The Cockcroft Report (1982)
Mathematics counts
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
Index
[pages 305 - 311]
References in the index are to paragraphs in the main report unless otherwise stated. An outline of the contents of each chapter will be found in the index under the entry for the chapter heading.
[To make finding references easier in this web version, I have added chapter numbers. Thus '9/439' means 'Chapter 9, paragraph 439'. If you spot any errors, I'd be grateful if you'd email me.]
A
Accommodation for teaching mathematics 12/603-7
primary 12/603
secondary 12/604-7
Additional mathematics 9/439, 9/478
Adult life, mathematical needs of Chapter 2
Make it count 2/13
Research study 2/16-18
Outcome of research study 2/19-30
feelings of anxiety 2/20-2
use of approximation 2/23
dislike of mathematics 2/24-5
understanding of percentage 2/26-7
reading of charts and tables 2/28
use of calculators 2/29
strategies for coping 2/30
Mathematical needs of adult life 2/31-4
Numeracy 2/35-9
Advanced Further Education (AFE) Pool 15/761
Advisory Council for Adult and Continuing Education (ACACE) 2/14-15, 2/18
Adults' mathematical ability and performance 2/16n
Use of mathematics by adults in daily life 2/16n
Agriculture 3/135-7
Aims and objectives in the primary years 6/367-71
A Level mathematics see Sixth form
Algebra 5/201, 6/294, 6/318, 9/451, 9/461
use in employment 3/77
Applied mathematics at A Level 11/565-75
Assessment and continuity Chapter 8
Assessment 8/414-26
marking 8/415-17
should be diagnostic and supportive 8/415-16
not possible to mark every piece of work 8/417
recording of progress 8/418-19
testing 8/420-3
purpose of testing 8/420
standardised tests 8/421-3
as part of transfer procedure 8/423
evaluation 8/424
Assessment of Performance Unit 8/425-6
practical testing 8/426
Continuity 8/427-35
within school 8/427
at time of transfer to new school 8/428-35
need for consultation between schools 8/430
tests at time of transfer 8/432
use of information from previous school 8/433-4
transfer at 16+ 8/435
Assessment of Performance Unit (APU) 5/205-6, 6/340, 8/425-6, 9/453, 10/534
Association of Graduate Careers Advisory Services (AGCAS) 13/639, 13/654
Association of Teachers of Mathematics 15/730-1
Attainment in mathematics
at age 11 6/339-44
levels to be expected 5/189
'profile' 5/190, Figure B
high attaining pupils 6/330-3, 9/474-81
low attaining pupils 6/334-8, 9/459-66
very high attaining pupils 6/331, 9/482
very low attaining pupils 6/337-8, 9/467-9
Attitudes to mathematics
of parents 2/24, 5/207
of pupils 5/205-6, 6/345-7
of young employees 5/198-204
B
Bachelor of Education (BEd) degree
see Initial training courses, statistical information relating to mathematical education
Bank of objectives (TEC) 4/152
'Basics', the 5/276-8
Bath study 3/45, 3/59-66, 3/68-9, 3/71, 3/73, 3/77, 3/104, 4/166, 5/199-204, 9/446
Berufsschule (West Germany) 16/791
Blueprint 3/41
Books, use of 6/312-14, 9/476, 11/563, 12/615
Burnham salary scales 13/654, 13/658-62, 15/750
Business Education Council (BEC) 3/113, 3/115, 4/149, 4/154-8, 4/164, 4/168
C
Calculation 3/70-2, 5/263-8, 6/298-303
beginnings of 6/304-5
mental 3/70, 5/254-6, 6/316
of time 6/301
Calculators and computers Chapter 7
rapidly increasing availability 7/372-3
implications for mathematics teaching 7/374
Calculators 7/376-95
no adverse effect on computational ability 7/377
mathematical understanding still necessary 7/378
motivating effect on pupils 7/379-80
good habits of use essential 7/381
use in primary years 7/384-8
use in secondary years 7/389-92
calculators should replace logarithm tables 7/391
provision of calculators in secondary schools 7/393-4
use in examinations 7/395
Computer studies 7/396-401
not part of mathematics 7/397
demands on mathematics teachers 7/398-400
demands on advisory staff 7/401
Computers 7/402-13
can assist teaching of mathematics 7/402-6
more software required 7/407
use in primary years 7/408-9
use in secondary years 7/410-11
use by individual pupils 7/412-13
Calculators, use in employment 3/73-4, 3/133, 3/134
Canada 16/790
Catering and hotels 3/141- 3
Centres for mathematical education 15/758
Certificate of Extended Education (CEE) 11/598-601
Certificate of Secondary Education (CSE) 3/68, 3/105, 4/150, 4/162, 5/189, 5/194-7, 9/440-1, 9/443-7, 9/470, 9/472, 10/519-20, 10/535, 10/537, 10/541, 11/599-601, Figure E
Chelsea College 15/758
City and Guilds of London Institute (CGLI) 3/115, 4/149, 4/151, 4/159-60, 4/165
Classroom
accommodation 12/603-7
equipment 12/608-13
materials related to industry 3/107-9
Clerical work 3/133
Communication, mathematics as a means of 1/3-4
Computation see Calculation
Computers 7/402-13
computer studies 7/396-401
employment in computing 3/144
see also Calculators and computers
Concepts in Secondary Mathematics and Science (CSMS) 6/341, 9/453, 15/757
Confederation of British Industry (CBI) 3/43, 3/50
Consolidation and practice 5/248
Construction industry 3/138-40
Continuing Mathematics Project 3/109
Continuity 8/427-35
see also Assessment and continuity
Coordinator, mathematics 6/354-8, 15/723, 16/772-3
'Core' at A Level 11/576-8, at 16+ 9/451-2
Council for National Academic Awards (CNAA) 4/167, 11/577, 14/670, 14/686
Craftsmen 3/125-7
Crowther Report 2/36
Curriculum
primary 6/286-324
secondary 9/451-82
mathematics across the 6/325-9, 9/483-5
Curriculum and method courses in initial training 14/676-86
D
Denmark 16/783, 16/788, 16/790
folkeskole 6/351, 16/790
tradition of in-service training 16/790
Department of Education and Science (DES)
secondary school teacher shortage survey 13/621
10% survey of school leavers 5/193-5, Appendix 1
1977 survey of secondary school staffing 13/623-33, Appendix 1
Discussion 5/246
Display facilities in schools 12/614
Double-subject mathematics at A Level 4/173, 4/177-82, 11/558, 11/586-9
E
Elements in the teaching of mathematics 5/240-1
Employment, mathematical needs of Chapter 3
Views expressed before Committee set up 3/40-4
Employers' views expressed to Committee 3/45-58
little real dissatisfaction 3/46
change of levels of recruitment 3/50
relationship between level of criticism and level of unemployment 3/51-2
provision of remedial training 3/56-8
Research studies 3/59-66
Findings of research studies 3/67-82
range of mathematics required 3/68
methods of calculation 3/70-2
use of calculators 3/73-4
fractions 3/75-6
algebra 3/77
estimation 3/78
measurement 3/79-81
metric and imperial units 3/82
Implications for the classroom 3/83-6
Employers' selection tests 3/87-98
reasons for using tests 3/88
lack of training of those who set tests 3/91
level at which set 3/92-3
ambiguous questions 3/94
methods of marking 3/95
provision of specimen papers 3/96
tests shared by groups of employers 3/97
see also SLAPONS
Liaison 3/99-116
school/employers 3/99-112
local groups 3/103
identification of mathematical need 3/104-6
classroom materials 3/107-9
visits 3/110
attachments for teachers 3/111-12
school/FE 3/113-15
link courses 3/114
need for sustained effort to maintain liaison 3/116
Future needs 3/117-19
Mathematical needs of some areas of employment 3/120-148
operatives 3/122-4
craftsmen 3/125-7
technicians 3/128-32
clerical work 3/133
retail trade 3/134
agriculture 3/135-7
construction industry 3/138-40
hotels and catering 3/141-3
work with computers 3/144
nursing 3/145-8
Engineering and technology, entrants to degree courses in 4/182
Engineering apprentices
criticism of applicants 3/54-5
mathematical needs 3/126-31
Engineering Industry Training Board 3/41, 3/43, 3/55
English, examination results in 5/193-197
Equipment for teaching mathematics 12/608-13
primary 12/609-11
secondary 12/612-13
Establishments of higher education, provision of support for teachers 15/740-3
Estimation 3/78, 5/257-62
Evaluation 8/424
Examinations at 16+ Chapter 10
should not impose inappropriate constraints 10/518
Fundamental principles 10/521
Single system at 16+ 10/522-30
a proposal 10/524-30
papers to be 'focused' 10/524-6
'reference levels' 10/530
Teacher assessment 10/531-6
provision should be made for 10/535
training for teachers necessary 10/536
Evidence of achievement for lower attaining pupils 10/537-56
schemes at present in use 10/541-4
view of Committee 10/545-56
graduated tests 10/547-56
feasibility study recommended 10/553
graduated tests in relation to single system at 16+ 10/555
Examinations, use of calculators in 7/395
Exposition 5/245
'Extra Mathematics' 9/480-1, 10/528
F
Facilities for teaching mathematics Chapter 12
Accommodation 12/603-7
primary 12/603
secondary 12/604-7
Equipment 12/608-13
primary 12/608-11
secondary 12/612-13
Display facilities 12/614
Libraries 12/615
Reference material for teachers 12/616
Financial arrangements 12/617
Falling rolls
effect on promotion opportunities 13/654
opportunity to rearrange teaching accommodation 12/607
opportunity to redeploy primary trained teachers 13/651
possible effect on mathematics teaching 13/622
Financial incentives for teachers of mathematics 13/654-64
Folkeskole (Denmark) 6/351, 16/790
Formula sheets, use at A Level 11/590-4
Foundation list of mathematical topics 9/455-8
Fourth International Congress on Mathematical Education 5/209, 5/212
Fractions 3/75-6, 6/300
France 16/785
Further and higher education, mathematical needs of Chapter 4
Further education 4/149-66
TEC courses 4/150-3
BEC courses 4/154-8
CGLI courses 4/159-60
RSA courses 4/161
Match between school, employment and further education 4/162-6
demands of course often greater than demands of job 4/163
craft and technician apprentices often on same course 4/164
attitudes towards mathematics of FE students 4/166
Higher education 4/167-82
non-university sector 4/167-9
university sector 4/170-82
Universities Statistical Record 4/170
undergraduates with A Level mathematics 4/173-9
undergraduates with double subject mathematics 4/177-9
degree courses in mathematical studies 4/180-1
decrease in entrants with double subject mathematics 4/180
degree courses in engineering and technology 4/182
Mathematical requirements of professional bodies 4/183-6
G
Gallup Poll 2/18
Germany 16/783, 16/785, 16/788, 16/790, 16/791
Girls
mathematical performance 5/208-16
need to increase numbers on A Level courses 13/647
see also Appendix 2
Graduated tests in mathematics 10/547-56
Grants for students during training 13/652- 3
Graphical work 6/293-4
Grouping of pupils 6/348-52, 9/491-501
Guidelines for teaching mathematics 6/359-62
H
Head of mathematics department 9/507-17, 15/721, 15/723
High-attaining pupils 6/330-3, 9/474-82
Higher education establishments as providers of in-service support for teachers 15/740-3
Higher education, mathematical needs of
see Further and higher education
Holland 16/783, 16/785, 16/788
Hotels and catering 3/141- 3
I
I Level mathematics 11/595-7
Imperial units 3/82, 5/273-5
Individual learning schemes 9/499-501
Induction period
for teachers 14/702-6
for advisory staff 15/736
Initial training courses Chapter 14
Routes into teaching 14/666-7
Entry qualifications 14/668-9
Recent changes in teacher training 14/670
Views of recently trained teachers 14/671-4
Professional training 14/675-91
curriculum and method courses 14/676-86
preparation for teaching in primary and middle schools 14/679-80
preparation for specialist teaching of mathematics 14/681-4
time allowance for curriculum and method courses 14/685-6
school experience 14/687-91
Requirement to undertake initial training 14/692-4
Main mathematics courses in BEd 14/695-9, size of groups 14/696-8
Balance within initial training courses 14/700-1
Induction 14/702-6, provision very uneven 14/704
Future developments 14/707
need to review and evaluate initial training courses 14/708
HMI appraisal of initial training courses 14/710
In-service support for teachers Chapter 15
Reasons why support essential 15/715-18
Types of in-service support 15/719-58
school based support 15/720-4
meetings with other teachers 15/725-7
visits to other schools 15/728-9
professional mathematical associations 15/730-1
mathematics advisory staff 15/732-9
mathematics advisory teachers 15/739
establishments of higher education 15/740-3
in-service courses 15/744-9
diploma in mathematical education 15/750-1
Open University 15/752-3
radio and television 15/754-5
research into mathematical education 15/756-7
centres for mathematical education 15/758
Financial support 15/759-66
Institute of Mathematics and its Applications (IMA) 13/655
International Congress on Mathematical Education, Fourth 5/209, 5/212
Investigational work 5/250-2
L
Language, use of in mathematics 6/306-11
Liaison
schools/employers 3/99-112
schools/FE 3/113-14
see also Assessment and continuity
Libraries
provision 12/615
use of 11/563-4
Link courses 3/114
Links with other curricular areas 6/325-9, 9/483-5
Logarithm tables, continuing use of 7/391
Logic 6/295
Low-attaining pupils 6/334-8, 9/459-69
M
Main mathematics courses in BEd 14/695-9
size of groups 14/696-8
Make it count 2/13
Marking
of employers' tests 3/95
of pupils' work 8/415-17
Mathematical Association 15/730-1
Diploma in Mathematical Education 15/750-1
Schools and hidustry Committee 3/98, 3/102
Mathematical education in other countries 16/782-92
diversity of approach 16/784
curriculum 16/785
examinations 16/786
qualifications of teachers 16/787
shortage of teachers 16/788
teaching style and syllabus content 16/789
in-service training 16/790
attainment of school leavers and vocational training 16/791
Mathematical needs of adult life
see Adult life
Mathematical needs of employment
see Employment
Mathematical needs of further and higher education
see Further and higher education
Mathematics
see Mathematics in schools, Primary years, Middle schools, Secondary years, Sixth form, Why teach mathematics?
Mathematics and the young entrant to employment 3/104
Mathematics in Education and Industry (MEI) 3/106, 11/581
Mathematics in middle schools see Middle schools
Mathematics in schools Chapter 5
Attainment in mathematics 5/189
Comparison of examination results in English and mathematics 5/193-7
difference in position of grade boundaries 5/197
Attitudes towards mathematics 5/198-206
young employees 5/199-204
discussion in Review of research 5/205-6
Parents and schools 5/207
Mathematical performance of girls 5/208-16
girls perform less well than boys 5/210
different expectations of girls and boys 5/211-13
need to be aware of differences 5/215
Teaching mathematics through medium of Welsh 5/217-20
lack of teaching materials written in Welsh 5/218-20
Teaching mathematics to those for whom English is not the first language 5/221-4
Teaching and learning of mathematics 5/225-75
essential to establish confidence 5/225
subject to use and to enjoy 5/226-7
mathematics difficult to teach and learn 5/228-30
Understanding 5/231-3
Memory 5/234-7
Rote learning 5/238-9
Teaching methods 5/240-1
Classroom practice 5/242-52
exposition 5/245
discussion 5/246
practical work 5/247
consolidation and practice 5/248
problem solving 5/249
investigational work 5/250-2
Mental calculation 5/254-6
Estimation 5/257-62
Approaches to calculation 5/263-8
use of non-standard methods 5/265-7
Measurement 5/269-72
Metrication 5/273-5
'The basics' 5/276-8
Modern mathematics 5/279-83
Mathematics in the primary years
see Primary years
Mathematics in the secondary years
see Secondary years
Mathematics in the sixth form
see Sixth form
Math/Science Network 5/216
Measurement 3/79-81, 5/269-72, 6/291
Mechanics, as part of A Level course 11/566-75
Memory 5/234-7
Mental calculation 5/202, 5/254-6, 6/316
Mental mathematics 6/315-20
Metrication 5/273-5
use of metric and imperial units in industry and commerce 3/82
Micro-computers see Calculators and computers
Micro-electronics Education Programme 7/406
Middle schools 13/629, 16/768-73
levels of qualification of teachers 13/629
staffing 16/770-1
mathematics coordinator 16/772
continuity and liaison 16/773
'Milk round' of universities, DES participation in 13/641
Mixed ability groups 9/495-8
Modern mathematics 5/279-83
Multi-base arithmetic 10/530
N
National Foundation for Educational Research (NFER) 13/640, 14/671-4, 14/704
National scholarships for intending teachers of mathematics 13/652
Nottingham study 3/45, 3/59-66, 3/68-9, 3/71, 3/73, 3/77, 3/104, 4/166, 5/199, 9/446
Nuffield Mathematics Project 6/286, 15/725
Number and computation 6/298-303
Numeracy 2/35-9
Nursing 3/145-8
O
Objectives and aims in the primary years 6/367-71
O Level 4/150, 4/162, 5/189, 5/194-7, 9/439-41, 9/448, 9/470-2, 10/519-20, 10/535, 11/599-601, Figures E and F
Open University 15/752-3, 15/762
Operatives 3/122-4
Organisation of teaching groups
primary 6/348-52
secondary 9/491-507
P
Parents, attitudes of 2/24, 5/207
Percentage 2/26-7, 3/72, 5/266
Place value 6/298-9, 6/341-2
Postgraduate Certificate in Education (PCGE) 14/666-7, 14/680-4
Practical work 5/247, 6/289-97
Practice and consolidation 5/248
Primary years, mathematics in the Chapter 6
Primary mathematics curriculum 6/286-324
practical methods not new 6/286
practical work 6/289-97
measurement 6/291
shape and space 6/292
graphical work 6/293-4
logic 6/295
general activities 6/296
number and computation 6/298-303
fractions 6/300
computation of time 6/301
beginnings of calculation 6/304-5
language 6/306-11
'verbal cues' 6/309
use of books 6/312-14
mental mathematics 6/315-20
solving problems 6/321-4
Links with other curricular areas 6/325-9
links with science 6/327-8
Children whose attainment is high 6/330-3
need for suitable provision 6/332-3
Children whose attainment is low 6/334-8
children whose attainment is very low 6/337-8
Attainment at age 11 6/339-44
'seven year difference' 6/342
Attitudes to mathematics 6/345-7
Organisation of teaching groups 6/348-52
vertical grouping 6/349
groups based on attainment 6/350
team teaching 6/351
Time allocation 6/353
Mathematics coordinator 6/354-8
duties 6/355
support essential 6/357
Mathematics guidelines 6/359-62
need for regular revision 6/361
Schemes of work 6/363-4
Small schools 6/365-6
Aims and objectives 6/367-71
Probability and statistics at A Level 11/566-75
Problem solving 5/249, 6/321-4
Professional bodies, mathematical requirements for entry to 4/183-6
Professional training for teachers 14/675-94
Project On Statistical Education (POSE) 16/775
Pure mathematics at A Level 11/565, 11/576-8
Q
Qualifications of teachers, levels of 13/625- 31
R
Radio and television 15/754-5
Raising of school leaving age 3/52, 9/440
Rangoli patterns 5/224
Recording of pupils' progress 8/418-19
'Reference levels' in examinations at 16+ 9/472, 10/530
Reference material for teachers 12/616
Rehearsal 5/237
Remedial classes 6/337-8, 9/467-9
Remedial training provided by employers 3/56-8
Research into mathematical education 15/756-7
Research studies
Concepts in Secondary Mathematics and Science (CSMS) 6/341, 9/453, 15/757
Make it count 2/13
mathematical needs of adult life 2/16-18
mathematical needs of employment see Bath study, Nottingham study
Mathematics and the young entrant to employment 3/104
Project on statistical education (POSE) 16/775
Review of research into mathematical education 5/188, 5/205-6, 5/234-7, 5/240-1
views of recently trained teachers 14/671-4
Young people and employment 3/48
Retail trade
criticism of entrants to 3/53
mathematical needs of 3/134
Review of research into mathematical education 5/188, 5/205-6, 5/234-7, 5/240-1
Rote learning 5/238-9
Royal Society of Arts (RSA) 3/98, 4/149, 4/161
S
Schemes of work 6/363-4, 9/510
School experience in initial training 14/687-91
School leavers, DES 10% survey of 5/193
School Mathematics Project (SMP) 3/108, 5/279-81, 11/581
Schools Council Mathematics Committee 11/578, 11/585
Scotland 15/748, 16/785
Secondary years, mathematics in the Chapter 9
Differences in attainment between pupils 9/436-7
Difference between syllabus and curriculum 9/438
Changes in last twenty years 9/439-41
introduction of CSE 9/440-1
Influence of examination syllabuses 9/442-50
CSE limited grade examinations 9/447
Courses for 11-16 year old pupils 9/451-82
foundation list of mathematical topics 9/458
provision for lower attaining pupils 9/459-66
provision for very low attaining pupils 9/467-9
provision for pupils for whom CSE and O Level are intended 9/470-3
provision for high attaining pupils 9/474-81
'extra mathematics' 9/480-1
provision for very high attaining pupils 9/482
Mathematics across the curriculum 9/483-5
Time allocation 9/486-90
Organisation of teaching groups 9/491-501
teaching in setted groups 9/493-4
teaching in mixed ability groups 9/495-8
individual learning schemes 9/499-501
Deployment of teaching staff 9/502-6
Head of department 9/507-17
duties 9/508, 9/510-16
need for time to carry out duties 9/509
Selection tests, employers 3/87-98
Setted groups 6/350, 9/493-4
'Seven year difference' 6/342, 9/436
Shape and space 6/292
Shell Centre for Mathematical Education 5/188n, 15/756n, 15/758
Shortage of mathematics teachers 13/621-2, 13/631
see also Supply of mathematics teachers
Sixth form, mathematics in the Chapter 11
A Level mathematics 11/558-94
proportion of students who proceed to further study 11/559
need for course to be balanced and coherent 11/560
teaching of A Level courses 11/561-4
applications of mathematics 11/565-75
A Level core 11/576-8
need for regular review 11/578
the variety of A Level syllabuses 11/579-85
monitoring of syllabuses and examinations 11/585
double subject mathematics 11/586-9
use of formula sheets 11/590-4
I Level mathematics 11/595-7
Sub I Level courses 11/598-601
O Level and CSE courses 11/599-601
Skill 3/41, 3/47, 3/52
SLAPONS (School Leaver's Profile of Numerical Skills) 3/98, 10/541, 10/543
Small schools 6/365-6
Software for computers 7/407, 7/409, 7/411
Some other matters Chapter 16
middle schools 16/768-73
teaching of statistics 16/774-81
mathematical education in other countries 16/782-92
statistical information relating to mathematical education 16/793-7
Standardised tests 8/421- 3
Standing Conference on University Entrance (SCUE) 11/559, 11/577
Staffing, survey of secondary schools 13/623-33
Statistical information relating to mathematical education 16/793-7
schools 16/794
entrants to higher education 16/795
entrants to teacher trnining courses 16/796
qualifications of teachers 16/797
see also Appendix 1
Statistics courses
A Level 11/566-75
I Level 11/597
Teaching of 16/774-81
statistics a practical subject 16/776
need for in-service training for teachers 16/778
teaching materials required 16/780
Structural apparatus 6/299, 12/610, 12/613
Supply of mathematics teachers Chapter 13
The present situation 13/620-33
primary schools 13/620
secondary schools 13/621-33
DES survey of secondary school staffing 13/623-33
levels of qualification of teachers 13/625-31
teachers in middle schools 13/629
teaching of younger pupils in comprehensive schools 13/630
deployment of teachers qualified to teach mathematics 13/632-3
Rates of entering and leaving teaching 13/634-6
Methods of increasing supply of mathematics teachers 13/637-50
need to improve public image of teaching 13/640
need to make greater efforts to recruit teachers 13/641
mathematics degree courses as preparation for teaching 13/642-7
need to encourage more girls to study mathematics 13/647
entry to teaching from other employment 13/648-9
training and retraining courses 13/650
Employment of primary trained teachers in secondary schools 13/651
Grants during training 13/652-3
Financial incentives 13/654-64
additional payment to teachers of mathematics 13/655-64
Need to employ newly trained mathematics teachers 13/665
Support for teachers
see In-service support for teachers
Surveys, DES
secondary school teacher shortage survey 13/621
10% survey of school leavers 5/193-5, Appendix 1
1977 survey of secondary school staffing 13/623-33, Appendix 1
Syllabus development 9/450
T
Teachers of mathematics
attachments to industry and commerce 3/111-12
deployment within mathematics departments 9/502-6
financial incentives 13/654-64
levels of qualification 13/625-31
meetings with other teachers 15/725-9
membership of professional mathematical associations 15/730-1
methods of increasing supply 13/637-50
need to employ newly-trained 13/665
need to improve public image 13/640
need for greater efforts to recruit 13/641
need for in-service support 15/715-18
rates of entering and leaving teaching 13/634-6
reference materials for 12/616
support for see in-service support
training of see Initial training courses
transfer from other employment 13/648-9
use of primary-trained in secondary schools 13/651
use to teach other subjects' ('mismatch') 13/632-3
views of recently trained 14/671-4
Teaching of mathematics 5/225-41
classroom practice 5/242-52
facilities for see Facilities
organisation of teaching groups 6/348-52, 9/491-501
shared teaching 9/505
team teaching in primary schools 6/351
through the medium of Welsh 5/217-20
to those for whom English is not the first language 5/221-4
Technician Education Council (TEC) 3/113, 3/115, 4/149-53
Technicians 3/128-32
Television and radio 15/754-5
Testing
by employers 3/87-98
in schools 8/420-3
see also Assessment of Performance Unit
Time allocation
for curriculum and method courses in initial training 14/685-6
for double-subject mathematics at A Level 11/587
in primary years 6/353
in secondary years 9/486-90
Training and retraining courses 13/650
Training of teachers see Initial training
Transfer between schools 8/428-35
U
Undergraduates, mathematical qualifications of 4/170-82
with double-subject mathematics 4/177-9
entering degree courses in mathematical studies 4/180-1
entering degree courses in engineering and technology 4/182
Understanding 5/231-3
Understanding British Industry project 3/111
Unemployment among school leavers 3/51-2, Figure A
United States of America 16/783, 16/788, 16/790, 16/791
Universities, mathematics degree courses in 13/642- 7
see also Undergraduates
Universities Statistical Record 4/170, 4/180n, 16/795
Use of mathematics by adults in daily life 2/16n
V
Vacancies for school leavers 3/51-2, Figure A
Variety of A Level courses 11/579- 85
'Verbal cues' 6/309
Vertical grouping in primary schools 6/349
Views of recently trained teachers 14/671-4
Visits
school/industry 3/110
by teachers to other schools 15/728
W
Way ahead, the Chapter 17
changes in recent years 17/799
major changes in mathematical education essential 16/780-1
need to improve overall quality of mathematics teaching force 17/802
agencies from whom response is required 17/803-9
need to support and encourage implementation of change 17/810
Welsh, teaching mathematics through the medium of 5/217-20
shortage of teaching materials 5/218-20
West Germany 16/783, 16/785, 16/788, 16/790, 16/791
Why teach mathematics? Chapter 1
Reasons for teaching 1/2-8
means of communication 1/3-4
use in other fields 1/5
inherent interest 1/7
The difficulty of learning 1/10-11
Implications for teachers 1/12
Women and mathematics 5/216
Work, schemes of 6/363, 9/510
Working Mathematics Group 3/109
Y
Young people and employment 3/48
Appendix 5
 
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