Maths CAA Series: December 2002
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Abstract |
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1. Introduction |
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2. "The Mathematics Problem" |
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3. Views of mathematics from engineering practice |
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4. Changes and challenges in engineering education |
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Acknowledgements/References |
Abstract
This article is a departure from the usual for this column because it is not focused on CAA. Instead, I want to discuss some issues concerning engineering mathematics at university level, and perhaps suggest how CAA (computer-aided assessment) issues are relevant. This is offered as an opinion piece, and I hope to be provocative!
1. The REMIT project: Reassessing the roles of mathematics and IT in the university education of civil engineers
I have been conducting a research project over the last six months, and shortly due to finish, which has been
1. making a survey of the current role of mathematics in UK engineering education, with a particular focus on civil engineering, and
2. trying to identify some visions of the future roles for mathematics. A sub-theme of this has been the various roles played by IT in teaching and learningThis project also builds on a previous research project that I did in 2001, "The Mathematical Components of Engineering Expertise" [1], which investigated the mathematical ideas and techniques used by civil engineers in professional practice, by means of interviews and observations carried out in a large engineering consulting firm.
I'd like to emphasise that I'm mainly reporting here on mathematics as used by CIVIL engineers, who generally are not the greatest users of mathematics, compared with mechanical, electrical and aeronautical engineers, and thus not all of what I will say extends to other engineering disciplines.
2. "The Mathematics Problem"
In universities, mathematics is usually described nowadays as a huge problem looming over engineering education, for example:
Each year the A-level results come out showing increased pass rates, yet we do not see any improvement in the ability of students to tackle the mathematics of engineering degree courses. … The situation is serious, and getting more so. Most university engineering departments now find it necessary to provide remedial teaching for students whose mathematical foundations are not adequate for university first-year maths. Ian Pyle [2]
This is not only a problem for engineering courses, of course. Regular readers of this column will be familiar with what has come to be known in the UK as the "mathematics problem", originally characterised in a 1995 report, Tackling the Mathematics Problem [3]:
There is unprecedented concern amongst mathematicians, scientists and engineers in higher education about the mathematical preparedness of new undergraduates … The serious problems perceived by those in higher education are:
(i) a serious lack of essential technical facility-the ability to undertake numerical and algebraic calculation with fluency and accuracy;
(ii) a marked decline in analytical powers when faced with simple problems requiring more than one step;
(iii) a changed perception of what mathematics is -in particular of the essential place within it of precision and proof.A report in 2000, Measuring the Mathematics Problem [4], reiterated these findings, and advocated the diagnostic testing of students upon arrival at university and that "prompt and effective support should be available to students whose mathematical background is found wanting by the tests". Several national projects have recently been funded to address these issues [5]. Also, I have the perception that a lot of work in CAA is being driven by the need to address these issues.
Can I make a provocative point here? To characterise something as a problem implies a need to fix it, and it seems to me that the problem that people are trying to fix comes down to a view that:
School education does not produce students who are mathematically ready for university education, therefore (in the long term) school education needs to be fixed and (in the short term) students have to be made ready for mathematics at university (and preferably in a way that is economical and requiring minimal staff resources).
Perhaps I am caricaturing too much: but one has to wonder, what is changing in our basic conceptions of university mathematics education? Here is a recent comment made to me by a lecturer specialising in engineering mathematics teaching at a large technical university:
We're pretty traditional - you would not see much difference between what we do now and 20 years ago, except that the level is lower now.
No doubt the same thing could be said in a large number of UK universities.
As part of my research for REMIT, I have discussed the issue of mathematics teaching with engineers (mainly civil) and mathematicians in many universities. I come away from that experience with a personal feeling that the present system is not fixable, and moreover a feeling that the present system presents to students a form of mathematical training which does not match the requirements of modern engineering practice. I won't speak of modern scientific or mathematical practice here, a but I'm sure similar questions can be asked.
3. Views of mathematics from engineering practice
Under the present circumstances, it is not surprising for engineering academics to focus on the mathematics problem at the interface between school and university - because of the pressing need to recruit students into engineering courses, and to retain them.
Recruitment to civil engineering courses has declined drastically, down by 50% since the mid-1990s, and the mathematical nature of engineering degrees is a key issue (students must have A-level mathematics to enter a BEng/MEng course; school students are being turned off studying mathematics; less than 10% of students elect to do a full A-level in mathematics, and all physical science, mathematics and engineering departments are fishing in this declining pool of candidates; etc etc.).
Also, as is well known from the reports already mentioned, the highest failure rates (up to 30%) in first-year courses are occurring in mathematics and mathematics-related modules. The problems that are reported generally come back to those suggested by the Tackling report: a lack of fluency, of comfortableness, with mathematical symbolism.
I think that employers in civil engineering are somewhat bemused about this situation. I suppose there has always been a view from professional practice that academics are overly conservative and a bit out of touch with the realities of practice, but this view is becoming intensified as a skills shortage grows in civil engineering. The industry needs young engineers and there are not enough of them; the entry points to the engineering profession at age 18 appear overly restrictive, and there is a lack of diversity of higher education courses (over the last 20 years, there has been a huge decline in practically-oriented HE courses for civil engineering, which have become perceived as academically second-rate compared with the analytically-oriented BEng and MEng). Sir Duncan Michael, former chairman of the engineering consultancy Ove Arup writes:
Today engineering uses more mathematics than ever, but whose job today does not use mathematics? However, the explicit use of mathematics, hands on and manipulative by each engineer is probably less now than it has been for the last 50 years, maybe 100 years. All the lovely software that we are writing to use our super-reliable cheap computing power has liberated the engineer from his mathematics. But his educators are in no hurry to tell him. My proposition is that we now accord a place to mathematics for engineers which is too powerful and which directs our actions to the overall disbenefit of engineering and the economy. Our engineering as a whole would be better if mathematics were reduced from its overwhelming influence on personal progress … I want to develop qualitative or soft mathematics as respectable for engineers. Think not of the 10% of the populace who are allowed to be candidates to become engineers today. Think instead of the 90% whom we exclude from even hoping to become engineers, for their lack of measured mathematics achievement in their teens. [6]
The role of mathematics in engineering practice has changed significantly in the last 20- 30 years as a result of a widescale restructuring of the construction industry and the roles of civil engineers within it. Today, it is generally the case that few civil engineers are carrying out much explicit mathematics on an everyday basis, compared with 30 or 40 years ago. Rather, in a multidisciplinary team-working environment a relatively small number of mathematics specialists can provide the support required, even for very complex design projects. Underpinning this change in the profile of mathematics is the ubiquitous role of software in engineering practice.
This has led some engineers to question whether mathematics remains as a key component of engineering practice. I think this is misconceived; that in fact, mathematics may seem to be disappearing from (most) practice, but it is actually changing its character. Some forms of mathematics-based analysis have all but disappeared (e.g. the many specialised manual techniques for structural analysis calculations), but others remain, and are becoming more important - especially, the "implicit" mathematics that underpins professional engineering judgement.
4. Changes and challenges in engineering education
One of the things will happen in the next few years is a re-think by the engineering profession about entry routes to professional engineering via university courses, and efforts to promote the diversity of HE engineering courses. The Engineering Council (UK) has recently announced a comprehensive review of the rules and standards governing the education and development of registered engineers [7]; also the Joint Board of Moderators (which grants accredited status to degrees in civil engineering) has caused quite a stir amongst civil engineers by announcing in May 2002 that it will no longer (for a 2 year trial period) "insist that A-level Mathematics (or equivalent) is a prerequisite for entry to a JBM accredited course". This change is intended not as a invitation to "dumb down" engineering degrees, but rather to invite universities to offer new courses to fill the present shortage in vocationally-oriented graduates [8].
As engineering departments review their courses and entry requirements, they will still be looking to mathematicians to provide mathematics teaching. The courses will most likely be rather different in character from the present: less chalk-and-talk, more problem-solving in engineering contexts (perhaps based on groupwork), more use of computer software. This presents an opportunity and a challenge to mathematicians, to consider the teaching and learning of mathematics in new contexts. I hope that mathematicians will be ready to take on this opportunity, and not be unduly shaded by the gloomy shadow of the "mathematics problem".
Acknowledgements
The REMIT project is a collaboration with Professor Richard Noss, Institute of Education. We are grateful to The Ove Arup Foundation for a grant to carry out this research.
References
[1] Funded by the Economic and Social Research Council. Project website: www.ioe.ac.uk/rnoss/MCEE .
[2] Ian Pyle, "Mathematics - The lost art?". In G. Cutler & S. Pulko (eds), PROGRESS 1: Student progression and retention in engineering, conference proceedings, October 2001. Download from: http://www.hull.ac.uk/engprogress/Prog1Papers.htm (these proceedings
contain a number of interesting papers on engineering mathematics).
[3] Tackling the Mathematics Problem - a joint report of the LMS, IMA and RSS, 1995. Download: www.lms.ac.uk/policy
[4] Measuring the Mathematics Problem - a joint report of the Engineering Council, IMA, LMS and LTSN Centre for Maths Stats and OR, 2000. Download:http://www.engc.org.uk/publications/pdf/mathsreport.pdf
[5] Funded under the FDTL4 initiative - see http://ltsn.mathstore.ac.uk/FDTL/index.shtml .
[6] Duncan Michael, "Gold Medal Address - Values and change: benefit or problem?". The Structural Engineer, 79, 19, 26 - 31 (2 October 2001).
[7] www.engc.org.uk .
[8] Personal communication with Professor James Croll, Head of Civil and Environmental Engineering at University College London and Chair of the Joint Board of Moderators. See the discussion published in the "New Civil Engineer" magazine, 14 November 2002.