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 12 Facilities for teaching mathematics
[pages 183 - 187]

602 In the third part of our report we discuss the resources which are required to teach mathematics. We begin by considering the facilities which should be available in primary and secondary schools.

Accommodation

603 In most primary schools each class spends the greater part of the day in its own classroom or class base, moving elsewhere only for activities such physical education and music. Each class needs facilities for practical work in mathematics but no special accommodation is required. In schools whose accommodation includes areas for practical work which are shared by several classes, it can be convenient to assemble certain pieces of mathematics equipment, for example apparatus for measurement of various kinds, in one part of such practical areas. They are then readily accessible to children from several classes.

604 We are in no doubt that in secondary schools mathematics should be taught in suitably equipped specialist rooms and that their provision makes it easier for good practice to develop, especially in schools in which there is good leadership from the head of department. This is underlined in the following extracts from the report of the National Secondary Survey (1) 'The problems of teaching mathematics are increased by inappropriate accommodation and some of the best practice seen would have been impossible if the teachers had not enjoyed suitably equipped bases in which to work.' 'Observation showed, and statistical analysis confirmed, that display material, experimental and practical work, the use of realistic material, and the mathematical use of puzzles and games were all more likely to be found in schools in which mathematics was allocated specialist accommodation.' However, sufficient suitable accommodation for the teaching of mathematics is not yet available in many secondary schools. In their written submissions, many teachers have drawn attention to the need to provide suitable specialist accommodation for mathematics teaching. Some of the teachers whom we have met during our visits to secondary schools have also stressed this need and have pointed out the difficulties of carrying from room to room all the mathematics equipment which is required.

605 About ten to fifteen years ago some of those engaged in mathematical education were advocating the provision of a 'mathematics laboratory' in each secondary school. However, we believe it has become clear that the provision of a single specially equipped room of this kind does not meet the need satisfactorily. This is in part because of the timetabling problem of enabling mathematics classes to use the facilities which the room provides at the time at which they are needed. More importantly it assumes, in our view wrongly, that only one mathematics class will need facilities for practical work at any one time. We believe that it is preferable for certain rooms to be designated for mathematics and for these to be grouped together. If it can be arranged that one of the rooms is somewhat larger than the others, with certain extra facilities such as side benches and a sink, this is an advantage. All the rooms should have tables or desks with flat tops, good blackboard facilities which include a square grid for graphical work, storage facilities for books and equipment, and display boards on the wall. Power points should be available to make possible the use of equipment such as an overhead projector or microprocessor.

606 The provision of grouped specialist accommodation provides many opportunities for the mathematics department in a school. Among these we would include

• opportunity for greater cooperation and mutual support among those who teach mathematics in a school;
• opportunity for those who teach mathematics to observe each other at work;
• opportunity for the head of department to oversee the work of the department more easily and assist its members - this can be especially important in a school which is short of well qualified mathematics staff;
• opportunity to share equipment and other resources more effectively;
• opportunity for better display of pupils' work and other relevant material in circulation areas as well as in classrooms;
• opportunity for flexible use - for example, if one room has certain additional facilities it is possible for classes to exchange rooms at short notice; a set of grouped rooms also enables team teaching techniques to be used if desired, and makes it easier to provide cover for absent staff.

Equipment

608 Throughout our report we have stressed the importance of practical experience at all stages of the mathematics course. In order to provide such experience the necessary equipment must be available. Much of what is required is neither elaborate nor expensive but it needs to be available in sufficient quantity and to be readily accessible.

609 In infant classes it is essential to have plenty of small objects which can be used for sorting and counting. There must also be equipment that can be used for measuring, including sand, a sink with a variety of capacity measures and simple balances with appropriate weights. Older children need other measuring devices such as rulers and tape measures, balances and scales of various kinds, and timing devices.

610 Young children need to use simple structural apparatus of various types, such as those in which units can be physically combined into larger pieces or in which collections of units can be represented by larger pieces. At a later stage a different type of structural apparatus should be available which provides a physical representation of units, tens, hundreds and thousands. Apparatus of this kind can assist children to understand the concept of place value. Real or plastic coins should also be available; these can be used both to develop familiarity with handling money and as another form of number apparatus.

611 All children in primary schools need to use a variety of two- and three-dimensional shapes. There should be a supply of simple drawing instruments including shape templates, rulers, protractors and compasses; children also need to use plumb lines and spirit levels. Paper printed with grids of various shapes and sizes is necessary for some kinds of graphical work as well as for work with patterns and shapes. Its use can also help to develop the concept of area, as can work with 'pin-boards' and 'peg-boards'. Some electronic calculators should also be available. All of this equipment, together with such things as scissors, coloured paper, card, elastic bands, string and glue, needs to be easily available when required and careful thought should be given to the way in which it is organised and stored. It is desirable that a stock of the equipment which is in frequent use should be available in each classroom or class base; it is likely to be more convenient to store equipment which is used less frequently in a place in which it can be easily accessible to all classes.

612 Practical equipment of similar kinds should also be available in secondary schools. Cardboard, scissors, gummed paper, glue, plastic counters, small plastic shapes and three-dimensional models are amongst the relatively cheap materials which can assist the mathematical development of pupils. Supplies of paper marked with grids of various kinds in lines and dots should be available as well as equipment which will enable simple statistical investigations to be carried out. In order to undertake the measurement of various kinds, the reading of tables, charts and diagrams, and the geometrical work of a constructional nature which is implicit in the content of the foundation list which we have set out in paragraph 458 [in chapter 9], very much more practical material will need to be available in secondary classrooms than is commonly found at present. Much of this material, for example a collection of two- and three-dimensional shapes of various kinds and sizes, can be produced by the pupils themselves as part of their work in mathematics and no great expenditure need be involved. However, the 'basic' equipment such as pencils, rulers and compasses which is necessary for work of this kind must be kept in good condition if pupils are to be able to produce work of good quality.

613 We have already advocated that electronic calculators should be available for use by pupils. Some pupils may still need to make use of structural apparatus for number work and a supply of this kind of material should also be available. It is likely to be convenient to divide the storage of practical equipment between classrooms and a central store. Whatever method of storage is used, it is important that all equipment should be readily accessible when it is required.

Display of material and pupils' work

614 It is usual in primary schools to display pupils' work on classroom walls but much less use is made of display in many secondary classrooms. The report of the National Secondary Survey (2) says that 'mathematical display material was found in only some 40 per cent of schools, and this on a charitable interpretation, including schools with only very limited displays of wall charts or children's work. The proportion of schools in which this material was purposefully used as part of a progressive scheme of work was smaller'. Well organised and up to date displays of material and pupils' work can provide a valuable resource for teaching whose use should not be underestimated.

Libraries

615 An increasing supply of books about mathematics which are of general interest has become available in recent years, often in paperback editions. However, copies of these books are not always available in schools nor do some teaching schemes give sufficient encouragement to pupils to read them. In secondary schools, mathematics books of general interest can often remain unnoticed if the classification system which is used to arrange books on the library shelves has the effect of interspersing these books among advanced mathematical texts and similar books which are suitable only for sixth form pupils and teachers. It is desirable that books about mathematics which are of general interest, especially those which are suitable for younger pupils, should be placed together on the same shelf so that they are easily visible. In secondary schools which have a grouped set of mathematics rooms it may be preferable to have a small mathematics library in the mathematics department.

Reference material for teachers

616 In both primary and secondary schools there should be a supply of reference books for teachers relating to the teaching of mathematics. These should include some of the publications of the professional mathematical associations as well as of the DES, HM Inspectorate and Schools Council. There should be copies of any teachers' guides which relate to textbooks in use in the school and also a selection of mathematics textbooks, other than those which are in general use, which can serve as an additional resource for teachers. In our view it is a proper use of money allocated for mathematics to purchase books of this kind.

Financial arrangements

617 We are aware that very considerable differences exist between schools not only in the provision for teaching mathematics but also in the amount of money which is made available to maintain and improve that provision. It is essential that sufficient money should be made available to maintain adequate stocks of books and equipment. It is also essential that flexibility exists in the way in which money allocated for mathematics can be used. For example, some of the work which we have recommended, especially in secondary schools, will require equipment of a kind which is not readily available from suppliers of educational equipment. It is therefore necessary that arrangements for obtaining supplies should not be such as to make it difficult for schools to obtain from other sources some of the equipment which they require.

Footnotes

(1) Aspects of secondary education in England A survey by HM Inspectors of Schools. HMSO 1979.

(2) Aspects of secondary education in England A survey by HM Inspectors of Schools. HMSO 1979.