelling. Currently over 30 are available for trialling.

These resources follow a traditional approach; however, related engineering examples, which help students learn to apply mathematics to solve engineering problems, are an important feature and are being added to the workbooks during the project and it is hoped to include contexts specific to various branches of engineering such as mechanical, electrical and electronic, civil and chemical. Typical examples include: black body radiation, bending moments, vibrations, complex impedance and motion under gravity.

The importance of contextual and engineering problem-solving approaches to motivate the learning of mathematics for engineering students is recognised by the inclusion of two workbooks devoted to engineering case studies. The first engineering case study on 'Modelling Motion' has been drafted and trialled. It is planned to base the second on 'Modelling Waves'.