Classroom We have suggested emphases on the teaching of mathematics which are different from those found in many schools at present. Testing     professional mathematical associations 15/730-1 Staff from the original schools often remained as part of the staff of the new middle schools and so were in some cases required to teach pupils of an age of which they did not have experience or for which they had not been trained. In such cases, the number of periods timetabled as 'mathematics' could appropriately be reduced for these pupils.   Any maths A Level8.07.67.57.06.66.36.5 Courses leading to entry by a third method, the non-graduate Certificate in Education, which provided academic and professional training by means of a three-year course, are now being phased out and it is no longer possible to enrol for courses of this kind. It was developed largely by teachers of mathematics and in many schools there would at the present time be no computer studies in the curriculum at all if mathematicians did not undertake the teaching. Mr DJ Lee However, research certainly suggests caution against over-optimism in assuming a very direct relation between attitude and achievement.' 194 Some of those who have written to us have drawn attention to figures published each year in DES Statistics of education Vol 2 which show that the proportion of pupils who achieve O Level grade A, B or C or CSE grade 1 in English at some stage during their school career is much higher than that of those who achieve these grades in mathematics. tion of statistics to the analysis of data arising from study in several different areas of the curriculum and to develop a course which did not concentrate mainly on techniques. Table 17 Estimated percentages of mathematics curriculum 'suitably' staffed They are inevitably arbitrary, but a deliberate decision was made to err on the side of generosity in respect of qualifications which seemed to lie near the boundaries between categories. W Parsloes Manor School, Barking The curriculum therefore includes the syllabus; it is concerned with the way in which the syllabus is presented in the classroom as well as with other matters which are important. This fact in itself could be thought to provide a sufficient reason for teaching mathematics, and in one sense this is undoubtedly true. Commercial Union Assurance Company Limited Although it is possible to carry out some of the duties outside normal school hours, certain of them can only be performed while teaching is in progress and the necessary time needs to be provided within the timetable. either spatial visualisation or mathematical ability is not yet fully understood, but in view of the fact that differences between the sexes in mathematical attainment are more marked in some countries than in others (16), there would seem to be factors other than differences in ability in spatial visualisation which influence differences in mathematical attainment. The second is what he calls in another article (13) Cable's Comparison Factor. Rotary Club of Oadby Mr DJ Rooke Daynecourt Comprehensive School, Nottinghamshire Teacher assessment is, however, less common in O Level examinations even though, in some cases, provision exists for this to be included or for pupils to submit project work which can be taken into account during the awarding procedure.     Maths graduates11.817.414.35.910.8 In these subjects, not only is mathematics learned and practised in a practical context, but the message is conveyed that mathematics is useful in the technical, scientific and employment worlds, particularly in the traditional worlds of boy's employment and interests. (It is this group of courses which we have called 'mathematical studies' in the main body of the report; see note to paragraph 150 [in chapter 4].) Low-attaining pupils 6/334-8, 9/459-69     examinations 16/786 35 The words 'numeracy' and 'numerate' occur in many of the written submissions which we have received. Curriculum Unless the will exists to make the necessary financial provision and to provide the necessary time, no appropriate plans for in-service support can be formulated, either within a school or an authority, or on a regional or national basis. Professors of Mechanical Engineering in the Northern Universities 789 Our discussions with teachers in other countries, as well as the letters from the exchange teachers to whom we wrote, revealed a very wide range both of teaching styles and syllabus content.     Stock271154712025991153 R Each class needs facilities for practical work in mathematics but no special accommodation is required. As yet the number of families who possess a microcomputer is still relatively small but it seems clear that this number is likely to increase very considerably within the next few years. London Transport Executive *Examinations 16-18 A consultative paper. *Schools Council Project Learning through science   Any maths A Level29.126.827.828.530.532.133.7 Mr JR Johnson Computation should be tested at appropriate levels but, in our view, this should be done within a series of applications to problems in defined areas such as shopping, travel etc and not by examples testing the four operations in isolation. In our view the ability to obtain a degree in mathematics does not necessarily imply an ability to teach mathematics well without further training. [page 231] Thus '9/439' means 'Chapter 9, paragraph 439'.] These teachers frequently also teach mathematics to the pupils in their charge but are often less confident in this area; nor is the mathematics syllabus always planned in consultation with the mathematics department. Schemes at present in use In addition, the costs of providing courses of in-service training in departments of education in local authority maintained colleges are redistributed between authorities through the Advanced Further Education (AFE) Pool. This clearly limits the time which is available for the oversight of mathematics teaching within the school. 1977-78 Television and radio 15/754-5 152 TEC has published a mathematical 'Bank of Objectives' as a resource to be used in the preparation of mathematics units; it has also issued a set of 'standard units' based on the materials in the Bank. However, this overall figure conceals very considerable differences between different kinds of school, and also between different schools of the same kind. Professor CAB Smith On the other hand, in some countries internal assessment procedures within schools can mean that pupils can be required to repeat a year if their progress is adjudged to have been insufficient. Four of these items were on place value, and of the other five place value items, boys did better on four. Hertfordshire LEA Indeed, we find Norfolk College of Arts and Technology 159 Courses at craft level for those employed in technical jobs are offered by CGLI. William Tyndale Mathematics Centre, ILEA Dr MJR Shave All teachers312,663430,977436,296438,871443,028 The Diploma is an extension of the Certificate; in general it provides broader coverage at the same level and not study in greater depth. The submissions which we have received make it clear that this is indeed the case and we find it hard to believe that such variety can be justified. Professional bodies, mathematical requirements for entry to 4/183-6 B10 In order to see how girls' performance in mathematics might be improved, it is necessary to look at details of the differences. Books, use of 6/312-14, 9/476, 11/563, 12/615 We have also been given to understand that, in some Canadian provinces, the conditions of service of teachers require them to undertake some in-service training each year. 288 We believe that the public criticism of recent years, to which we referred in paragraph 278, has caused some teachers in primary schools to wonder whether they have been right to adopt the broader approach which we have described. However, by no means all of these schools contained pupils covering the full range of ability; for example, some were grammar schools and some were secondary modern schools. 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. [page 272] Stafford College of Further Education Computers 7/402-13 Such a person might perhaps be a teacher from another school, a mathematics adviser or advisory teacher, the warden of a teachers' centre or a member of the staff of a teacher training institution. A10 Tables 15 to 18 are based on information obtained from the Survey of Secondary School Staffing carried out by the DES in 1977. Boots Company Limited 601 We consider that one of the reasons why some pilot CEE courses have been successful is that they have required students to approach the mathematics course in a different, and often more adult, way. Efforts to introduce pupils to as much of the examination syllabus as possible result in attempts to cover the ground too fast for understanding to develop. Ms E Drury Table 33 Services to management and financial work: Graduates in mathematical studies A calculator provides a means of carrying out such calculations in a still more straightforward way and we believe there can be no doubt that calculators should replace logarithm tables as the everyday aid to calculation. 1977-78   Mathematics across the curriculum 9/483-5 Even in schools in which computer studies courses are well established and are taught by those who teach mathematics, the use which is made in the mathematics classroom of the computer facilities which are available seems often to be very limited. 'Best' grades have been defined in the order presented in Table 5; for example, if a pupil obtained O Level grade E and CSE grade 2 it is the CSE grade which has been included, whereas if a pupil obtained O Level grade E and CSE grade 4 it is the O Level grade which has been included. Four of these items were on place value, and of the other five place value items, boys did better on four. Mathematics Teachers' Centre, Brunel University Table 1 School population Bradford College For this reason there are some classrooms in which although the teaching and discussion are in Welsh, children work from books which are written in English. 286 The use of practical methods in the primary classroom is sometimes thought to be of relatively recent introduction but this is not the case; work of this kind has been advocated for very many years. 799 Changes of many kinds have led to increasing pressure on teachers during the last fifteen years.     rates of entering and leaving teaching 13/634-6 A8 The table which follows analyses examination results in Additional Mathematics at O Level or AO Level according to the age at which the best result was obtained. Mr D Griffiths this are those which we have already given in paragraph 591 above. Since the summer of 1975 results have been expressed in terms of five grades and an unclassified category. Comprehensive 11112 to 18: Small (2)44) University of East Anglia Mr DA Sturgess Use should be made in mathematics lessons of material gathered from newspapers and other printed sources as well as of information which pupils are themselves able to provide. Finally, it is important to develop the ability to work with others in the discussion of possible approaches and to be able to communicate progress which has been made by means of words, diagrams and symbols. We are aware of increasing pressure in recent years from some members of the public and from some local councillors for the introduction of 'blanket' testing in mathematics for all pupils. Appreciate the concept of scale in geometrical drawings and maps, and the use of co-ordinates to locate areas (as on a street map) and points (as on an ordnance survey map). A, B, C or 123.934.724.634.525.634.5 nature of work with a microcomputer offers opportunity for pupils to develop greater understanding of many of the mathematical concepts which they will meet. The examination results of this latter group are therefore included only up to the time at which they left school. Many LEAs provide a standard record card which schools are required to complete and which accompanies a pupil on transfer to another school. Mrs F Conway   Small schools 6/365-6 If, as we believe should be the case, mathematics plays a part in many areas of the curriculum, children may do quite a lot of mathematics outside the time specifically allocated to it. DES 1981. Table 1 School population It follows therefore that a mathematics degree course should provide within its structure a set of options which are suited to the needs of those who feel that they may wish to teach but who have not yet made a firm decision to do so. Teachers holding the Certificate in Education having followed a secondary course with mathematics as a second or subsidiary subject provided their first or main subject was related. Logarithm tables, continuing use of 7/391 A19 Tables 24 to 26 provide information about entry to initial training courses. Consequently the numbers shown in Table 21 are somewhat larger than those in Table 20. 17 The way ahead Perhaps the most important characteristics with which a new teacher of mathematics can enter teaching in the 1980s is a determination continually to monitor and reappraise his teaching and his curriculum. Even in classrooms in which there is plenty of discussion teachers may need to take steps to ensure that boys do not dominate the discussion and that girls are given opportunity to play their full part. Low-attaining children need to join with their fellows in experiencing the pleasure of simple work with shapes and the discovery of pattern. F   Evidence of achievement for lower attaining pupils 10/537-56 Preparation for the specialist teaching of mathematics Practice and consolidation 5/248     Use of mathematics by adults in daily life 2/16n We are aware that there are some teachers who would wish us to indicate a definitive style for the teaching of mathematics, but we do not believe that this is either desirable or possible. 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.   Research studies 3/59-66 On appointment they should be provided with a proper programme of induction which includes opportunity to see advisers at work in other authorities; there should also be opportunity for further training from time to time. Staff of Rodford Junior School, Bristol     Leavers48216551781 *Mathematical Association   Maths graduates:   Grants during training 13/652-3 These complaints were followed in 1975 and 1976 by articles and letters in Blueprint, the newspaper of the Engineering Industry Training Board, which also expressed dissatisfaction with the mathematical attainment of some entrants to the industry. Fennema's work confirmed, for the learning of mathematics, findings obtained by workers in other areas, that boys are more likely to attribute their successes to stable causes such as ability and their failures to unstable causes such as lack of effort, while girls attribute their successes to unstable causes such as the effort they put into their work, and their failures to stable causes such as their lack of ability. Falling rolls We have, however, been told that there are some mathematics co-ordinators in middle schools who are not themselves mathematically qualified; we find this disturbing. The ordinary degree course lasts for three years, the honours course for four years. Indeed, the immediate future may present an unrivalled opportunity to achieve a significant improvement in the size and quality of the mathematics teaching force - an improvement which we believe to be essential.   Reasons why support essential 15/715-18 Mr JH Smith Canada 16/790 It was rare to combine mathematics with non-science subjects.   Attainment in mathematics 5/189 It does seem possible that high levels of employment, and so a smaller pool of applicants from which to choose, may result in greater criticism from employers about the mathematical abilities of their young recruits. This information can be gathered from a number of sources at different age levels. Mr C Ormell Miss BJ Berry Comprehensive 11112 to 18: Small (2)44) Mr DS Fielker 358 There is at present a great shortage of teachers who are suitably qualified to become co-ordinators but we believe that every effort should be made to train and appoint suitably qualified teachers in as many schools as possible. 612 Practical equipment of similar kinds should also be available in secondary schools.