Cockcroft (1982)

Notes on the text
Preliminary pages Foreword, Membership, Contents, Introduction

Part 1
Chapter 1 Why teach mathematics?
Chapter 2 The mathematical needs of adult life
Chapter 3 The mathematical needs of employment
Chapter 4 The mathematical needs of further and higher education

Part 2

Chapter 5 Mathematics in schools
Chapter 6 Mathematics in the primary years
Chapter 7 Calculators and computers
Chapter 8 Assessment and continuity
Chapter 9 Mathematics in the secondary years
Chapter 10 Examinations at 16+
Chapter 11 Mathematics in the sixth form

Part 3

Chapter 12 Facilities for teaching mathematics
Chapter 13 The supply of mathematics teachers
Chapter 14 Initial training courses
Chapter 15 In-service support for teachers of mathematics
Chapter 16 Some other matters
Chapter 17 The way ahead

Appendices

Appendix 1 Statistical information
Appendix 2 Gender differences in mathematical performance
Appendix 3 List of those who made submissions
Appendix 4 Visits and meetings
Appendix 5 List of abbreviations

Index

Report of the Committee of Inquiry into the teaching of mathematics in schools under the chairmanship of Dr WH Cockcroft

London: Her Majesty's Stationery Office 1982
© Crown copyright material is reproduced with the permission of the Controller of HMSO and the Queen's Printer for Scotland.

ISBN 0 11 270522 7

Chapter 17 The way ahead
[pages 242 - 245]

798 Our terms of reference have required us to consider the teaching of mathematics in schools in the light of the mathematical needs of pupils when they proceed to further or higher education or to employment, as well as of their needs as adults. In the first part of our report we have sought to identify these needs, in the second part to discuss the ways in which a balanced and coherent mathematics curriculum can provide for these needs, and in the third part to identify the provision and support which is required to enable good mathematics teaching to take place.

799 Changes of many kinds have led to increasing pressure on teachers during the last fifteen years. These years have been a time of rapid social, technological and economic change. There has been a move to comprehensive education in almost all parts of the country and the school leaving age has been raised; in some areas the reorganisation of local authorities placed additional strains on teachers. The 'bulge' in the birth rate, which reached its peak in 1964 and led to a rapid increase in the teaching force, has been succeeded by the present sharp fall in the number of pupils in many areas and so to uncertainty and reduced opportunities of promotion for teachers. Pressure on mathematics teachers in particular has also arisen from the introduction of new mathematics syllabuses resulting in the need to teach courses of a different kind, often without opportunity to undertake the necessary preparation and in-service training. The introduction of CSE has created examination pressures on pupils and teachers which did not exist earlier; metrication and the introduction of decimal currency led to initial difficulties in terms of the availability of suitable books and other teaching materials in many schools. More recently the rapid increase in the availability of electronic calculators, without sufficient guidance as to the use which could and should be made of them in the classroom, has presented further problems to many teachers. Finally, throughout these years there has been a continuing shortage of mathematically well qualified teachers in both primary and secondary schools.

800 Alongside these changes, there has been increased public criticism of the education system, and especially of mathematics teaching, expressed by parents and employers as well as by many in political and public life. In these circumstances it would be surprising if the morale of some of those who teach mathematics had not suffered. Yet these years have also been a time of mathematical development during which many teachers have given willingly of their time to join, for example, in local working groups, in curriculum development and in other kinds of in-service work. In many schools good work is being done in the teaching of mathematics and very many teachers are making considerable efforts to satisfy a public expectation of achievement in mathematics which is by no means always realistic. Nevertheless, as we hope our report will have made clear, there are at present many pupils who are being offered mathematics courses which are not suited to their needs and many teachers of mathematics who lack suitable qualifications. For these and other reasons, the mathematical education which many pupils are receiving is not satisfactory. We therefore believe that major changes are essential.

801 Those who teach mathematics must take into account the great variation which exists between pupils both in their rate of learning and also in their level of attainment at any given age. It follows that mathematics courses must be matched both in level and pace to the needs of pupils; and therefore that a 'differentiated curriculum' must be provided so that pupils will be enabled to develop to the full their mathematical skill and understanding, a positive attitude towards mathematics, and confidence in making use of it. Examinations at secondary level must also be better suited to the needs of pupils than is the case at present.

802 We believe, too, that it is essential to improve the overall quality of the mathematics teaching force. This means that active efforts must be made to attract more well qualified mathematicians into the teaching profession, to retain those mathematics teachers who are well qualified and effective, and to provide increased levels of in-service support and training. Good support at classroom level is essential for all who teach mathematics; this requires not only the provision of adequate teaching facilities and equipment, but also good leadership by mathematics coordinators and heads of department who have been trained for their task.

803 Among the suggestions and recommendations which are included in our report are many to which teachers themselves can respond and, indeed, for whose implementation teachers themselves must accept the main responsibility. We therefore hope that teachers will read with particular care those parts of the report, notably Chapters 5 to 11, in which these suggestions are concentrated and consider how best they can help to bring about the changes we are recommending. For example, computational skills should be related to practical situations and applied to problems. Mathematics teaching for pupils of all ages should include exposition, discussion, appropriate practical work, problem solving, investigation, consolidation and practice, as well as mental and oral work. Assessment should be both diagnostic and supportive, and teaching should be based on a scheme of work which is appraised and revised regularly. All of this and more is necessary if mathematics teaching is to be effective; all of this is in the hands of teachers.

804 On the other hand, we have made several suggestions and recommendations which teachers cannot implement by themselves and which require action by others. For example, in Chapters 6 and 9 we have stressed the importance of the roles of the mathematics coordinator and head of department; it is essential that these teachers should be given training for their task and continuing support to enable them to carry it out. Those who teach mathematics require the support of effective advisory services as well as opportunities for in-service training of various kinds; they also need suitable facilities and equipment in their schools. Responsibility for provision of these kinds must rest primarily with local education authorities. We discuss the facilities required to teach mathematics in Chapter 12, and in-service support for teachers in Chapter 15.

805 Several of our recommendations relate to examinations and tests. In Chapter 10 we argue that examinations at all levels should provide suitable targets and reflect suitable curricula. They should enable candidates to demonstrate what they know and should not undermine the confidence of those who attempt them. We recommend that in the new single system of examination at 16+ there should be a range of papers in mathematics focused at different levels. We also recommend that a study should be commissioned to consider whether it is possible to devise a means of providing evidence of achievement for lower attaining pupils in ways which will assist, and not conflict with, the provision of suitable courses for these pupils; the outcome of such a study could have a bearing on the need for employers' tests, which are discussed in Chapter 3. We recommend in Chapter 8 that in the near future an overall appraisal should be prepared of the educational implications of the mathematics testing which has been carried out by the Assessment of Performance Unit. Action in these matters must rest primarily with examination boards and, in certain respects, with central and local government. In studying our recommendations they should bear in mind the needs of pupils in later life, which we discuss in Chapters 2, 3 and 4.

806 No efforts to improve the quality of mathematics teaching are likely to succeed unless there is an adequate supply of suitably qualified mathematics teachers. In Chapter 13 we discuss the supply and recruitment of teachers and include proposals for greater flexibility within the salary system, for financial incentives to suitably qualified students and for a guarantee of employment for newly trained mathematics teachers. In many of these matters we believe that primary responsibility rests with central government; local education authorities as employers of teachers also have considerable responsibility.

807 All who teach mathematics require initial training which fits them both mathematically and professionally to start teaching. We hope that those who are engaged in initial training in mathematics will review the content of their courses in the light of our discussion of mathematics teaching. We would draw the attention of all who are responsible for teacher training to our discussion in Chapter 14, in which we recommend a review and evaluation of the initial training of all who will teach mathematics.

808 Finally, we have drawn attention in the course of our report to the need for curriculum development of various kinds leading to the preparation of materials for use in the classroom. For example, work is required to develop materials which will reflect the content of the 'foundation list' we have set out in Chapter 9 and also to develop the range of materials which are written in Welsh. We suggest in Chapter 7 that materials are required which will enable teachers to exploit the use of calculators as an aid to mathematics teaching and that software of good quality is required for use with microcomputers. We hope that those public and private bodies which fund curriculum development and educational research will bear our suggestions in mind when considering proposals which are submitted to them.

809 In this chapter we have set out our recommendations in a way which many will not have expected. Our report includes many suggestions which we could have set out in a list, but we have preferred instead to draw attention to them by the use of heavier type in the main body of our report. We have done this because we believe that the teaching of mathematics must be approached as a whole and that the significance of many of the points which we could have set out separately becomes more apparent when they are read within the context of our argument. We have therefore identified instead, in paragraphs 803 to 808, six agencies whose active response to our report we believe to be essential if the changes in mathematical education which we are recommending are to be brought about. These agencies are teachers, local education authorities, examination boards, central government, training institutions and those who fund and carry out curriculum development and educational research. It will not be sufficient if only some of these agencies respond, since the contribution of all will be necessary if progress is to be made. Educational change cannot be accomplished overnight and the full implementation of our proposals will take time. For this reason we believe it to be essential that action should not be delayed and that the necessary resources for this action to begin must be made available.

810 But even the active cooperation of the six agencies we have identified is not likely to lead to lasting results unless there is support from a seventh, the public at large, including especially parents, employers and those engaged in public work. The setting up of our Committee demonstrated a widespread view that action was needed in order to meet the perceived national need for a numerate population. During the past three years we have received many expressions of support for our work which indicate a widespread belief that every boy and every girl needs to develop, while at school, an understanding of mathematics and confidence in its use. In our view this can only come about as the result of good mathematics teaching by teachers who have been trained for their work and who receive continuing in-service support. It must therefore be the task of all who share this belief to support and encourage the implementation of the changes which we believe to be necessary and to make it clear that, as part of the education which our children receive, mathematics counts.