Select Committee on Science and Technology Appendices to the Minutes of Evidence


Memorandum submitted by the London Mathematical Society

  The London Mathematical Society (LMS) welcomes the opportunity to submit evidence to the Inquiry. The LMS has played an active role in the discussions on mathematics in the schools for many years. Its most influential single contribution was producing (in collaboration with the Institute of Mathematics and its Applications and the Royal Statistical Society) the report Tackling the Mathematics Problem in 1995. Members of the Committee who have read this report and also those published by the Engineering Council and the Institute of Physics[42] will see that there is little or no difference between us and our colleagues in science and engineering about the issues.

  We strongly urge those members of the Committee who have not yet read the reports to do so. They demonstrate clearly that the problems that concern us are not merely problems for mathematics and mathematicians, they affect all of science and engineering in the UK.

  The majority of the members of the Society are engaged in university teaching. Much of this is to science and engineering students, and the extent to which we are able to provide what their home departments want is heavily dependent on what they have covered at school. Moreover, we consider that students who intend to read mathematics at university should follow the same basic curriculum as those who intend to go on into science. They may profit from enrichment along the way and some extra material at the end, but their core needs are much the same. Following essentially the same curriculum also allows students to delay their decision about what to study at university until they are applying for a place, or even until they actually begin their university course.

  In our response, therefore, while we focus on mathematics in its role as part of the science curriculum, our comments apply more broadly. We do not envisage a substantially different curriculum for potential mathematicians. On the contrary, we would consider this a mistake.


  1.1.  The present system (it cannot really be called a curriculum) based on A-levels evolved during a period when only a very small proportion of the age cohort went on into higher education. It may have been appropriate then; it certainly is not well suited to the present situation. We strongly support the concept of a curriculum for 14-19 year olds and we consider that this requires the introduction of some sort of baccalaureate or the certificate proposed by Dearing.

  1.2.  As Dearing proposed, mathematics should be compulsory, but there should be a separate course for students not intending to read mathematics or a subject that depends on it.

  1.3.  We make no specific proposals here about the material to be included. If the idea of a curriculum is accepted, we would expect to discuss the details with the Qualifications and Curriculum Agency (QCA). Much of what we would expect to see in the curriculum is in fact already there; the question is how much of it is taught and how and to whom. That is not to say that we are content with what most students are being taught, but rather that we do not see changing the official curriculum as the way to improve the situation.

  1.4.  There should be no public examinations during the period, only at the end, though in saying this we do not mean to exclude the possibility of modular examinations.

  1.5.  As a matter of urgency, measures must be put in hand to remedy the serious shortage of mathematics teachers in the schools.


  2.1.  Given the level that has been achieved at age 14, the present content is, on the whole, not unreasonable, though we are less satisfied about what is actually taught in many classrooms. We are also concerned about the balance; in particular there seems to us to be far too much time devoted to data handling, In any case, we do not see how there could be a major change in content unless there are also changes in what is taught up to age 14, and we do not expect this to happen in the near future. We would, however, hope that over the next few years there will be a general raising of standards and some adjustments, but these are matters to be discussed directly with the QCA. Such discussions are already taking place and will, we assume, continue.

  2.2.  The devil, however, is in the detail, for example in the materials provided to teachers and in the examinations. It is also in the structure. That a topic is in the curriculum does not necessarily mean it will be taught, still less that it will be adequately covered. For example, the summary to the recent Royal Society/Joint Mathematical Council report on the teaching of geometry[43] states, "Overall, for mathematics 11-16, we conclude that the geometrical content of the new National Curriculum, with a few adjustments, forms an appropriate basis for a good geometry education." Yet the authors immediately go on to say, "In order for this to be achieved, however, considerable changes are needed in the way geometry is taught."

  2.3.  In the same way, while there is a reasonable amount of algebra in the National Curriculum, that is all too often not reflected in the classroom. Teachers have realised that time spent on other parts of the curriculum is more likely to increase the number of C grades at GCSE, and it is this on which their school's performance is judged. Weakness in elementary algebraic manipulation is one of the most serious problems reported by university science departments and indeed mathematics departments as well.

  2.4.  We understand that the QCA has plans to redesign the GCSE examination and remedy this problem. It would, of course, automatically disappear if GCSE were to be discontinued, as we understand is also being considered and which would be consistent with a 14-19 curriculum. It remains, however, a clear example of how merely putting something into the curriculum may not be enough. If there are topics or indeed whole subjects that we consider should be taught, the structure — including the assessment — must be designed to ensure that they are.

  2.5.  Finally, we remind the Committee that there is a serious shortage of qualified mathematics teachers which on present form is likely to get worse, not better. If there are not enough teachers with adequate qualifications in mathematics, the subject will not be well taught, however well designed the curriculum may be.


  3.1.  It is not so long ago that only a small proportion of the age cohort continued in full time education after age 19. Now about 35 per cent go on to higher education, and the Government intends that the figure will soon rise to 50 per cent. School is no longer the end of formal education for most students. Instead, there is now an interface between school and university in much the same way that there is an interface between primary and secondary schools.

  3.2.  This has two very significant consequences. First, an important consideration in designing the 14-19 curriculum must be to prepare students for higher education, to give them the knowledge and skills they will require for further study, whatever subject they choose. Second, because almost all students with two or more A-levels now go on to higher education, there is ample opportunity for them to study a subject that interests them but which is not available at A-level. It is therefore not as necessary as it may have been in the past to offer a very large menu of subjects from which they can choose "a la carte". It is a luxury we can no longer afford, either in terms of the cost of provision or in its effect on preparation for university study.

  3.3.  Instead of the present system of a more or less free choice among a very large number of subjects at A-level, there should be some sort of structure leading to a school leaving certificate like the French or International Baccalaureate or the certificate proposed by Dearing. Indeed, without such a structure, we cannot really speak of a curriculum.

  3.4.  There is a widely held view that the universities can determine a de facto sixth form curriculum by their admissions requirements. If, for example, science departments demand A-level mathematics, then students will be obliged to study mathematics at A-level. In fact, only a few institutions, and a few subjects such as medicine, can do this. Most departments in most universities operate in a buyers' market for places. This has always been the case to some extent, but the ever-increasing financial pressures on universities have made departments much more vulnerable. Students can determine the entry requirements simply by not applying in sufficient numbers with the appropriate qualifications.

  3.5.  For example, while Further Mathematics was once considered a prerequisite for most mathematics courses, few, if any, departments now insist on it. That is not because they decided that it was unnecessary, but because fewer and fewer students were offering double mathematics. In its recent report, the Institute of Physics writes that it is now considering a Physical Sciences degree especially designed for students with low qualifications in mathematics, largely because there are not enough applicants for courses in physics who have adequate mathematical backgrounds.

  3.6.  The result, at least in mathematics and science, is that universities are more and more being required to teach what could have been done more cheaply and also more effectively at school. (The pace and style of teaching at university are necessarily quite different from at school, and the students are older and more independent.) The problem is worse for students who are reading science and engineering in universities than for those reading mathematics. Because they do far less mathematics as part of their course, any time wasted is a greater proportion of the total that can be devoted to the subject.

  3.7.  There are strong reasons for making mathematics compulsory for all students up to age 19. For example, many UK students in courses in the life sciences now enter university with no mathematics beyond GCSE, and with a two year gap since they last studied the subject. These students find it very difficult to learn the mathematics they need. As a result, many never acquire the mathematical background that is standard for their contemporaries in other countries.

  3.8.  Although mathematics should be compulsory in the sixth form (ie in the last two years at school), there should be different courses for different groups of students. In particular, those who are not planning to study mathematics or a subject dependent on mathematics should not be expected to follow the same course as those who are, with only the stopping point being different. They should have a course specifically designed for their needs. It would also be better to have it continue over two years, rather than being rushed through as the present AS-level is.

  3.9.  Statistics would probably constitute a larger proportion of the less demanding course than of the one for students who intend to continue their mathematical studies at university.

  3.10.  At present, applied mathematics at A-level consists largely of mechanics. We would prefer to see this broadened to reflect what applied mathematics has become over the past 50 or more years.

  3.11.  The relatively small core and the correspondingly large amount of optional material at A-level have serious consequences for the teaching of mathematics at university. Any material that is not in the core has to be taught at university, and to a class most of whom have done it before. This is very wasteful of resource and of students' time, and again the problem is worse for students in science and engineering than for those studying mathematics.

  3.12.  While there should be more than one distinct mathematics course, we see no advantage in allowing choice within the courses. It is hard to see how this choice really benefits the student. Those who are going to study some mathematics at university will be able to cover the topics later, while for the others the choice is largely unimportant.

  3.13.  Allowing students within a school to select different options also increases the amount of teaching that has to be done. Even if we were convinced it was advantageous we would still assign it a much lower priority than teaching mathematics to more students and at a pace that they can cope with. The shortage of qualified teachers is bound to limit what can be accomplished, at least in the short and medium term, and that makes it all the more important that we make the most effective use of the qualified teachers there are.


  4.1  If there is to be a real curriculum for ages 14-19, we see no need for national testing during this time. Suitable school leaving examinations will set the targets that students will have to reach at age 19, and this, together with the existing inspection process, should suffice to ensure that what happens along the way is appropriate. Indeed, where there is diversity in the students' achievements at the beginning of a course, national tests at the half-way stage may make it harder, not easier, for schools and colleges to reach the desired end point. We have recently seen an example of this with AS-level mathematics.

  4.2.  National tests take up a great deal of time, not least the time devoted to preparing for them. They tend to restrict what is taught to what can be easily examined. They can lead both teachers and students to concentrate on preparation for the tests rather than actually learning the subject. This can make it difficult for many students to acquire one of the valuable transferable skills that they are meant to acquire at school and university, the ability to learn. It is disconcerting to be asked by one's students at the very beginning of a course for copies of previous examinations; more importantly it is a clear indication of what they have been taught to see as the centre of the learning process.

  4.3.  National tests are very expensive and use resource that could otherwise be devoted to teaching and learning. In our view they are necessary, but the policy should be to have as few as are absolutely necessary to ensure that the required material is being taught and to the right standard. A single set of public examinations at the end of a four or five year course should not distort teaching too much; to have examinations almost every year is another matter altogether.

  4.4.  We do not mean to exclude modular examinations, but if they are used they should be essentially final examinations in stages, not national assessment throughout the whole period.

January 2002

42   Tackling the Mathematics Problem (London Mathematical Society, 1995, ISBN 0-7044-16247); R Sutherland and S Pozzi, The Changing Mathematical Background of Undergraduate Engineers (The Engineering Council, 1995, ISBM 1-898126-65-8); Measuring the Mathematics Problem (The Engineering Council, 2000); Physics-Building a Flourishing Future (Institute of Physics, 2001, ISBN 0-7503-0830-3). Back

43   Teaching and Learning Geometry 11-19. (The Royal Society, 2001, ISBN 0-85403-563-X). Back

previous page contents next page

House of Commons home page Parliament home page House of Lords home page search page enquiries index

© Parliamentary copyright 2002
Prepared 11 July 2002