Mike Savage and Tony Croft say universities must support entrants with maths weaknesses
Is there a "maths problem" at 18-plus? The universities are in no doubt - there is a problem and it has been getting worse since 1990.
Lecturers teaching first-year maths modules have known for some time that all was not well although, until recently, much of the evidence was anecdotal. Many of their students were getting the basics wrong and doing silly things which students with a good A-level grade were not expected to do. Here are two typical examples: In the first it was thought that the student had merely made a mistake, yet when quizzed he replied: "What you do to the numerator, you must also do to the denominator; and so cancelling the square roots gives x5 divided by x which is x4." Discussion with the student revealed this lack of understanding of indices, whereas in the second example writingreveals a common misunderstanding of the rules for algebraic manipulation.
Such examples are now commonplace at 18-plus. Many students enrolling on courses making heavy mathematical demands, such as engineering or physics, are severely handicapped by a lack of essential technical facility - particularly a lack of fluency and reliability in numerical and algebraic manipulation and simplification. Across the entire university sector this gives rise to high failure and drop-out rates, quite apart from the difficulties of trying to teach students with insecure foundations.
What makes the problem worse is that among the A-level students are others with "equivalent" qualifications, for example, AGNVQ. There is evidence that students from such backgrounds are even less well prepared than those who have an A-level maths at grade E.
The report Measuring the Mathematics Problem, (Engineering Council, 2000), has identified strong evidence of a decline since 1990 in the basic maths skills of new undergraduates. Independent studies show that the decline in basic maths skills has been rapid. The performance of grade C students in 1997 is no different from that of students with grade E in 1993 and those with grade N in 1991. The decline affects students throughout the grade range (A-E) in A-level maths.
Should A-level maths be changed yet again? Or is it time for universities to address the problem?
The nature of learning maths means that most students require considerable time and practice to develop confidence and competence. It is unlikely that improvements can be expected from schools while there is a shortage of mathematically qualified teachers.
Ausebel's dictum "Find out what students know and then teach them accordingly" is the basis for the three main recmmendations from Measuring the Mathematics Problem. First, students on maths-based degree courses should have a diagnostic test on entry. Second, prompt support should then be available to students who need it. Third, a national database should be set up for diagnostic questions and tests.
In some institutions the first of these recommendations is being acted on, with more than 60 departments of maths, physics and engineering testing their new students in this way.
The provision of follow-up support is more problematic. A number of universities are exploring follow-up strategies. These include streaming by ability and teaching streams separately. Some departments have recruited school teachers to teach the weaker groups (as opposed to lecturing) and allow more teaching hours. Others have introduced remedial lectures alongside first-year courses. There are two problems here - students time and attention, and the danger of overloading weak students with the additional material.
Another strategy is to replace a mainstream maths module with a lower-level transitional module to bridge the gap, but then students may find that they are not covering techniques required for their engineering or science modules for example. Several universities have established supplementary resources and drop-in surgeries, but these are insufficient. What many students need is an extended and systematic programme of study.
The report's most radical proposal, but the one which has the most virtue educationally, and which promises a more robust long-term solution, is to consider redesign of university curricula so that mathematically demanding components follow later, giving time for basic skills to be developed. Many aspects of engineering and science rely on maths for their description and analysis. However, holding back parts of the curriculum while a firm mathematical foundation is laid in year one would allow students to develop confidence.
Earlier reports, since 1995, contain many recommendations but little evidence that any of these have been implemented successfully, if at all.
Now is the time for the problem to be acknowledged at the highest level within the universities, QCA and the Government. A second step would be to implement more widely the recommendations in Measuring the Mathematics Problem.
Professor Mike Savage is an applied mathematician based in the Department of Physics and Astronomy at Leeds University, and Dr Tony Croft is manager of the Mathematics Learning Support Centre at Loughborough University. They were among the participants in the Engineering Council report 'Measuring the Mathematics Problem', available on www.engc.org.uk