 |  |
| www.dg.dial.pipex.com | 395 readers since 24 Jun 2007 |
| |
| www.dg.dial.pipex.com | 395 readers since 24 Jun 2007 |
Newsom (1963) Notes on the text
Part 1 Findings
Part 2 The teaching situation
Part 3 What the survey shows
Appendix I List of witnesses
|
The Newsom Report (1963)
Half our future A report of the Central Advisory Council for Education (England) London: Her Majesty's Stationery Office 1963
Chapter 18 Science and mathematics
A. SCIENCE 421. A boy is usually excited by the prospect of a science course. What is it that appeals to him? He experiences a sense of wonder and a sense of power. The growth of wheat, the birth of a lamb, the movement of clouds put him in awe of nature; the locomotive and telephone he sees as man's response; the switch and the throttle are his magic wands. If he cannot produce a sunset he can change the colour in his test tube. He comes readily to his teacher hoping most to learn how to control events, though from time to time, as he grows older, he stops to ask why things behave as they do. In some way we have to show him how scientific knowledge is acquired, by what hard means advances are made. If he finds this dull, his teachers must accept part of the blame. The girl may come to the science lesson with a less eager curiosity than the boy, but she too will need to feel at home with machinery and will be subject to the prestige which science has in the world. In the future she may earn her living in as scientific an occupation as the boy. Whether science to her is friend or enemy she will be better equipped by having some inkling of its nature. 422. What are the essentials of the scientific method? To see, to wonder why, to attempt explanations, to test these by taking a closer look, is a common enough sequence of experience. The scientist repeats this process deliberately and in a controlled situation, learning to look closely, record accurately and say clearly what inferences have been made. It is not necessary to do anything esoteric to get the feel of being a scientist in this sense. But, for most of the pupils we are discussing, this is best obtained by trying out the process in practical work. 423. It is the next steps that are more difficult, and much more adult. They involve a personal willingness to give way to fact rather than to maintain prejudice. The mature scientist has a sense of the tentativeness of even the best scientific theories, he knows that somewhere along the line it becomes a matter of judgement whether a scientific law is worth retaining or not. How much of this can be presented to and absorbed by how many of our pupils is simply not known. But the teaching should not actively encourage naive attitudes of acceptance of revealed truth in the science lesson. The more naive the pupils, the more important this negative principle is. Too much of the tradition of science teaching is of the nature of confirming foregone conclusions. It is a kind of anti-science, damaging to the lively mind, maybe, but deadly to the not so clever. For them, in science as in mathematics, the spirit of genuine enquiry is essential. 424. The common practice of exploring a wide field in the first years of the science course, perhaps under the heading of general science, provides all the opportunities that we need. All the topics found in the typical science course, and many others, can be used. They will rarely be elementary in the sense of belonging to the elements of the formal development of the subject. 425. A girl may know that when she pedals, her bicycle generator can light the lamps. She may not wish to take a generator to pieces, but by enquiry she can find out that the school or home lighting is probably produced by another generator, driven by a steam turbine, at the nearest power station. Using a pressure cooker with the weight removed, and a paper windmill, but taking care to avoid a scalding, she can simulate a turbine. How does the steam get such power? Let her watch water boiling in a beaker, let her use a thermometer, let her find how long the water takes to come to the boil, how much longer for one quarter to boil away. How much further the topic can be pursued depends upon her willingness to speculate and to follow up her ideas. It may be appropriate to discuss the heat from a gas fire, or a coal fire, and to remember the coal at the power station. Quite probably it is too early to discuss how the sun's heat got into the coal, or into her muscles so that she could pedal. It is almost certainly unwise at this stage even to appear to exhaust the subject, which can be left open for further examination and experiment later. A train of thought has been followed; experience has been used as a basis for ideas; as a by-product, and, for a moment, something about the nature of scientific enquiry may be appreciated. Like so many by-products, in relation to the less able, this one will run to waste if it is not deliberately garnered. The technique is no hard selling one, it demands the well placed question here and there, the odd five minutes of insight at the end of an hour and a half in the laboratory. We would hope that by the time they are fourteen many of our boys and girls will have a tolerably clear idea of what it means, in the school science course, to take a scientific attitude to a question. Transference to other situations may have to wait on the maturity of the pupils themselves. 426. The field of science is so wide that what is done in schools can jump from one facet of the subject to another without much sense of cohesion developing. This appears quite suitable to the roving curiosity of the pupils when they enter the secondary school. By about the third year it would be appropriate to concentrate on a few relatively extended pieces of work rather than a large number of excursions into this or that aspect of the subject. At this stage a certain ruthlessness in selecting what will be attempted and what will not is essential. Even when a topic for enquiry has been selected, the ramifications to which it can lead need to be kept under control, if a sense of definite accomplishment is to result. On a farm for example there are many more things than milk yields, cropping, manuring and the like. There are heavy awkward things to move about, gates whose hinges must take a strain, tractors which at the price of dramatic changes in the liquid with which they are fed put energy at the farmer's service. This wealth of possibilities is an opportunity rather than an embarrassment. It could allow teacher and pupil jointly to discuss and settle what they will pursue; to take the pupils into partnership is to bring an adult element into the situation from the point of view of personal relationships as well as subject matter. 427. Conversely, seemingly limited topics can be made, with a little ingenuity, to yield something particular the teacher may have in mind. Measuring the temperature of a greenhouse at various points at a given level could give a near at hand example of isotherms, moving a kitchen table involves leverage, friction, centre of gravity and force (if it is moved by slightly raising one end before pushing it, rather than by just pushing). To find material for science for our pupils it is only necessary to look around. This immediacy is just what they need. It should give them a certain kind of alertness to their surroundings and some common sense in coping with them. School and life will not remain in separate compartments. The one will reinforce the other. 428. Perhaps this is sufficient to make the point that a great deal of real science can be extracted from relatively few enquiries. To be of its fullest value it needs a good deal of unhurried discussion and writing up what the pupil has done and discovered from the whole exercise. It is all the more appropriate for our pupils for that. Science is a practical subject ready made for doing more for the 'basic skills' than most - not forgetting reading, for sometimes it will be possible to use written instructions in the form of worksheets or general guidance cards. Moreover, science is well placed to encourage the use of books both for reference and for general interest. There is a particularly good supply of such books and their variety stretches from those which simply supply information to books fully worthy of the title 'literature'. They should be readily available and fully used. As science receives more time, with the improvement in the supply of science teachers, great care needs to be taken not to fill the extra time with too much additional subject matter. No amount of increase in quantity could compensate for lack of quality. This applies as much to the keeping of good records by the pupil as to any part of the work. Good records will help to give shape to what can become a rather untidy process of learning, and will help to give the confidence that comes from a sense of accomplishment. They are more important as a means of showing the pupil what he has done, than as a check by the teacher. 429. The need for practical work, often done in conjunction with the teacher, is probably much greater for our pupils than for the abler ones. An abler pupil can generalise (not without danger) from a few examples and apply his general conclusions to other situations, but our pupils need a greater variety of experience before generalisations can begin to form in their minds. They need to come at their work frequently enough too. Just to 'do science' for a double period each week may be merely to provide them with long enough intervals in which to forget. For this reason alone the contribution that other subjects (mathematics and geography in particular) can make towards their scientific education is doubly valuable in the present condition of scarce resources. Once again we underline the fact that the need of our pupils for teamwork among the staff as a whole is greater than that of abler pupils. 430. With very slow pupils, who have limited powers of consciously transferring experience in one situation to a different situation, it may rarely be possible to generalise effectively. What has science to offer them? It can provide an absorbing activity in the solving of a very simple problem: 'How can I get water from the tap to turn the wheel round?' 'How can I get these seeds to germinate quickly?' In the solving they will be thinking of possibilities (hypotheses) and the means of trying them out (experiments) without consciously knowing that this is scientific method. Their disappointments can be educative and their successes triumphant. They will then have something to talk about, perhaps draw, or even write about. Many experienced teachers of the very slow have found in very simple science a means of re-energising the disheartened. 431. Most of what we have said about the earlier part of the course is applicable to the spirit in which science will be taught in the later years too. But, as far as the content of the work is concerned, there could be dramatic changes for many pupils in their fourth and fifth years in the secondary school. The principle of choice applies easily to science, but perhaps some rethinking needs to be done about the range of choice that could be offered. As things are, the choices which are available usually correspond to the formal divisions of the subject - physics, chemistry, biology. It is doubtful whether these divisions have a natural relationship with the requirements of our pupils. We should prefer to see choices much more organically linked to what pupils' want to be, or to a particular interest, or to some part of their curriculum. 432. For some, a natural choice would be the science which is particularly relevant to an occupation or to a further education course which they hope to follow. For some girls, a course might be based on investigating the nature and qualities of apparatus and materials used in the home as we suggested in the last chapter; it might require a different laboratory from what is now the standard kind. Some schools already run successful courses organised around rural crafts and occupations; they are good not only for their direct scientific purpose but also because looking after living things is good for people, and acquaintance with the countryside as the home of a basic industry can help to develop responsible attitudes in our pupils. Could this be matched for the town by using some other industry; building might be a case in point? It would be worthwhile to discover whether effective courses of study can be built around, say, electrical apparatus and circuits (or the internal combustion engine) which are a combination of handicraft and science. Here the word handicraft is to be interpreted very widely and the time for both handicraft and science would be brigaded [combined]. We have in mind something more wide ranging than a course in, say, motor vehicle maintenance, for, unless some of the larger scientific ideas are distilled, it will remain a course about engines alone - useful but of limited illumination. These are only examples, merely an indication of the kind of direction in which it may be fruitful to go. 433. If we are to begin where our boys and girls are, it will not be at the beginning of a logically organised course but somewhere in the middle. Perhaps with 'How does an electric motor work?' 'What are the factors which determine the heating power of an immersion heater?' Such questions could be tackled from actual investigation of simple enough models by finding out what the important factors in the situation are and investigating them further. But it would need a large supply of apparatus which is rather different from what is customary at present, apparatus in the form of easily assembled and dismantled kits which make up into something which works and can be seen working. There is opportunity, too, for making models in the handicraft room - rough and ready models which work and which are suitable for pupils who find working to accurate limits difficult, as well as the more sophisticated models which give great pleasure because they look so good and work so well when they are well finished. The whole question of courses and materials for teaching science to the ordinary boy or girl needs bold and thorough experiment. It may be that some courses offered by the school could be short courses of a term or two. 434. It may be said that some of these suggestions would lead the school into regions suitable only for industry or for further education. There are two kinds of reply. The first is simply to ask what is wrong with a school course which overlaps with industry or further education. It is often said that the schools should give as general a grasp of scientific principles as possible and leave the applications to industry or to further education. Doubtless there is much truth in this, but it can be inhibiting. A general grasp comes out of particular instances. There is some danger of saying to the schools 'You are out of touch, but you mustn't touch'. The fewer the boundaries between school, industry and further education the better for all. What is quite certain is that the schools would need to have good liaison with industry and with further education if they are to put the most appropriate items into their syllabuses and to treat them appropriately too. Secondly, we would reiterate that we are thinking of courses which use interest in a technology to give starting points for important pieces of work in science, not as confining the science to a kind of technological training. 435. The pupils are living and will live in a world which is permeated with scientific reference. It is not a mere side issue that science at school should help them to deal with this situation. Once again the science teacher is in a strong position. His material is ready to hand, sometimes it will actually be sent through the post to his home and to those of his pupils. The laboratory notice board could act not only as a platform for good scientific matter, but as a pillory for bad. The pupils will not be slow to bring material and not slow to see that 'Contains the new phenolthiocene' is meaningless, or that statements beginning 'It has been scientifically proved ...' need taking with some caution. A teacher, willing to be led up the garden a little, will do a great deal to help pupils to read in an adult manner, not just to read. 436. It is not only pseudo-science but real science that will come within the ambit of class discussion. Much scientific knowledge, even of science teachers, is hearsay; someone trustworthy is being believed. The pupils, interested in what is sometimes called 'magazine science' are in much the same case. They talk about atoms, molecules, electrons and they may read about a large number of other so called particles. Could they not discuss the credibility of what they read? It is so easy to slip over into the land of uncritical wonder. They might be stirred by the thought that all our theories represent temporary resting places in an unending quest. Emotion and science are not utter strangers. Might not Newton's famous words about being on the seashore with the whole ocean of truth undiscovered before him make an appeal to ordinary boys and girls as much as to the sixth former? 437. Even their own generalisations might receive a more careful look towards the end of the course. To 'explain' pressure in terms of the random motion of gaseous molecules which are like very small billiard balls is to replace what has been seen by what is imagined. To look closely at Boyle's Law with the mind's eye is to see that, if it were universally true, air would need to be infinitely compressible - and where do molecules go then? Even a slow class which has enjoyed its science course may be willing to entertain such questions. We do not yet know how far it is possible to go if we are willing to draw on all the faculties of quite ordinary people, and it is important to remember that a time will come when the leaving age will be sixteen, with all this means for greater maturity. 438. Science leads, not only to its own problems, but straight to moral problems too. It does so in the outer world, and it follows automatically that it should do so in school. This is not just a matter of atomic bombs. The advance of medical knowledge brings its problems, and it has helped to present this and the next generation with the problem of the pressure of population on food supply. Such a matter might come up under health education, or under rural studies with its reference to crops, fertilisers, the struggle to improve wheat strains and the like. Again, a substantial course on the science relative to the internal combustion engine could connect up with what this invention has done to our lives as individuals, as sociable as well as social beings, and it is directly relevant to the world's energy resources. To have 'done' such problems once in current affairs or modern history is not quite enough. Awareness is reinforced by discovering awareness in many other people; even at the lowest, to find that 'Old Stinks' (or his modern equivalent) is human is something. He may even, with propriety, discuss whether it is right to assume that what is not amenable to scientific investigation is somehow unreal. It is not unthinkable that the notice board in the science laboratory should sometimes display a poem; poets as well as scientists are observers. 439. The difference between knowing the facts and in some measure committing oneself to a personal attitude about their bearing on one's own actions stands out most clearly in that part of the science curriculum which deals with sexual reproduction. It is becoming clearer every day that, in the society in which we now live, the schools cannot contract out of the whole question of sexual conduct. The facts, as part of the make-up of the natural world, will be dealt with by science teachers; some, but not necessarily all, will also be the teachers who deal specifically with the problems they pose for personal conduct. The fact that in other directions, too, science leads to questions of moral principle, will help to put the specifically sexual questions in a more general framework. One of the main questions at issue, in the personal side of sexual behaviour, is how free we really are in our own actions when another personality (whether the child or the partner) is involved. Whatever doubts and hesitations teachers in our schools may have about positive moral teaching, surely they will not doubt that one of the cornerstones of civilised existence is the principle that nobody, merely for his own ends, has rights in the life of another. This is what resistance to the great political heresies of our times is about. It lies behind the long struggle for freedom from slavery, and behind much of our hard won legislation on conditions of labour. Should it not be put to our pupils that they too are subject to the same principle? If they are slower at seeing connections and arriving at generalisations than others, is it not all the more necessary that they should be shown that the connections exist? This is a matter for the policy of the school as a whole; the teachers of science will need to know clearly what this policy is. Nowadays, the challenge to express an opinion may crop up without notice in a most uninhibited manner from the pupils themselves. At least the major answers should be ready. 440. Finally, a point about the science course itself. It would be comparatively easy to go through an interesting and useful course without dwelling on the great unifying concepts - the energy chain, evolution, the balance of nature, the simpler quantitative laws (perhaps understood pictorially) and the like. They may be beyond some pupils; but those who have any chance of grasping them, even though apparently fleetingly, should have the opportunity.
B. MATHEMATICS 441. Mathematics has much to offer to boys and girls of ordinary ability at the secondary stage. It has a self-evident usefulness which can be a great advantage in arousing the interest of pupils who become bored by classroom tasks that may appear to them to be unrelated to their everyday experience. 442. Mathematics is a difficult subject, but not as difficult as it is often made out to be. Most people have a greater capacity for mathematical understanding than they are aware of, and a large reservoir of undeveloped mathematical competence certainly exists among youngsters of ordinary ability which good teaching and an enlightened approach could reveal. Few, if any, of our pupils are ever likely to become mathematicians, but some may well come to find satisfaction in mathematical work if its purpose has first been clearly seen and confidence established through the successful use of mathematics as a tool. 443. Recently and dramatically both the flavour and range of the mathematics which children are experiencing in an increasing number of primary schools are changing almost out of recognition. The secondary schools of the future can expect to base their mathematics teaching on foundations of interest and understanding to an extent that has never been possible before. These developments present a challenge and opportunity at the secondary stage. 444. The basis of all practical mathematics is a sound knowledge of the 'facts' of elementary arithmetic - addition and multiplication tables, tables of quantities in common use. Many of our children will not have acquired facility in the four processes of addition, subtraction, multiplication and division in the primary schools, at least not with any permanence or security, and when, at the secondary stage, the four processes are found to have been inadequately learned, mere repetition of elementary exercises will fail to put matters right. Calculation must be reintroduced as an adjunct to more adult practical tasks that the pupils are anxious to do well but which cannot be tackled without the use of some mathematics. 445. Multiplication tables left unused are easily forgotten and other calculation skills can be as quickly lost. To keep these arithmetical tools in good condition is as important for all boys and girls, whatever their vocational interests, as for carpenters to keep their chisels sharp. Regular and fairly frequent practice in computation is therefore essential. The teacher of mathematics who has pupils of less than average ability needs a close knowledge of what they are doing outside the periods given to mathematics and must comb all the other subjects in which they show interest for material with which to build good lessons in mathematics itself. The teacher is presented with a serious difficulty in that to draw all examples from actual situations may leave uncovered or insufficiently practised important mathematical concepts which pupils could profitably master, given the opportunity and a reasonable amount of time. Just to do calculations about imagined real situations will not necessarily make an exercise 'practical'. Nor will this prevent boredom. The areas of carpets can be found too often. 446. The teacher seeking graded exercises may well feel the necessity of turning to textbooks. Unfortunately, textbook problems can rarely illustrate spontaneously the immediate interest or activities of the pupils. They tend inevitably to be artificial, too plainly, in the pupils' eyes, contrived in order to make work and take up classroom time. Even today, many textbook problems are unrealistic - halfpennies in money sums of over £100 - merely in order to complicate a computation; or are drawn from situations which our pupils never meet. Examples from country life may have no relevance for the city dweller; problems about high blocks of flats may be meaningless for the pupil living in a rural area. There is no release for the teacher from the need for forethought, invention and a great deal of time week by week spent in the preparation of fresh material for purposeful classroom work. The essence of good teaching of mathematics for our pupils lies in variety and continuous adaptation, each new opportunity being seized as it arises. 447. Several recent publications give good examples of the kind of mathematical work derived from real situations which we have in mind and material of this nature is being used with marked success in many schools. Almost unlimited opportunity for valuable and stimulating lessons can arise from school activities; from the study of local activities or farm life, for example, from local history and geography, social science, biology. Pitching a tent, buying and bottling fruit, calculating crop yields can all lead to constructive mathematical work. Map reading, surveying, the study of contours, meteorology, navigation, dressmaking - all these can provide the right kind of incentive. Even the 'new mathematics' may have something to offer for some of our pupils where there is a well-qualified and well-versed enthusiast on the staff. 448. Though the schools need more mathematical expertise at their disposal than they have at present or are likely to have in the near future, almost all members of staff can and should help. The teacher with direct responsibility for mathematics must guide other members of staff in exploiting every situation which can lead to interesting mathematical work. The specialist will need to advise non-specialists on how to introduce mathematical ideas in logical sequence through their own particular subjects or interests. Careful guidance will be necessary if fragmentation is to be avoided and in order to ensure a common precision in the use and language of mathematics. If the best advantage is to be taken of the many opportunities for stimulating interest that arise in the general work of the school, the staff must work as a team. There will need to be a clear school policy and regular meetings to secure the proper planning and coordination of the mathematical work. 449. The less able the pupils, the simpler the work will need to be, the less rigorous the approach and the more closely related to practical needs. But an approach in which at least some of our pupils wake to the need for mathematics and see the purpose in terms of a vocation or leisure pursuit can revolutionise attitudes and reveal unexpected mathematical aptitude. The basic mathematical equipment for successful everyday living must be acquired before leaving school. Personal budgeting and 'social arithmetic' - gas and electricity accounts, what rates and taxes are about, how local and welfare services are paid for, and even their cost - should find a place in the curriculum of every pupil, not necessarily in the mathematics periods. The decimalisation of British money, and, eventually we hope of weights and measures, will remove a serious stumbling block in the teaching of mathematics. Considerable emphasis can profitably be given to the use of decimals and to the decimal system generally. 450. In calculation, as in reading, there is inevitably for many pupils a good deal left to be done at the secondary stage. Facility in calculation comes only with time, with practice and with increasing maturity and understanding of mathematical ideas. The emphasis in calculation should always be on accuracy rather than on speed, for speed is of little consequence - it grows of itself from a habit of accuracy. Success and confidence is all-important whether at the primary or secondary stage and computation should be done in short and easy stages. Facility cannot be acquired once and for all by a concentrated drive, but grows through constantly applying previously learnt mathematical techniques in new contexts. A drive for accuracy of a 'brush up your calculations' type when pupils are in sight of leaving school and there is a strong vocational motive can, however, prove most rewarding. 451. There is particular value in taking advantage of the pupils' increasing vocational interests during the last years of school and in relating a wider range of mathematical work to employment and to the work of colleges of further education. 452. To teach the use of tables, ready reckoners, charts and diagrams, and to give ample practice in the use of rulers, tape measures, the compass, protractor, set squares, vernier callipers and measuring instruments of all kinds is important. Engineering drawing has special interest for boys; and girls, too, can show talent for technical drawing if they are given the right encouragement. There can usefully be some undisguisedly vocational studies, for example in running savings schemes, designing and executing controlled experiments in rural studies, costing, and catering. 453. A desk calculating machine can widen the scope of the enquiries which can be tackled by a class and makes possible all manner of social and physical statistical investigations which are well within the understanding of pupils of ordinary ability in the secondary schools. Some mathematical models and working apparatus which are nowadays produced commercially are both well constructed and beautiful to look at; a carefully selected collection can be a great asset to mathematics teaching. Pupils should be encouraged also to construct apparatus and illustrative material for themselves. 454. For this, a well-equipped mathematics room is needed to which pupils can go for practical project work in mathematics as well as for formal lessons. Flexibility in the timetabling of mathematics work and in the use of the mathematics room is desirable to allow for both single and double periods. It is not suggested that all mathematics teaching should take place in a special room. 455. Rapid developments are being made in the use of teaching machines and the techniques of programmed learning; these may prove to be valuable aids to teachers both with new work and for revision. Much research remains to be done before the contribution that they are likely to make to the teaching of our pupils can be assessed. Any real success with teaching machines will depend on teachers having adequate induction courses and on well-designed programmes becoming readily available which teach the kind of mathematics that makes sense for our pupils. Mechanical aids can be of great help in remedial work. 456. Much has been said in this chapter about computation and practical arithmetic. A broader outlook to the mathematical syllabus as a whole is, of course, required. We are encouraged by the extent of the new thinking that is taking place all over the country about the teaching of mathematics and by the enthusiasm shown by teachers in attending courses on mathematics. There is no lack of ideas, but judgement is required in their application and this can come only with experience in the actual teaching situation. 457. Have we developed far enough new approaches to mathematics for the slow arithmetician comparable to the successful new approaches to reading for the backward reader? Pupils who are backward in mathematics need not necessarily be excluded from assisting classmates in some of the practical mathematics work undertaken - they can gain something by noticing how others set about a job and even by holding the end of a measuring tape if this contributes to an understood purpose. 458. Some classes are seriously hampered by having to include pupils who, though not necessarily backward in other subjects, need remedial treatment in mathematics. If remedial work is required, it needs to be given in separate small groups: the presence of the teacher and individual help is essential. There can be no prescribed rules: every case in unique. 459. Most adults who have experienced success either in academic work or practical or physical activity can look back and pick out some particular moment of time when the subject 'went critical'. The learner suddenly catches the knack of riding a bicycle, of playing piano arpeggios, of feeling the rhythm of a poem. Professional mathematicians have these moments of enlightenment throughout their successful working lives, for in mathematics as in the other sciences, and, indeed, in most subjects and activities, understanding may come suddenly and unexpectedly, only after long periods of groping endeavour. So it is for children. Many adults, perhaps most, 'get by' with minimum rule of thumb techniques in mathematics which bear no relationship to the real language of mathematics and which cannot lead to understanding. Our aim in the teaching of mathematics to all pupils, to those of average and below average ability no less than to those with marked academic talent, should be to bring them to an interest in the content of mathematics itself at however modest a level. For success, the teachers with special responsibility must themselves have a real enthusiasm for mathematics and for mathematical ideas and language, and this must be based on good personal mathematical attainments and experience. Teachers must also have a sympathetic understanding of the interests, needs and difficulties of their pupils, and a thirst for experiment in finding and exploiting mathematical situations which arise in the pupils' daily experience. 460. Mathematics and science, closely interlocked, are the basis of the most revolutionary of recent developments in society and in the everyday lives of all young people. Even the slowest pupils are interested in progress and success, and in demonstrating that mathematics can contribute towards success. We may best hope to give all pupils before leaving school some realisation of its intrinsic value. 
|
