A Thousand Words to Shape the Future
A Response to QCA from The Mathematical Association
Mathematics has a vital role as one element in a balanced and rich education for all young people. It is important both because of its intrinsic interest and because it enables us to understand many aspects of the world and provides a range of skills which are invaluable in everyday life and the workplace at all levels. It thus serves both to enrich the life of the individual and to provide them with skills which are of importance to society.
A good mathematical education is not something that is only for a small group of advantaged or clever students. All students should acquire fluency and understanding with the mathematical ideas that they meet and be able to apply them confidently to a wide variety of problems arising from within mathematics and through its multitude of applications. Clearly some students will encounter and be able to make sense of a wider range of ideas than others, but all should be helped to develop a confidence with ideas at whatever level is appropriate to them.
Mathematics, like science to which it contributes so much, does not have a good image in this country: many adults, often highly educated in other areas, seem almost proud of their lack of skill and interest in the subject when they would be ashamed if they had to admit to poor literacy skills. By contrast in many countries in the world success in mathematics is held in high esteem. We need to change our ingrained cultural attitudes to mathematics so that it becomes a subject that is highly valued because of its great power and its endless fascination. However, changing attitudes is not an easy task and there are no simple instant remedies.
Mathematics is a difficult subject to teach and to learn, but finding sufficient good teachers and retaining them in the profession has been a serious problem for many years and will present a major continuing challenge for the foreseeable future. Good teachers of mathematics have a deep understanding of the subject, a sympathetic awareness of how students can learn it effectively and above all an ability to communicate their enthusiasm and inspire students to accept the challenges that it offers. To recruit and retain good teachers requires working conditions that allow them the time and the freedom to carry out their difficult task without endless trivial constraints and excessive pressures. They can then capitalise on the boundless opportunities made available by the rich variety of resources and ideas, including the immense possibilities of ICT in all its many forms, which can make mathematics accessible and exciting to all students.
Besides the teacher shortage there are other serious barriers to raising standards and to generating interest in the subject. The current assessment system, together with its accompanying league tables, targets and performance measures, is far too dominant and has a deleterious effect on both teachers and students. It encourages a mode of preparation for tests and examinations which focuses solely on the standard questions that appear on papers and leads to the exclusion of more interesting and challenging problems and applications at all levels. These are the very things that are of importance to employers and higher education, because they stimulate interest and encourage independent thinking.
In a report published in 1979, HMI reflect on classroom practices in secondary school mathematics:
The impression which a pupil receives of mathematics at school and the memories which he carries of the subject into later life depend on the style of teaching he receives.
In the majority of the classrooms the teaching did not aspire to do more than prepare the pupils for examinations.
The work was predominantly teacher-controlled: teachers explained, illustrated, demonstrated, and perhaps gave notes on procedures and examples.
What was lacking in this approach, even at its best was a sense of genuine enquiry, or any stimulus to curiosity or appeal to the imagination. There was little feeling that one can puzzle out an approach to fresh problems without having to be given detailed instructions.
Sadly, what HMI said over 25 years ago is still every bit as true today: indeed we would argue that the situation is very much worse and that an examination driven approach is one very significant factor that causes attitudes among students towards mathematics to deteriorate from an early age and is, moreover, making it ever more difficult for enterprising and innovative teachers to give of their best.
A major priority for the future is a substantial rethink of both the frequency and the manner in which we assess students. Both society and the individual clearly require some system of certification to acknowledge achievements, but that system should encourage positive attitudes, a real mastery of the mathematical ideas encountered at each stage and an ability to apply those ideas to genuine problems at an appropriate level. That requires much more than mere structural reform: thoughtful consideration has to be given to how the system can assess whether a suitable degree of mastery with skills has been attained and whether those skills can be applied to problems with confidence. In terms of today's style of examination the marks deemed to represent a pass need to be set at a far higher level. However, we should not be bound by our current curriculum or modes of assessment: if we are genuinely to raise standards in mathematics among our students, sustained and radical thinking is needed.
To ensure real improvements we need:
- a commitment to long term sustained development, rather than frequent superficial changes;
- a substantial involvement of people with expert knowledge and classroom experience in formulating and developing policies at all levels;
- systems of assessment and accountability that both sustain and strengthen the weak and acknowledge the achievements of all, whilst encouraging thoughtful and independent minded innovators to flourish.
We look forward to a time when education policy and the assessment system are largely removed from direct political control, so that they are not constantly subject to short term considerations and influences. Only then will it be possible to create a climate in which mathematics is a subject that people can approach with confidence, enthusiasm and success.
10th March 2006
The Mathematical Association
259 London Road
Leicester
LE2 3BE
Tel: 0116 221 0013
HMI 1979 Aspects of Secondary Education HMSO
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