28 Entrants to first degree or first degree and first diploma courses: qualifications in mathematics 525 We believe that it would be appropriate to provide combinations of papers which would focus at grade 2 (appropriate for candidates expected to gain grades 1,2 or 3), at grade 4 (for candidates expected to gain grades 3, 4 or 5, though with the possibility of achieving grade 2) and at grade 6. 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. (10) Assessment of Performance Unit Mathematical development. I     'reference levels' 10/530   Requirement to undertake initial training 14/692-4 622 A shortage of teachers of subjects which are at some stage optional in schools can to some extent be overcome by reducing the number of pupils who study the subject, and sometimes also the time which is given to it. For example, the two problems On the other hand, the results of the survey suggest that there were nearly 1300 schools (about 30 per cent) in which less than half of the mathematics teaching was in 'suitable' hands and that these included some 150 schools (mainly modern schools) in which none of the teaching was by 197719781979 Reference material for teachers 12/616 292 All children should have experience of work with a variety of plane shapes and solids. Nevertheless, because the patterns for 1977, 1978 and 1979 are very similar, we believe that the picture they provide is unlikely to differ significantly from that which would emerge if it were possible to obtain information relating to a complete year group. The second is the ability to make subjective judgements about a variety of measures. Ms AD Green We believe that there will also be an urgent need for development work leading to the availability of additional classroom materials related to the content of the foundation list and making use of the approach which we are advocating.     curriculum 16/785 Miss HB Shuard, Mr A Rothery and Mr M Holt [page 182] 322 Mathematical explorations and investigations are of value even when they are not directed specifically to the learning of new concepts. Bifurcated Engineering Limited They refer to entrants to full-time and sandwich first degree or first degree and first diploma courses at universities in England and Wales who had home fee-paying status and whose entry qualification was based on A Levels. Objectives and aims in the primary years 6/367-71 Merton LEA The first is the extent to which university mathematics courses in their present form provide a suitable preparation for the prospective school teacher. Joint Matriculation Board All subject groups First issue 1905. HMSO 1978. Rotary Club of Oadby 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 [page 271] Professor RR Skemp Many comments, too, are anecdotal and, understandably, many of those who have written to us appear to have knowledge of only one training institution. Vacancies for school leavers 3/51-2, Figure A     levels of qualification of teachers 13/629 Under 2525-2930-3435-3940 & over   Links with other curricular areas 6/325-9 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.     Maths graduates6.415.612.27.16.4 Courses provide a means whereby teachers from several schools can come together for a special purpose, either to consider a particular aspect of mathematics teaching or to add to their own knowledge or qualifications. 586 The fact that mathematics at A Level can be offered as either one or two subjects causes a number of problems. [page 85] College of Preceptors Dr B Thwaites     Maths graduates10.319.813.27.78.0 Often, too, the mathematics co-ordinator teaches only the older, and perhaps also the higher attaining, pupils. (1) See paragraph A21.     classroom materials 3/107-9 Concepts in Secondary Mathematics and Science (CSMS) 6/341, 9/453, 15/757   % taking mathematics5.76.38.96.65.26.2 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. On the other hand, the interval of a week or a fortnight between sessions may make it difficult to maintain continuity in certain types of course. Some of the difficulties arise from the central position of mathematics within the curriculum and from its role as a service subject; others arise from the shortage of suitably qualified mathematics teachers. An arrangement of this kind enables children to experience greater continuity of teaching and still to be well known to their class teacher. In Denmark and Holland we gained the impression from educationalists that there was little criticism of the mathematical attainment of school leavers. More common criticisms found in the Lancaster study were of inability to take work seriously, lack of interest, unwillingness to work, bad time keeping and poor attendance. West London Institute of Higher Education We believe that it is not profitable for pupils to spend time practising the traditional method of setting out long division on paper, but that they should normally use a calculator. 'I never use it because of the risk of major mistakes.' Mr PJD Halpenny DES 1981. 13/14-1811/12-1811/12-1610/11-14 Destinations of graduates in mathematical studies University of Reading School of Education     shortage of teachers 16/788 Mrs L Roland 'There is no area of knowledge where a teacher has more influence over the attitudes as well as the understanding of his pupils, than he does in mathematics. Mr RJ Margetts It’s a pleasure I’m so happy many have passed the recent CS exam using my reviewer. 747 The range of mathematical knowledge and experience which exists among teachers on the same course can often be very wide and it is not easy to ensure that the content and level of a course is suited to all those who are taking part in it. *University Departments of Education Mathematics Study Group At another new girls' school, Cheltenham Ladies' College, Miss Dorothea Beale acknowledged that although she wished to introduce mathematics into the curriculum, it would spell financial ruin for the school, because parents did not wish their daughters to study it. In some parts of the country it has become the custom for mathematics advisers WH Smith & Son Limited Indeed, the demands of the further education course are likely to be considerably more than the demands of the job itself, a point to which we return when we discuss these courses in the next chapter. % of maths curriculum'suitably' staffed: (1)Type of school [page 128] pected that the mathematics coordinator or the head of department will play a major part in providing support for students on teaching practice. They did not, therefore, in the first instance lead to a great increase in the number of A Level syllabuses since the two sets of examinations served eight boards. Examinations at 16+ Chapter 10 We draw attention to the fact that we have not been able to obtain information about the CSE and GCE results of students aged 16 to 19 who are studying in tertiary and FE colleges. Mr John Kirkham A third pattern is of a range of tests at different levels which pupils may attempt in succession. Mrs S Heaney It is equally important that those responsible for the early stages of these courses should take account of the fact that many of their students may not have studied the double subject.     time allowance for curriculum and method courses 14/685-6 University Departments of Education: *Confederation of British Industry (Wales) Debenhams Limited HMIHer Majesty's Inspector(ate) 348 In most primary schools children work in mixed ability classes which usually contain children of only one year group. Metal Box Limited For instance, the combination of papers focused at grade 6 would be one on which a candidate who was awarded grade 6 would be able to obtain about two thirds of the marks which were available.     Stock4091131362239685 FEFurther Education Furthermore, it is difficult to find everyday situations which require fractions to be added or multiplied and there seems to be little justification for teaching the routines for adding, subtracting, multiplying or dividing fractions to the majority of children during the primary years. 544 We therefore hope that schools which are at present using tests of some kind for their lower-attaining pupils will review the content of their tests so as to make sure that they do not lead to, or result from, a narrow curriculum but instead contribute to its widening in the ways we have suggested. Thirty years ago no problem arose. Rotary Club of Barnstaple Cotton and Allied Textiles Industry Training Board 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.     use in examinations 7/395 Wood puts forward two hypotheses to explain the differences. South Glamorgan LEA Mr MD Fellows 1978-79 We do not believe that an LEA can ensure that the quality of mathematics teaching in its schools is adequate unless it has within its advisory staff adequate mathematical expertise to carry out the necessary assessment and identify schools which are in need of assistance. Universities Council for the Education of Teachers   Understanding 5/231-3 The number reading mathematical studies increased by about 19 per cent, physical sciences by about 17 per cent (but physics itself by about 28 per cent) and engineering and technology by about 34 per cent. In the words of the report: A much more elementary application is that the sum of two numbers, each less than 50, must be less than 100. Normal College of Education, Bangor These pupils will need to be treated individually and special arrangements made for them. The cost of organising such sessions is likely to be small in comparison with the cost of the original course. City of Bradford LEA Hull College of Higher Education Rotary Club of Bangor   Requirement to undertake initial training 14/692-4 However, such practice should be carried out in order to enable the skill to be used in the solution of problems and not as an end in itself.   Not including mathematics86134834344 Research into mathematical education Dr W Tagg We have received criticism of modern courses taught in this way from those who see such courses as too abstract and difficult for the average pupil. Mr G Hubbard Such teachers usually concentrate largely on language work and are not always skilled in the teaching of mathematics or in the diagnosis of associated learning difficulties. We cite as an example multi-base arithmetic. * In its most straightforward forms, the activity of sorting objects and of recording the results in diagrammatic form is practised in most infant classes and forms the basis on which the concept of number is built. Professor Dr H Bauersfeld mathematics in these two years gained university places. In some cases these courses are equally weighted but often the second subject is given less, and sometimes very much less, time. Dr MG Cooper Rotary Club of Bedford 653 It has been represented to us that the recruitment of mathematics graduates to PGCE courses might increase if the existing system of means-tested grants for these students were to be abolished. need for time to carry out duties 9/509 Because pupils from several middle schools very often proceed to the same upper school, liaison is necessary not only with first and upper schools but also with other middle schools in the area. '* The aim set out in the paper from which these words are taken was for the introduction of a national 'induction' scheme in the school year 1975-76. Porth Textiles Limited (20) Weiner G in Deem R Schooling for women's work Routledge and Kegan Paul, 1980. 691 We draw attention finally to the fact that special attention needs to be given during practice to students preparing to teach in secondary schools who have taken a second method course in mathematics. The teacher needs therefore to seek opportunities for drawing mathematical experience out of a wide range of children's activities. Incorporated Association of Preparatory Schools The teacher in charge of the class is normally responsible for the greater part of the work of the class, including mathematics. Mrs M Holloway Time allocation In the major Asian languages, each number up to 40 has its own name. A3 The only information which is available about the examination performance of pupils in schools on a national scale comes from the annual 10 per cent survey of school leavers in both maintained and independent schools which is carried out by the DES and Welsh Office. Cumbria LEA Business Education Council (BEC) 3/113, 3/115, 4/149, 4/154-8, 4/164, 4/168 In this way pupils of high attainment, for whom the tests would not be designed, would not be able to enter for them at a very early age. L Mrs JE Carrick The first is by following a course leading to the degree of Bachelor of Education (BEd). Rotary Club of Letchworth Garden City Professor Dr U Knauer As with so many other things, it is a sensible balance which is required.   Double-subject maths79.473.773.771.860.457.055.0 Canada 16/790 *Barbers of Fulham This means that all entrants to BEd courses are now required to have obtained this qualification; it will apply to entrants to PGCE courses from September 1983. Dr AG Howson Fifthly, the increasing availability of calculators and computers requires all who teach mathematics to reconsider the content of the mathematics curriculum and the methods which they use in the classroom. (13) Wood R Cable's Comparison Factor: Is this where girls' troubles start? On all tests, however, the overlap between the sexes is very large, and it would be a gross distortion to expect that most boys would be better than most girls at, for example, tasks involving spatial visualisation. We would also point out that such improved progress is in Many of the vocational courses which have a mathematical component operate under the regulations of the Business Education Council (BEC), the Technician Education Council (TEC), the City and Guilds of London Institute (CGLI) and the Royal Society of Arts (RSA). Newham LEA Society of Education Officers Information which has been remembered in this way is also easier to retrieve because association between the purpose for which it is required and the information which is stored in the 345 During every mathematics lesson a child is not only learning, or failing to learn, mathematics as a result of the work he is doing but is also developing his attitude towards mathematics. Source: Graduate Teacher Training Registry There is need for close cooperation between education tutors and mathematics tutors so that education theory can be seen by mathematics students to be firmly grounded on practice in schools and in this way to make a valid contribution to their initial training. Over the years 1973-1979 these constituted about 92 per cent of all entrants to these courses at universities in England and Wales. Additional factors relating to mathematics are the fact that mathematics is thought to be a difficult subject to teach and that, because it is a compulsory subject for all pupils up to the age of 16, mathematics classes are likely to be larger and to contain a higher proportion of less well motivated pupils than is the case with many other subjects which are often optional after the age of 14. Advisory Unit For Computer Based Education Kirklees LEA West Midlands College Standing Conference on University Entrance St Katharine's College, Liverpool Evidence submitted to the Committee Mr DW Purdy A further requirement has recently been introduced in respect of entrants to teacher training who expect to become eligible to join the teaching profession in or after September 1984. topics whose relevance to the mathematics course as a whole did not become apparent to pupils. (13) Wood R Cable's Comparison Factor: Is this where girls' troubles start? We have not therefore found it easy to decide on the extent to which either criticisms or compliments which we have received relating to teacher training remain valid at the present time. Clothing and Allied Products Industry Training Board *Engineering Professors' Conference It can also result from teaching which pays too little attention to practical experience or which moves ahead too rapidly so that understanding does not have time to develop. The primary years ought also to be seen as worthwhile in themselves - a time during which doors are opened onto a wide range of experience. Dr BM Kingston We estimate that between 5 and 10 per cent of all pupils, though not necessarily of the pupils in anyone school, are capable of working beyond the limits of existing O Level Mathematics syllabuses by the time they are 16. We support the view that the distinction should no longer be maintained. 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. Buckinghamshire LEA   Systems analysis502153175818 Subject choices and numbers with double-subject A Level qualifications in mathematics: 1973 and 1979 Mr GB Corston   Double subject maths7.06.26.05.44.54.05.3 Source: Universities Statistical Record Mental mathematics 6/315-20 Mr DA Keane in each authority. taking main method courses in mathematics320.5342393.3291.2234.7310     'profile' 5/190, Figure B 632 In our discussion so far we have considered the proportion of mathematics periods taught by teachers with various levels of qualification. A further scheme at one training institution allows holders of higher national certificates or diplomas, or some equivalent qualification, to complete a BEd degree in five terms; we have been told of other institutions which would be willing to adapt their courses in order to cater for such entrants if they were forthcoming in sufficient numbers. It is highly probable that many of those who take mathematics as a second subject will be required to teach it.     professional mathematical associations 15/730-1 These items were on computation with whole numbers and money, and on entirely verbal items involving naming geometric shapes and making a deduction from given verbal (non-numerical) information. Furthermore, problems of timetabling sometimes mean that students are not able to be present for all the mathematics periods in the week.     see also Supply of mathematics teachers It should not, however, be supposed that in-service support is needed only to remedy the deficiencies of those who lack suitable qualifications. Albury Manor Comprehensive School, Surrey (1) See paragraph A22. 486 In recent years the proportion of the teaching week given to mathematics has decreased in most schools as additional areas of study have been introduced into the curriculum. Source: DES 1977 Survey of Secondary School Staffing As existing middle schools recruit new staff the situation may change, but the advisers reported difficulty in attracting mathematically qualified teachers to work in middle schools. Although the overall pass rates for boys and girls were very similar (boys 73.4 per cent, girls 73.0 per cent), at the highest grade boys were more successful; 10.1 per cent of girls obtained a grade A pass, as against 15.4 per cent of boys. Okehampton School and Community College, Devon Other sciences Mr D Hindson Gallup Poll 2/18 [page 276] [page vii] This would seem to underline the fact that many craftsmen need to use only a very limited range of mathematical skills. (i) MenAge at 31 March Homerton College Mr BJ Wilson We therefore welcome the decision of the Mathematical Association to establish a Diploma for teachers of low-attaining pupils in secondary schools. Chelsea College 15/758 676 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. Marking schemes are usually kept very simple, often with just one mark for each answer and frequently no credit is given if, as a result of a single mistake in one part of the question, several subsequent answers are incorrect, even though the mathematical operations involved have been carried out correctly. Skills of estimation develop on the job but employers often complain that young entrants to industry and commerce lack a 'feel' for both number and measurement, even in terms of the units, whether metric or imperial, which they can be expected to have encountered at school or in everyday life. We believe that energetic efforts should be made to explore ways in which diploma courses can be made available in areas which are remote from training institutions. However, whatever the pattern, we believe that it is necessary to ensure that the periods given to mathematics are suitably distributed through the week and also occur at different times during the day so that there is not, for example, an undue proportion of periods at the end of the afternoon. Clarks Limited He can write down the number which is 1 less than 2010 and probably also the number which is 1 more than 6399. It is important at the outset to distinguish between three kinds of training for which this term may be used. Concepts in Secondary Mathematics and Science (CSMS) 6/341, 9/453, 15/757 Mr C Cleveland A calculator can be of no use until a decision has been made as to the mathematical operation which needs to be carried out and experience shows that children (and also adults) whose mathematical understanding is weak are very often reluctant to make use of a calculator. Standing Conference on University Entrance (SCUE) 11/559, 11/577 207 Parents can exercise, even if unknowingly, a considerable influence on their children's attitudes towards mathematics. In a few cases, a further development has been that several employers in the same locality have agreed to use the same test. Metrication 5/273-5 However, we believe that the reasons which we have given make a more than sufficient case for teaching mathematics to all boys and girls and that foremost among them is the fact that mathematics can be used as a powerful means of communication - to represent, to explain and to predict.   Entry qualifications 14/668-9 Mr DJ Lee A small number of those which have been sent to us cover a reasonably wide range of mathematical topics but most, including the SLAPONS tests, concentrate wholly or in great part on the testing of computational skills, very often divorced from any context. We have received a number of submissions in which it is argued that such courses should be maintained even although they are not economically viable. P The school curriculum. However, as has been pointed out in official publications of various kinds over many years, formal algebra is not appropriate for lower-attaining pupils. Unless the Secretaries of State take effective action in this field we do not believe that sufficient resources to improve the quality of mathematics teaching will be made available.
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