Mr M Williams In West Germany salaries of teachers in The use of formula sheets in A Level examinations 173 Mathematics is the only subject other than music which it is possible to offer as either one or two subjects at A Level. British Rail   Double subject maths35.036.934.433.834.533.032.4 B28 Dweck has investigated a phenomenon she calls 'learned helplessness' (30). The result of this is that nearly three times as many boys as girls entered for A Level mathematics in 1979: 12,350 girls as against 34,670 boys.     need to improve public image 13/640 In our view students should not be admitted to a second method course in mathematics unless their degree course has contained a reasonable mathematical component or they are mathematically qualified in some other way.     entrants to higher education 16/795 91-9910331135 †As defined in Appendix 1, paragraph A12.     RSA courses 4/161 It will be a consequence of this development that greater demands will be made on girls' mathematics. and D or 231.746.532.646.633.847.6 673 In response to a group of statements about the adequacy of their initial training, these teachers felt, in general, that their training had prepared them better for the subject content of their mathematics teaching and for classroom management and organisation than for dealing with discipline problems, assessing pupils' progress or dealing with the whole range of ability, especially in mixed-ability groups. Measurement should be linked with number work and attention drawn, for example, to the fact that the mathematical structure of metres, decimetres and centimetres is identical to that of hundreds, tens and units. Schools Calculators Working Party Add and subtract small sums of money without a calculator. Subject group: (1)Year of completing degree course In the first place modern A Level syllabuses were associated with the School Mathematics Project (SMP) and Mathematics in Education and Industry (MEI). Information provided for us by the Universities Statistical Record gives details of the occupations chosen by graduates in mathematical studies who completed their degree courses at universities in England and Wales in 1979; this is shown in Appendix 1, Table 31. Brighton Polytechnic Institute of Biology (2) See paragraph A21. Boys were significantly better at building from a diagram a model which needed four hidden blocks to make it stand; in 1979, 82 per cent of boys succeeded, but only 63 per cent of girls. based on the experience of teachers who had spent time on secondment to various large firms. It follows that any improvement in the standards of mathematics in schools must come largely as a result of the efforts of those teachers who are already in post; they must, therefore, receive all possible support to enable them to improve the effectiveness of their teaching. We are aware that one scheme which has recently been developed for use with secondary pupils in mixed ability classes has been designed on the basis that all pupils in the class will work at different levels within the same topic. Geography was examined separately in order to investigate whether its allegedly increasing mathematical emphasis was reflected in the mathematical qualifications of those enrolling. These may be concerned with such matters as the preparation of guidelines in mathematics, the preparation of teaching and assessment materials, arrangements for continuity and transfer between schools or liaison with local employers. Pirelli Limited Mr D Wells     secondary 12/604-7 We give our own estimate of the shortage of mathematics teachers in paragraph 631. For such a policy to be effective, it would of course be necessary for schools to be made aware of the nature and purpose of such courses so that they could advise their students appropriately. We believe that all schools should examine the extent to which the form of organisation which they are using. Secondary school teachers have been shown to interact more with boys than they do with girls (25) and to give more serious consideration to boys' ideas (20); they also give boys more opportunity to respond to higher cognitive level questions (26).   Not including mathematics86134834344 In the latter case they are able, in consultation with local firms, to make use of the Bank of Objectives. The first task of a mathematics adviser must be to monitor the quality of the mathematics teaching in the schools for which he is responsible; in LEAs which do not have an adviser specifically for primary mathematics this must entail close contact with the advisers who work in primary schools.     levels of qualification 13/625-31 Permanent home employment (2)93440610804041102419 We believe that there are many of each who are able to work more effectively if some form of group teaching is used. University of Sheffield (Careers Advisory Service) Technicians 3/128-32 Universities, mathematics degree courses in 13/642- 7     diploma in mathematical education 15/750-1 504 There is a further reason why it is undesirable for non-mathematicians who teach only a few periods of mathematics in the week to teach pupils whose attainment is low. [page 220] Nor do we believe that initially there should be an attempt to establish any direct correspondence between one of more levels in any graduated tests and specific grades in the 16+ examination. The report of the Bath study comments that 'on a number of occasions the feeling came through to us very strongly that the sort of teacher appreciated by many pupils is one who can control the class, expects pupils to work hard, explains things briefly and clearly, gives plenty of practice and is prepared to help pupils individually'.   All71007420768279838123 On the other hand, we in no way wish to discourage those who are following such courses successfully from continuing to do so.   Any maths A Level (4)27.126.127.027.828.328.728.0 676 We start our discussion of curriculum and method courses by drawing attention to two matters which we believe to be of importance whatever the age range to which the course relates.     school/employers 3/99-112 Although in the case of some pupils the choice presents no difficulty, many schools prefer to postpone the choice for as long as possible for some of their pupils and for it to be possible for a pupil to change courses if the first choice proves to be wrong. Mr A Richards Practical and oral testing should also be included and a principal aim of any scheme of testing which is used should be to help pupils to acquire the feeling for number and measurement to which we have referred earlier in the report. L     tradition of in-service training 16/790 Interim findings from a survey of PGCE courses in university departments of education which is being conducted by Professor G Bernbaum at the University of Leicester show that in 1979-80 there were about 200 men and 200 women who were taking mathematics as a first method subject in PGCE courses at universities. Stokesley Comprehensive School, Cleveland 563 Most mathematics courses in sixth forms require students to undertake far less reading than is the case with courses in other subjects, including science. 14 Initial training courses     through the medium of Welsh 5/217-20 178 There have also been changes in the way in which those with double-subject mathematics have been distributed among the various degree courses. Wood puts forward two hypotheses to explain the differences.   I Level 11/597 *Mr E Jones 246 By the term 'discussion' we mean more than the short questions and answers which arise during exposition by the teacher. It is sometimes appropriate to set up an experiment, for example to discover the length of a seconds pendulum, or to employ the strategy of looking at a simpler related problem; an example of this latter strategy is that the number of squares (of any size) on a full-sized chessboard may be too many to count, but a 2 x 2 and a 3 x 3 board are more manageable, and a pattern begins to emerge. In service 1 April645224210435680594133471633 Great Cornard Middle School, Suffolk Hounslow LEA     in secondary years 9/486-90 Whether or not it is true, as is sometimes suggested, that each person has a 'mathematical ceiling' (and so far as we are aware no research has been undertaken to establish whether or not this is the case), it is certainly true that children, and adults, learn mathematics at greatly differing speeds. (25) Becker J A study of differential treatment of females and males in mathematics classes unpublished doctoral dissertation, University of Maryland, 1979. These include 'service' courses for students whose A Level studies require a knowledge of mathematics beyond O Level standard but who are not studying mathematics at A Level; O Level and CSE courses for students who wish to improve the result which they have obtained in the fifth form; and courses designed primarily for 'new' sixth formers, that is those who are not studying any subject at A Level.     curriculum 16/785 [page 220] At the present time the course fees for courses such as Mathematics across the curriculum are high because courses of this kind which the University offers are required to be financially self-supporting. However, in due course seven of the GCE boards introduced their own modern syllabuses for single and double subject and the total number of A Level syllabuses increased sharply. *Schools Council Mr F Hall     training for teachers necessary 10/536 These centres were seen as places in which teachers could meet and where the ideas and activities put forward in the Nuffield Teachers' Guides could be 'discussed, elaborated and modified'. City of Sheffield LEA A further suggestion which has been made to us is that the DES should write to all who are starting the final year of a mathematics degree course pointing out the need for well-qualified teachers of mathematics and the attractions of teaching as a career.   Any maths A Level6.87.87.57.87.78.18.3 *By 1968 half of the pupils in maintained schools were continuing at school after the age of 15; by 1973 the proportion was approaching 60 per cent, though these figures conceal considerable regional variation. PGCE in the public sector* refers to the 'bewildering variety of practice that exists'. Business studies1851773.13.3 MEASUREMENT Unless both of these needs are held in mind, it is possible for certain topics to become ends in themselves rather than means through which wider mathematical understanding can develop. 704 The results of the NFER survey which we described in paragraph 671 showed clearly that the provision made for the teachers included in the sample had been uneven and often inadequate. Imperial units 3/82, 5/273-5 employees, most of whom are female, is predominantly arithmetic, although some tasks may include substitution of numbers into a formula, usually expressed in words, and drawing graphs of sales or production. Some children will acquire facility in measurement and in the use of drawing instruments without difficulty but others will require a long time and much practice to achieve a reasonable competence. 774 Surprisingly few of the submissions which we have received have made direct reference to the teaching of statistics. In all twelve developed countries which took part in the study, the performance of boys was higher than that of girls at the age of 13, and the performance of boys was further ahead on verbal mathematical problems than on computational problems. Engineering apprentices 753 We believe that the Open University, which has now developed considerable experience and expertise in the development of 'distance learning' courses in mathematics, could play a major part in improving the quality of the mathematics teaching force. Mr RJ Stone 256 However, a more important reason for including the practice of mental calculation is the now well established fact that those who are mathematically effective in daily life seldom make use 'in their heads' of the standard written methods which are taught in the classroom, but either adapt them in a personal way or make use of methods which are highly idiosyncratic. AGCASAssociation of Graduate Careers Advisory Services taking main method courses in mathematics766800.3888.8727.2636.2828 Micro-computers see Calculators and computers We are aware of a small number of instances in which a secondary school has arranged to teach mathematics to girls and boys in separate classes but the scale on which grouping of this kind has been carried out is as yet too small for it to be possible to draw conclusions. 797 The fourth area about which we have sought information relates to the qualifications of teachers and the subjects which they are teaching. more flexible mathematics courses, designed particularly for single-subject students, might not attract a significantly larger entry. There are, for example, schools in which the pupils take part in sailing and orienteering, both as a school activity and in their leisure time. Committee of Vice-Chancellors and Principals of the Universities of the United Kingdom We emphasise that these steps have been taken solely for the purpose of drawing up the table and should not be interpreted in any other sense.     major changes in mathematical education essential 16/780-1 Mrs MD Woods & Mr PA Rodgers Only then is it appropriate for the sum to be carried out without concrete materials.     methods of increasing supply 13/637-50 References in the index are to paragraphs in the main report unless otherwise stated. Mathematical needs of adult life [page 201] 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. They can be a source of exercises which have been carefully graded and are likely to provide revision exercises at suitable intervals. St Helens LEA     more software required 7/407     use in secondary years 7/410-11   Single-subject maths28.428.228.829.331.032.334.1   Double-subject maths13.211.010.710.58.89.09.2 Fluent performance is based on understanding of the routine which is being carried out; mechanical performance is performance by rote in which the necessary understanding is not present. double subject. Teaching (not only in schools)191820141115 B29 There is some evidence that boys see more clearly than do girls that mathematics will be useful in their future lives and work. 786 The part played by public examinations also varies considerably from country to country.     little real dissatisfaction 3/46 It points out that in some syllabuses there is only a restricted coverage of mechanics and that in others it is possible to avoid mechanics entirely. Staff of Ravenstone Infant School, London SW12 Mr K Madgett G     RSA courses 4/161 Holyhead County Secondary School, Gwynedd Rehearsal 5/237 Some reordering, reclassification and amalgamation of the data has been undertaken by members of the Committee and its secretariat. West Cumbria Careers Association, Working Party on Mathematics and Industry   Total number727.2636.2828 These employers expressed enthusiasm for the courses provided by the Berufsschulen and words such as 'meaning' and 'relevance' were used frequently in connection with the courses which were provided. This recalled the long buried anxieties caused by the pupil's arriving at an answer by a mental method and being required to produce a written solution demonstrating a method which had not been used'. Sub I Level courses 77 One of the more surprising results of the studies is the little explicit use which is made of algebra. Rotary Club of Penarth     changes in recent years 17/799 We have noted that those which have been produced most recently reflect an increasing concern with assessment. 720 We are in no doubt that school-based in-service support for teachers is of fundamental importance. 16 Some other matters     need for course to be balanced and coherent 11/560 Matlock College of Education A course on Mathematics across the curriculum is already being offered and a complementary course on Developing mathematical thinking is in preparation. [page 301] It also revealed that many people had far from happy recollections of their study of mathematics at school. Such co-operation could be assisted in secondary schools by the nomination of a member of staff who would identify the use which was made of statistics in the teaching of a variety of subjects and act as co-ordinator for the teaching of statistics; such a co-ordinator need not necessarily be a teacher of mathematics. The APU Primary Surveys confirm that there is a comparative lack of mathematical self-confidence among girls in England at an age as early as 11. 501 It is clear that considerable success can attend the use of such schemes in the hands of skilled teachers who are committed to their use, and are able to obtain a similar commitment from their pupils.