Those teaching maths to engineering undergraduates over the past few years have faced two problems: a greater diversity of intake and a lack of basic skills in number and algebra among many students, severely hindering the exposition and development of mathematical ideas necessary for their subject.
Students who lack these basic skills may have to face engineering modules that assume they have higher-level mathematical knowledge and skills. Such skills and knowledge cannot be acquired easily and quickly. Students may also lack an ability to deal with multi-stage problems.
In a first-year class of engineering students, those with good grades in A-level maths may be sitting alongside students with poor A-levels, and other students with various vocational qualifications, typically BTEC at level III. Often these are mixed in with students whose most advanced maths qualification was a poor grade at GCSE two years earlier. Some cannot add, subtract, multiply or divide numerical fractions, or recognise or plot simple straight-line graphs and have few skills in algebraic manipulation. Students coming from a BTEC background may have had little, if any, exposure to differential and integral calculus - basic tools required from the very start of an engineering degree programme.
Universities have tried reducing syllabus content. This helps the weaker students but disadvantages the stronger, making them less prepared for the mathematical demands of more advanced and analytical engineering courses. Some universities have established support centres giving additional tuition. However, university students cannot make up for the fact that they have not even heard of such terms as "derivative" or "integral" by visiting a support centre for a few weeks, at the same time as pursuing their engineering courses. Students cannot cope with the algebra of complex numbers while still learning basic algebra of real numbers.
In September 1997 the Engineering Council produced a revised version of its 1990 document on SARTOR (Standards And Routes To Registration) in which it seeks to ensure that engineering qualifications in the UK will continue to compare favourably with the highest standards internationally (Engineering Council, London 1997). The Engineering Council sets the standard fo registration as Chartered Engineer, Incorporated Engineer or Engineering Technician. Professional Engineering Institutions will assess applicants for membership against these standards. There are significant changes from the 1990 version of SARTOR.
The Engineering Council recognises the importance of maths in engineering education. Nineteen of the Engineering Institutions responded to an invitation to comment. A mathematics syllabus in response to the proposals in SARTOR 3 and the subsequent comments were largely incorporated into the final report Engineering Mathematics Matters, Institute of Mathematics and its Applications (IMA, Southend-on-Sea, 1999). They felt that any proposed common core in maths for IEng students should be radical in a number of ways.
The mathematics syllabus for IEng students should have :
* a significant reduction in syllabus content from the traditional course * a low-level starting point, allowing a thorough consolidation of basic techniques * an emphasis on developing confidence in the application of basic techniques * a thorough integration of modern mathematical technologies as tools * a motivation through transparent and modern applications * a relevance to the career aspirations of an Incorporated Engineer * a high-threshold criterion-referenced achievement stated in terms of learning outcomes.
On completion of an IEng accredited degree programme a student should:
* be confident in the application of a range of arithmetic and algebraic techniques * be able to solve problems using simple calculus-based techniques * be able to make appropriate use of modern technology, for example computer algebra * be able to make appropriate use of spreadsheets * have a working knowledge of simple probability and of basic statistical techniques.
Practising engineers have access to a full range of modern mathematical technologies when problem solving so that engineering students need to be exposed to and be proficient in technologies such as graphical calculators, computer algebra packages, and spreadsheets. A firm foundation in algebraic and numerical skills must be established to underpin the intelligent use of modern mathematical technology.
Dr L R Mustoe is director of Science and Engineering Foundation Studies in the Department of Mathematical Sciences, Loughborough University. E-mail L.R.Mustoe@lboro.ac.uk