Publications Archive

The Teaching of Science and Mathematics to the Blind

Summary: Report to Viscount Nuffield Auxiliary Fund. With section on raised diagrams

(with section on Raised Diagrams)

Report to The Viscount Nuffield Auxiliary Fund

Editor: R.C. Fletcher

First published 1968, second edition 1973

1965 The Viscount Nuffield Auxiliary Fund made to Worcester College for the Blind a two year grant, later extended to three years, to encourage the development of Science teaching in secondary schools for the blind and to try to give pupils in all schools for the blind a better opportunity to study Mathematics in accordance with modern approaches. The Craft Master at the College, Mr. W. J. Pickles, was released from teaching so that he could:

a. Examine existing practice in the teaching of Science and Mathematics in schools for the blind and help in co-ordinating effort by schools and individuals; and

b. engage in experimental work on apparatus for teaching Science and Mathematics and technical drawing to the blind.

Our main acknowledgement is to the Viscount Nuffield Auxiliary Fund which made this generous grant and whose Secretary, Miss Grace McDonald, helped us constantly with advice. But we express our thanks also to the Royal National Institute for the Blind, particularly for the help given by their Technical, Education and Accounts Departments: to firms who supplied us with materials: to the teachers in the schools for the blind: to those on the Staff of Universities and Colleges of Further Education who advised us in our research: to the City of Worcester Education Committee and to the Principal, Science teaching staff and photographic department of Worcester Technical College.

Editor:

R.C. Fletcher
Worcester College for the Blind,
Whittington Road,
Worcester. WR5 2JU
England.

    [Digitiser’s note: We regret that it has not been possible to reproduce the photographs and diagrams of the original print on the Internet.]

Contributors

Lord Cobham, President of the Governors, Worcester College

R. C. Fletcher, Headmaster, Worcester College for the Blind

S. C. Stephenson, Master in charge of Science Teaching, Worcester College for the Blind

R. Harwood, Lecturer in Physics, Worcester Technical College

Miss D. A. McHugh, Headmistress (till 1968), Chorleywood College for Girls with little or no sight

G. W. Brooks, Biology Master, Worcester College for the Blind

A. O. Pickles, Science Master, Dorton House School for the Blind

G. Jackson, Mathematics Master, Worcester College for the Blind

Miss A. M. Sims, Mathematics Mistress, Chorleywood College for Girls with little or no sight

F. H. G. Tooze, Headmaster, Tapton Mount School, Sheffield

J. Whittaker, Assistant Master, Tapton Mount School, Sheffield

W. J. Pickles, Craft Master, Worcester College for the Blind

Foreword

by

The Right Hon. the Viscount Cobham, K.G., P.C., G.C.M.G., G.C.V.O., T.D.. J.P., President of the Governors, Worcester College for the Blind, and President of the Royal National Institute for the Blind.

In submitting this Report to the Viscount Nuffield Auxiliary Fund, I would like to begin by offering the Trustees the warmest thanks of my fellow governors and myself for making it possible. Their grant has proved most valuable in our work towards the education of the Blind and we hope that this Report may stimulate others to further research. It is then with feelings of gratitude that I ask the Trustees of the Viscount Nuffield Auxiliary Fund to receive this Report which we hope will be read by all people at home and overseas who are concerned with the education of the Blind.

Some years ago, Sir Richard Livingstone gave his view of the minimum equipment needed by an educated man if he is to live intelligently in the modern world.

"He must be aware of the chief social and political problems; he must have an idea of the nature and power of science; he should learn something of the spiritual forces which alone give meaning and value to human existence".

This Report will surely enable those who are engaged in teaching the Blind to fulfil the second of these conditions with increasing efficiency.

Cobham

Introduction

by

R. C. Fletcher

The study of Science is not new at Worcester College for the Blind. We know that a stern Headmaster in the 1870's, the Reverend Samuel Forster, added lectures in Chemistry to a copious diet of Latin, Greek, Divinity, English, History, Mathematics, Geology, Music, French and German. When we remember that all embossing, whether of letters or diagrams, had to be done by hand, with no possibility of duplication, it is clear that we who teach the blind to-day have no monopoly of broad ambitions for them. It is doubtful if we would accept the labour incurred by those of a hundred years ago in mastering long texts which might be written in any one of a number of systems of embossed lettering and which indeed they might have had to copy out themselves. Again we know that Science was being taught when the School was inspected at the end of the first World War and photographs in a prospectus of 1925 show a practical Science lesson in progress.

But the emphasis in this College had traditionally been on the Arts, a sensible stress in view of the shortage of apparatus and the need to steer boys towards the vocational objectives of Law and the Church. The limitation of these aims was no longer acceptable after the Second World War. Physiotherapy had become a valuable career for blind men and women and for this a good knowledge of basic Science was required. Besides, teachers of the blind no longer felt comfortable about the argument that, while it might be wise for the blind to know sufficient about Science to enable them to speak the language of educated people, lack of the apparent possibility of wide or genuine practical experience precluded it as a valid object of study. When I was appointed in 1959, all boys took General Science to G.C.E. “O” level. Although there were no practical questions in the examination paper, the boys in fact did a good deal of practical work under the skilled eye and hand of a great teacher, the late Mr. H. H. Clarke, himself a Cambridge scientist and geographer. Impetus was added by the building of a new laboratory and the appointment to the Board of Governors of Mr. J. A. Oriel, who had a distinguished career as Chemist and Chemical Engineer with Shell.

Further stimulus to the Science teaching had come from the visit in the Spring of 1959 of Mr. A. Wexler, author of “Experimental Science Teaching for the Blind”, who had pioneered the teaching of Science to blind students in Australia and who can claim justly to be the originator of most of the ideas still current. His leaning had been towards Physics and his book, still valuable, contains not only clear statements of principle, but useful drawings of apparatus he had used. Mr. Wexler was the first person, we believe, to design and use a light probe.

Since Mr. Clarke also was a Physicist, the decision was made to approach Examination Boards for permission for our candidates to take G.C.E. “O” Physics. The claims of Chemistry had not been forgotten. Miss D. McHugh, Headmistress of Chorleywood College for blind girls and herself a highly qualified graduate in Chemistry, had discovered through many years of teaching the value of this study for blind girls. But for our boys Physics seemed preferable and the Oxford Local Examination Board, which demanded no practical test, agreed to accept us for this subject.

Results in the 1961 examination were encouraging in that all the boys passed. The question now was whether it was possible for blind pupils to study Advanced Level Physics, for which a practical examination is rightly required. The Governors of the College were understandably cautious about spending a sum of perhaps £1,000 in equipping our laboratory for the Sixth Form work, which might prove money wasted. Further, although Mr. Clarke was well qualified to teach at this level, he had already too full a time-table. City of Worcester Technical College had just helped us by preparing a boy, blinded in a science experiment accident in his previous school, for G.C.E. Advanced level Chemistry (theory only). We asked the then Principal, Dr. George Tolley, whether he wouId consider taking a partially-sighted boy, with an “O” pass in Physics, into an Advanced level class. He readily and generously agreed and the original candidate, Adrian Magill, who with his younger brother Brendan did so much to urge the development of Science teaching for the blind, was followed the next year by two further partially-sighted boys, John AIInutt and Godfrey Jackson. These three were all to obtain A and B grades and went on to gain a second class and a first class degree in Physics and a first class degree in Mathematics at University. One has been working with computers, another doing research at Sussex University, the third is now teaching with us.

The way seemed clear for the next step, to see whether totally blind boys could take Advanced Level Physics. Mr. S. H. Heath, at that time, 1964, Head of Physics at the Technical College and Mr. R. Harwood, a most capable and dedicated lecturer and teacher, agreed, with permission of the new principal, Mr. P. D. Collins, to make the experiment, despite the hard work involved in modifying apparatus, re-designing methods of teaching and giving extra coaching. Throughout the years since 1961 it has been Mr. Harwood who has made the initial experiments in teaching at this level and has applied all his skill and ingenuity to make and adapt apparatus for use by blind students, including his own fine version of the light probe. From the College we played our part by the production, where possible, of braille and tape test and by the embossing of more than a thousand diagrams, - a lengthy and difficult task. Those totally blind students at the Technical College succeeded in passing their “A” Physics examination.

Early in 1965 a fortunate coincidence brought Mr. Brian Young, Director of the Nuffield Foundation, onto the scene. Brendan Magill had written to the well known manufacturers of scientific apparatus for schools, Messrs. Griffin and George, expressing an interest in the development of special apparatus for teaching the blind. This letter was passed to the Nuffield Foundation and Mr. Young wrote a letter of inquiry to me. The result, from August 1965, was a generous grant from the Viscount Nuffield Auxiliary Fund, whose secretary, Miss Grace McDonald, has throughout the three years of the project given us constant and kind encouragement, to help in encouraging the development of Science teaching in secondary schools for the blind and (since Mathematics and Science are so closely allied) in giving pupils in blind schools generally a better opportunity than now exists to study Mathematics in accordance with modern approaches. A further subject for research was added, Technical Drawing with embossed line. This subject is basic to both Mathematics and Science and became the main interest of Mr. W. J. Pickles, who was seconded from teaching for the purpose of the Research project and whose manipulative skill and practical sense have proved so useful.

In our view the Research project has fully justified itself. We have become convinced that the study of Science is completely viable for blind students, at least at Secondary School level, and that they have a full right to study this subject. It is harder for them generally to gain experience of phenomena and their curiosity may not always be so easily whetted. But these two connected facts make it more incumbent upon teachers to stir their curiosity and to help them to gain that experience which will be a factor in giving them that self-confidence which they so badly need. The environment is hostile to the blind. The more they can master it in understanding, the happier they are likely to be.

Sighted people, if they possibly can, use vision to acquire experience. A girl I met recently, blind from birth and now, in early adult life, able through an operation to see, told me that almost immediately after gaining some sight she started to use it, exclusively, for moving about and was in consequence terrified. Sight is the dominant sense, with a strongly integrative function. Blind people must use the other four senses, which are apt to give less full and more fragmented impressions. In learning Science experience may be different from that of a sighted person. For example, experience of light must be presented through sound. Provided the student is enabled to understand the principles and provided he realises that his aural experience is different from the visual experience of a sighted person, the change of medium does not matter. It is understanding that matters in learning Science, not aesthetic appreciation.

Any means may be employed to give understanding. The real is better than the symbolical, - e.g. in Biology the living body, growing plants, meat from the butcher's. Yet models have their place, though blind students must be taught to interpret them, to magnify dimensions and to realise difference of texture. Sometimes a model can show principles better than the real object, because irrelevance can be discarded. It is essential for blind students to be trained in interpretation of embossed drawing and for teachers to understand what fingers can interpret. Because of the importance of embossed drawing to so many subjects, - Science, Mathematics, Geography, - we have in this report presented a good deal of detailed material on this topic.

It might be thought that much special apparatus is required to teach Science to the blind. We believed so at first. But we see clearly now that it is for several reasons better that the blind student should use normal apparatus (with, if needed, braille scales fixed), apart from certain special pieces of measuring apparatus which are described in this report. The blind student wants to work with sighted people, they should be able to use his apparatus. Commercial apparatus is vastly cheaper and much more quickly available than specially produced items.

What is really needed is a resourceful and imaginative teacher, with the patience to move at the slower pace which is essential, even for a clever blind pupil with aptitude. The more discovery there can be the better. But heuristic methods can be taken only so far. The teacher can at least see that the pupil does as much for himself as possible and that he has the fun of taking for himself the final step to the solution.

As a result of our research work on the teaching of Science to the blind, we were invited to present a "Workshop" at the International Conference of Educators of Blind Youth in Boston in 1967. With the financial help of the Viscount Nuffield Auxiliary Fund, together with the Royal National Institute for the Blind and the Wolfson Foundation, three of the present contributors, - Mr. Harwood, Mr. Pickles and Mr. Brooks, - took part in this workshop, of which Mr. Colborne Brown, Education Officer of the Royal National Institute for the Blind, and I were joint chairmen. If there is some repetition in this report of what was published in the proceedings of this Conference, I will apologise now. Principles and practice have not much changed. But we have expanded and consolidated what we had learnt by then. Miss McHugh's paper was read at the Conference.

Our final contributor on Science is Mr. S. C. Stephenson, the present Master in charge of Science teaching at this College, a most capable physicist and a fine teacher. Since 1967 apparatus has been bought for Sixth Form Physics teaching in the College itself and Mr. Stephenson's first Sixth Form pupil, a totally blind boy, has just obtained a “B” grade, with very good marks in the practical examination; There may be some overlapping in what the various contributors say. For this too I apologise, though repetition by different writers adds emphasis. The final two notes in the section on Science teaching comprise a short article by myself, with information from others, on suggestions for building a Science laboratory or laboratories for the blind and proposals for the content of a two year general science course.

The Research project had as its main object the Teaching of Science to the Blind, about the value of which there was considerable uncertainty at the time. The decision to include research into the teaching of Mathematics came second, but this was not, of course, to say that either the subject or research into it was less important. There was in fact, and still is, a great need for research into the teaching of a subject which presents great difficulties to a blind student, difficulties both of formation of concept and of means of work. It was said only a few years ago that Mathematics was not a suitable subject of study for the blind. That cannot be said now, though the difficulties remain.

Something at least has been done to improve means of work and to encourage co-ordination of method between schools and within schools. The first step taken was a meeting of Head teachers at Linden Lodge School in 1964. This was followed by a gathering of teachers of Mathematics at Worcester in March 1965, when Mr. Cyril Hope, author of "The Midlands Mathematics Experiment" spoke on "New Approaches". A working party was formed and the following summer, 1966, with the help of the Viscount Nuffield Auxiliary Fund grant, a three day conference was held in Sheffield, with H.M.I. Miss Biggs as Chief Instructor. Mr. Tooze the Headmaster of Sheffield School for the Blind, had already moved ahead with improved methods for teaching Mathematics to blind children of primary school age and it had been decided that the main research into the teaching of Mathematics during the three year period of grant from the Viscount Nuffield Auxiliary Fund should be based on his School. Mr. Tooze in 1967 helped to arrange and lead the workshop on "Number" at the Boston Conference and with an additional grant from the V.N.A.F. has produced a film on this subject.

At Worcester we were lucky to have for nearly forty years an able and distinguished teacher of Mathematics, Mr. R. W. Bonham. Mr. Bonham is the designer of the British braille Mathematics code, now fully correlated with Standard English braille and used throughout the English speaking world, except where the American Nemeth Code is preferred. As an experienced Inspector told us, he taught real Mathematics and it is certainly true to say that he took the teaching of Mathematics to blind pupils further than any other teacher. His pupil and successor, Mr G. Jackson, is a distinguished and talented teacher who understands fully the needs and difficulties of blind pupils. He contributes the first article on Mathematics in this report.

The second is by Miss A. M. Sims, Mathematics mistress at Chorleywood College, the grammar school for blind girls. The term "Modern Mathematics" needs analysis. It can be used to describe changes of apparatus and approach at primary level, the removal of dead wood at secondary level and the introduction of elements like sets and vectors, decreased emphasis on the value of calculation for its own sake. It has to be decided which aspects of modern Mathematics are most valuable in themselves and which can best be applied to teaching blind students, who are bound to find difficulty in interpreting and distinguishing certain diagrams, for instance a number of adjacent segments of a circle, despite the improvements in production and understanding of diagram described by Mr. Pickles in his full article at the end of this report. Miss Sims has for some years taught "modern" Mathematics selectively and methodically and it is interesting to read her comment on it.

At primary level Mr. Tooze, the third contributor, has experimented widely in the construction and use of apparatus. As we, he has taken full advantage of the Perkins upward braille writing machine, which enables a pupil to set out his working almost as easily as can a sighted child. Mr. Tooze has translated much from the methods now used in ordinary primary schools and has passed his own enthusiasms on to the children in his school.

It is not yet known how far the study of Science and Mathematics will be of direct use in employment. At the time of writing a totally blind student is in the middle of a University course in Electronics. A good understanding of Science is essential to a Physiotherapist. I am sure there is value in a knowledge of Rural Science for agricultural workers in emergent countries. Since a Worcester boy, Robert Marrs, was taken for training in Cambridge by the late Dr. Mutch and Mrs. Mutch and became the first British blind computer programmer, this channel has rapidly opened and there are now, I believe, over sixty blind computer programmers. An understanding of Mathematics is in fact useful to blind men and women in all professions. So too is the ability to interpret diagrams, perhaps particularly for those working at machines in industry.

Whatever the value of an understanding of Mathematics and Science in employment, there is no longer doubt of the educational value. Hard thought, close analysis, intellectual ingenuity and reasoned judgment are all required for both subjects. Through a study of Science curiosity is fostered, habits of repeated controlled experiment are demanded. The classicist and lawyer learn to apply great precision in the use of language and analysis of its meaning, the scientist and mathematician must do likewise when dealing with objects and symbols. In addition the blind student, in a study of Science, through the handling of tools learns a dexterity which does not come naturally to him and he learns to measure accurately, tackling a problem from many different angles.

We have not answered all the questions. We could cover only a small area. But at least through this three year project the Royal National Institute for the Blind became convinced that there was a strong case for establishing at a University a centre for research into the deep and various problems of educating the visually handicapped. The College of Teachers of the Blind also had long felt this need. A generous grant from the Royal National Institute for the Blind, supported by a grant from the Department of Education and Science, which has from the outset given quiet encouragement to the scheme, and another from St. Dunstan's has enabled the University of Birmingham with enthusiasm to establish such a research centre and to provide accommodation. This is now in action under its Director, Dr. M. J. Tobin. It has much to do and is already undertaking most valuable studies.

The Teaching of Science at Worcester College for the Blind

by

S. C. Stephenson

Science was first introduced to the College as an examination subject through a General Science Course, for which no practical examination was required. While a study of General Science is admirable for providing a good background knowledge over a wide field, it lacks precision and a pass in it was not always acceptable as a qualification for entry to University and Further Education Establishments, nor was it a solid enough basis for Advanced Study and careers. A more profound scientific knowledge was required. As the College is small (70 boys), we were compelled to concentrate our teaching efforts on one of the main sciences in order to teach it to the levels required. Physics was chosen as the subject on which we would place the main emphasis, chiefly because it appeared that it would be possible to adapt a larger proportion of the usual practical work for blind person participation in this science rather than the other sciences. We now teach Physics to the Ordinary and Advanced Levels of the Joint Oxford and Cambridge Examining Board.

We much regretted having to place less emphasis on the other sciences, but we do teach as much Biology and Chemistry as our timetable permits. Some of the difficulties in teaching Biology will be realised - we cannot use the microscope or micro-projector and the many excellent biological diagrams, nor can we carry out dissections. However, we, use:- plastic models of animal organs etc., parts of plants, skeletons, stuffed animals and the pupil's own body, to help to "illustrate" our teaching. Much of the ordinary school Chemistry practical relies upon visual observations and Use of measuring devices requiring vision. While we can overcome some of the consequent problems, it is still not possible to indicate a large number of the chemical reactions adequately, we feel. By somewhat modifying the usual introductory syllabus, however, it does seem possible to introduce some interest and under- standing of fundamental chemistry using small identification, exothermic and endothermic reactions, audible effects and other means of indication comprehensible to the blind and thus introduce at least partial pupil participation. We have found that a blind boy can be taught sufficient chemistry to obtain a good “O” Level pass in an external examination not requiring practical examination, but there is far less satisfaction to a pupil in having to forgo most of the usual practical. The same would be true of Biology. Another factor is the obvious danger in Chemistry practical of use of heating in most experiments and the "handling" of fairly dangerous chemicals, and, largely because of this, there are few uses of a Chemistry qualification in boys' future careers.

In attempts to try to make our Science teaching more interesting we have been greatly helped in recent years by newly available materials and newly developed special devices. Most of these have become available through the now completed 3-year Nuffield-aided Project of research in the teaching of basic Mathematics and Science to the blind, which was centred at the College. We have also benefited by the general Nuffield Science Project Scheme; chiefly, by its influence in causing the production of many interesting types of modern practical apparatus.

Naturally, problems arise when one tries to teach any subject to persons whose vision is poor; Science teaching renders a few of the general difficulties more acute and adds a few of its own - especially in the field of practical work and demonstrations. Our major difficulties are probably:- 1, the efficient communication of information other than by word-of-mouth teaching: 2, the finding of ways and means of creating and stimulating interest in the subject: and, 3, the arranging of pupil experiments in ways which are fully comprehensible to the blind.

Regarding the first of these problems, textbooks are the usual partial solution. Suitable books are very scarce in braille form and most of those available are too superficial. Apart from the fact that braille books lack the appeal of the splendid sighted books, with their stimulating photographs, colours and diagrams, theme are big production difficulties. For example, we have received, after long hard work by the R.N.I.B. presses, a good “O” Level book in braille, [Abbott - Physics (see Appendix 2)] which comprises 17 braille volumes per single sighted volume, and each braille volume measures 13 inches by 11 inches by 1½ inches! Necessary high production costs and long production delays cause us to have to limit the number of volumes we can have for class use. The sheer bulk of the book makes it less useful than it would be, otherwise, as a handy reference. Therefore, we are tending to use textbooks for occasional reference, own time reading material and as revision guides only. We have to use rather more class dictated notes than would be preferred, but, fortunately, boys soon learn to use the Perkins brailler for rapid brailling of notes. Each boy keeps a file copy of notes as his auxiliary textbook.

Diagrams are invaluable aids to comprehension in scientific literature. We have recently made progress in the production of special embossed diagrams for blind persons. Braille diagrams are not new, but special tools and materials recently available increase the versatility so that we can now draw almost everything we require. This is most helpful and in some ways it compensates for inability to use the blackboard and common visual aids. Also, our vacuum thermoforming machine provides a good means of copying diagrams at a reasonable speed. (Plastic sheet is used for the copies). Boys have to be carefully introduced to the technique of reading diagrams and usually some help with interpretation is needed with each new diagram, but there is no doubt that the diagrams are extremely useful. Many pupils learn to "read" them very quickly and, often, with little or no help. Even complex electrical circuits, with the usual symbols, can be read quickly and accurately by some persons, without help! It is possible to explain something of the idea of perspective in plane drawings of three dimensional figures, but, in such cases, it is often more helpful to use solid models made to illustrate the idea one wishes to convey, we believe.

Allied to diagrams is the process of drawing by the pupils themselves. It is very difficult for them to draw, but all pupils are taught basic drawing in Mathematics as well as in Science. As might be expected, the drawing ability varies greatly from person to person, and it can nowhere approach sighted standards of good drawing, but it is a useful asset as a means of communication. Pupils have to answer examination questions involving drawings in the answer (including graphs) and some elementary ability helps in the conveyance of ideas to the sighted persons who write down their answers. Special drawing tools have been developed (see Appendix 1).

Interested pupils suffer from the fact that there is a shortage of scientific literature (of a general nature) available to the blind. There is a tremendous strain on the hardworking organisations who produce braille and "talking books" for the blind - the demand is very great -- so the vast flood of scientific literature remains virtually untapped. More is being done to produce books, but the most valuable help in this sphere is given by volunteer readers, we find. They read direct to pupils or record on magnetic tape selections from modern books, scripts etc. Pupils must listen in their spare time and one might think this is not likely to be popular. However, blind persons have usually more free time than their sighted contemporaries, and aid of the kind just mentioned is welcomed by them.

Broadcast talks help to create interest and blind persons could get a great deal from their radio sets. Unfortunately for us, the excellent schools broadcasts are in the medium of television (in Science) and we find that, as such, they are of limited value at the College. It is rather uninspiring to have to listen to a description of demonstrations presented visually.

Most of the problems created by trying to make practical work and demonstration experiments comprehensible to the blind are obvious and so we know what we need to overcome them. As a general rule, we have not attempted to have many special aids or specially designed bits of apparatus constructed - the process is very costly and involves many production/development delays. Instead, we obtain ordinary laboratory apparatus and modify it, aiming to cause as little basic alteration as possible. In any case, pupils must know basic experimental methods of the ordinary type in order to answer examination questions. We believe we have made useful progress in the field of making practical Physics interesting and understandable to our pupils and we aim to do as much class practical as possible.

A few special aid devices, now available, are a tremendous asset (see Appendix 1). It might be of interest to readers of this account to hear of some of the ways by which we have tackled the problems.

Measurement of length is achieved by use of specially made braille (embossed) plastic rulers and of braille markers and braille centimetre scales, which we prepare and fit over the normal scales. Blind people cannot discriminate between individual millimetres, as a general rule, so we use only half-centimetre and centimetre marks, but a good pupil can estimate to the nearest millimetre fairly well. Some boys can even count individual millimetre indentations on a boxwood scale by finger-nail "feel". Similar marking methods are used to make instrument dials and volume graduations comprehensible to the blind; some- times we emboss the scales in metal.

The problem of finding the position of the level of a liquid in a tube, which occurs quite often in Physics, introduces our most useful special aid, the light probe. This is a small portable device, (in one form), something like a small pocket torch with a pencil-shaped head. It has a photo-sensitive transistor in the head unit and the miniature electronics circuit in the probe produces an audible note from a miniature loudspeaker; the musical pitch of the note rises as the illuminating intensity on the sensitive element increases. Here are a few of its uses:-

a. A sharp change of note occurs at the level of the surface of liquid in a transparent tube, (assuming that the probe is held on the side opposite to that of the main illumination), due to transmission differences between the liquid and the air. Even a transparent, colourless liquid does this, due to the meniscus reducing transmission. Hence volumes, lengths of liquid columns, pressures etc. can be measured.

b. The relative reflecting properties of black and white enable the probe to detect the position of a meter pointer, and so, with the probe, blind people can "read" devices like ammeters etc. (One assumes here the usual black pointer against white scale background).

c. The probe readily detects the spot of light acting as a pointer on spot galvanometers and the like.

d. In the light experiments, the paths of rays from rayboxes can be traced to show reflection, refraction and lens/mirror action.

Use of the probe is not without difficulty; one requires to train users so that they do not accidentally obscure the external illumination and get fake results and the external illumination must often be arranged suitably. It is also somewhat "audio-confusing" if many probes are in use simultaneously. For demonstration purposes, it is advisable to amplify the rather weak output from some form of light probe via an amplifier. In this way, we make use of these probes, photocells, infra-red sensitive cells etc. as detectors, showing by audible means when and how expected changes are occurring in demonstration experiments. Of course, we also use electrical contact methods where possible, e.g. a rod expanding when heated to close a small gap and make an electrical contact and cause a bell to ring.

The blind cannot use mercury thermometers, but one can devise contact devices to show them temperature changes. To measure temperatures we use various instruments, including the Nuffield bimetallic dial type thermometers, (usual method of dial reading). More accurately, we measure temperature with a thermocouple and calibrated spot galvanometer, or use the special electronic thermometer devised for the blind. The latter is an electronic "black box" producing a constant volume and frequency audible note. A thermistor is attached to the box via a protective connecting cable. The thermistor is the sensitive element and it is used as a thermometer, its resistance being temperature dependent, a large brailled circular temperature dial is fitted on top of the box, and, by turning a knob, one rotates a fee[able strong pointer over this scale. The knob also rotates a variable resistor slider inside the box and, when balance is achieved between its resistance and that of the thermistor, the sound cuts off sharply. This null point effectively moves over the scale as the temperature of the thermistor changes. This is a very good device, but supplies are very short at present. We have one working over the very useful range of -10°C to 110°C

Weighing is done by various means. We use lever and spring balances fitted with braille scales -- the pointer positions being determined by feel. It was found that sturdy chemical balances could be used directly, with only the minor modification of detecting by feel when the balance pointer was in the zero position. (Sturdy balances were found to be necessary because the blind accidentally knock delicate balances off their knife edges when they try to use them.) It is not really feasible to use milligramme weights because the handling and labelling difficulties are rather pronounced, but this deficiency only causes moderate inaccuracy at up to “O” level standards if one uses moderately large masses. (We have to braille label the ordinary weights, too). Recently, we obtained two specially modified "chaindial" balances. These utilise the standard "chaindial" method of adding 0.1 gramme units of weight by releasing chain from a drum and the drum is brailled so that 0.1 to 0.9 grammes can be added without handling. We now have a set of weights standardised incorporating the embossed braille labels. The balances themselves have been modified to indicate left or right imbalance by the emission of two audible notes - a high frequency note for left imbalance and a lower frequency note for right imbalance. True balance is indicated by no sound. Thus, with the new balances, the blind can easily weigh to 0.1 gramme with accuracy.

We use brailled stop clocks, interval timers etc. for timing. For more accurate work we have a specially made electric stop clock with Veeder counter read-out. With the latter, timings to approaching 0.1 second accuracy are theoretically possible.

The reader of this account may now see why we claim that we can, at least, attempt most of the standard experiments. Of course, measurement accuracy is not all that would be desired, but it is a fact that good pupils consistently obtain results of a very reasonable accuracy and many “A” level results well within 5% of the true values have been obtained.

A great many of the ordinary experiments can be carried out with minor modifications, or, none at all. For example:- air pressure can be demonstrated by trying to pull apart evacuated cups, or by collapsing cans; expansion can be shown by the breaking of a rod etc. The reader will think of many similar types of experiment where sight is not essential. It is surprising how many (and how well) simple electricity and magnetism experiments can be done.

The work is still somewhat in its infancy, but it appears that our main difficulty of rendering practical work comprehensible occurs in the wave property field and especially in this section of the light syllabus. The ripple tank is of no value to us, but we can indicate a number of wave phenomena by use of a sound modulated centimetre wave radio transmitter/ receiver system. Models and analogy demonstrations help with explanations, but interference, diffraction and the spectrum are only partially successfully demonstrated by our present methods. It is also not possible to show virtual images other than by models and drawings and true focussing is difficult to show fully satisfactorily. However, some success in the light image field is achieved by use of an elementary form of image scanning with light probes and similar apparatus.

We regret that we have not found it possible to operate fully a Nuffield Science course. Apart from apparatus cost there are a number of difficulties:-

a. much of the Nuffield apparatus is designed for visual effects and is rather difficult and costly to adapt for the blind,

b. the syllabus is rather long and our rate of progress is slower than in sighted schools,

c. the more standard experiments are sometimes rather more easily adapted for the blind.

Nevertheless, we try to use a good proportion of Nuffield apparatus, though we adopt any method, Nuffield or otherwise, to try to illustrate the work experimentally. We choose the method which seems best from our point of view and in an attempt to get a maximum of experiments in which pupils can participate.

In the whole of this article I have hinted at what is probably our biggest "enemy" - time. Apart from the longer time required to read or interpret diagrams and the more detailed explanations required than in sighted schools, it requires more time than usual to perform experiments and to "show" demonstrations (each pupil being "shown" individually). The same factor makes its presence felt in the external examinations and we are fortunate that we are given extra time allowance for these.

Despite the difficulties, I am sure that we can say that we have made reasonable progress in rendering Physics (and some other science) interesting and educationally useful to the blind. We still have a long way to go, but we are being stimulated by what appear to be new career openings in the computer field. It would seem that results so far give grounds for optimism.

The Teaching of Science to Blind Students

by

R. Harwood

During the past three decades the advances made in science have aroused great interest in most pupils in schools, the orbiting of satellites and transistorised radio receivers now being common place events. The advent of solid state physics has made the miniaturisation of many instruments possible and this alone has created an active interest in physics; the production of plastics and man-made fibres in chemistry and the use of the electron microscope to elucidate biological functions have all increased the desire of pupils to learn more about the underlying principles upon which these and other inventions work. This seeking after information is not confined to sighted people, it is very apparent in the case of blind students, but in their case careful preparation is more essential so that misconceptions do not occur.

In the past the attitude of most people, in fact all except a very small minority, to the teaching of science to the blind has been negative, the general feeling being that it cannot be done, it is too dangerous, and even if it were possible of what use is it to the student ? To study a science in full requires the ability satisfactorily to undertake experimental work and when this problem is carefully analysed it becomes apparent that much of the practical work is possible but some aspects will be impossible to the blind. The aim in teaching science to the blind must not be to produce scientists but rather to give necessary scientific background for the understanding of every-day occurrences and thereby increase the fullness of living. Examining the individual disciplines indicates that physics offers the opportunity of understanding the world around us, such as frictional effects, the boiling of liquids, the mode of operation of electrical appliances and so on, biology will cover many of the personal problems, growth of the child, adolescence and heredity, processes of digestion and like phenomena, whilst chemistry will explain the chemical reactions of the digestive system, production of materials such as nylon and the synthesis of products of all kinds.

Omitting the sense of sight, or accepting a very low acuity of vision, one still possesses the senses of touch, hearing, taste and smell with which to investigate the surroundings.

When we consider the complete electromagnetic radiation spectrum the visible section is a very small portion and thus we may with advantage look to possible alternatives, for example converting light radiations in the visible region into radio waves or sound waves. By using the shorter wavelength radio waves the properties of light can be demonstrated easily and effectively. Thus with the conversion of light into other frequencies that can be detected by other means blindness is not an insurmountable handicap. As with a sighted class the teacher himself is so important in producing the best results from the class and, particularly in the teaching of science to blind students, it is essential to have adequate time, space, apparatus, laboratory technicians, as well as patience, understanding and an enthusiastic well qualified teacher with the necessary ingenuity. Many of the so called difficulties resolve themselves with good teaching principles and it must be stressed that "good teaching" is the backbone of science education. Also the student must be given a lead and then allowed to experiment himself, being guided along the path, and the teacher must have that willingness to help the student help himself.

It has already been described in the Introduction how Worcester City Technical College came to be asked for its help.

After very careful, serious thought it was ultimately decided that an attempt be made on the G.C.E. Advanced Level course in Physics, the project to be carried out by the students attending Worcester Technical College classes, the College being well equipped with laboratories and staff to undertake the work. This then initiated the unique experiment of integrating first partially sighted, then blind students,--with a sighted class in the teaching of Advanced Physics.

General guide lines were set to govern progress and these were:-

a. the apparatus to which modifications were necessary should be standard apparatus and the modifications should be as simple as possible.

b. modified apparatus must be equally acceptable for use by both blind and sighted students.

c. any specialised equipment must be kept to a minimum, and

d. the physics must be taught on a practical basis with the students undertaking the experimental work themselves.

It was also borne in mind that some equipment adapted for these special requirements may be effectively employed in the sighted class.

The first three students, as had been said, had a little sight and so the full impact of totally blind students undertaking advanced practical work did not occur until later. These had studied the ordinary level physics at the College, for which, though much practical work had been done, there was no practical examination. At Advanced Level no student hoping for a valid certificate could be excused the Practical Examination.

It was felt right from the start that first partially sighted, then blind boys must do the experiments and record the observations themselves rather than make use of an assistant to do this work for them. When totally blind pupils were first accepted, an appraisal was made of essential items required and the general approach to be made. Although a light sensitive probe had been in existence for some time, the first one containing a valve amplifier, the introduction of transistors enabled a much more compact and better designed probe to be made. All the probes up to this time had consisted of the light sensitive unit, an oscillator and amplifier, and a personal earphone, the three separate items being linked by two lengths of twin flex. Although different persons had produced different probes, those available at this time all had this common pattern.

Such an arrangement would be potentially dangerous in the laboratory, so a fresh approach was made in which the light sensitive cell, oscillator, amplifier and loudspeaker were combined into one unit. Co-operation between Worcester Technical College and the Royal Radar Establishment resulted in such a unit being made, it was tested and modified and in its present form is functional and compact. The variation of light intensity falling on the photoconductive cell causes changes in its resonance which is then converted by means of the oscillator, amplifier and loudspeaker into an audio output. The intensity of the light modulates the volume of sound output but in addition there is also a small pitch modulation which in operation proves an added advantage. This probe is made with discrete off-the-shelf components and reduction in size could be easily possible. A similar probe has been produced by the Technical Officer of the Royal National Institute for the Blind and is commercially available. (see Appendix 1).

A start was made in the electrical experiments as these appeared most likely to allow of easy adaptations and modifications, and although the Wheatstone network arrangements could be carried out using an a.c. supply and a "buzzer" as the null point indicator this was not altogether satisfactory. The main drawback was that of not being able to determine the direction of flow of current and hence the direction of out-of-balance, and the introduction of a rectifier although solving this problem detracted from the simple-approach. Similarly such an arrangement would not work with potentiometric circuits where d.c. supplies were used. Restarting, but now introducing the spot type galvanometer as the detector, solved not only this immediate difficulty but proved very useful in other ways.

With this type of galvanometer with its built-in light source the light probe was sufficiently sensitive to detect the "cursor line" in the spot of light so that accurate location of the spot could now be made. The possibility of using the probe to locate the needle on the conventional type meter was reasonably satisfactory but it was found that erroneous readings did arise due to shadows cast by the probe or the student or both.

This did not arise with the spot type galvanometer, and an embossed, transparent, brailled scale can easily be fitted. The student can use either one edge of the light spot, which is easier in practice, or the cursor line and record observations of the same order of accuracy as the sighted person, and both can use the same instrument. This idea has been put into use by one of my colleagues for semi-automatic titrations in chemistry to indicate the "end-point". In any experiment where a null point is required, as for example a Wheatstone network or potentiometric work, the light spot is first centralised, producing a centre-zero instrument. The probe is then placed to (say) the right of the spot, the circuit momentarily completed and if the deflection is to the right then a buzz will be heard as the spot travels away from its zero position and again on its return. If no sound is heard then the probe is placed to the left of the zero and the procedure is repeated. The experiment then proceeds along the usual lines.

The galvanometer can also be shunted by the correct resistors to convert it into a multi-range ammeter, the ranges being governed by the values of the resistors used. In a similar manner the galvanometer can be attenuated by series resistors to give a multirange volt-meter. This has been found to be better in practice than the usual multirange meter and having to locate the position of the pointer, and in effect the ranges can be easily and safely controlled.

This could be made practically fool-proof as an extra little "box" to be attached to the galvanometer with the ranges brailled on the box. In the laboratory it has been convenient to shunt the galvanometer to give current ranges of 100 mA, 1 A and 5 A and to attenuate it to give voltage ranges of 1 V and 10 V. Furthermore the meter may easily be modified to serve as an ohm-meter but this has not been found necessary up to the present. For the usual type of electrical power measurement it is necessary to observe simultaneously values of current and voltage so that two galvanometers correctly modified would be required.

In addition the galvanometer can also be used in conjunction with a thermocouple and a suitable series resistor to measure temperature. A copper-constant thermocouple gives a virtually linear scale up to 200°C and suffers no damage by hard treatment. A thermistor will allow of simpler circuitry but can easily be damaged by high temperatures or harsh treatment. By varying the series resistor in the thermocouple various ranges can be easily obtained and again ranges of 10° and 100°C were found most convenient. Perhaps the main disadvantage of the thermocouple is the advantage of a stabilised cold junction for temperature measurement, but in the laboratory this is obtained by placing the cold junction in melting ice in a small glass container which is insulated with expanded polystyrene. If a temperature difference is required then the junctions are used directly. For less accurate determination of temperature a single junction thermocouple can be used and the necessary adjustment made for the ambient temperature. It is thus possible for quite inexperienced pupils to record their own temperatures by this means. An alternative to this is the audio thermometer produced by the R.N.I.B. which uses a thermistor and is controlled by rotating a pointer over a brailled scale until zero sound is produced. This is illustrated in the "Apparatus" section. [Digitiser’s note: We regret that it has not been possible to reproduce the photographs and diagrams of the original print on the Internet.]

The measurement of lengths can be satisfactorily completed using a plastic ruler with embossed graduations. The centimetre ruler in present production is subdivided into half centimetre divisions but with the more experienced students subdivisions of 2 millimetres can be used to greater advantage. Alternatively self adhesive plastic tape may be suitably embossed and then attached to a straight edge. In order to measure small lengths of the order of millimetres to within 1% error the micrometer screw gauge may be simply modified by attaching a disc which is subdivided in the edge into fifty equal divisions and the face is then embossed at every fifth division and braille numbers added. A double ended pointer which is a friction-tight fit on the sleeve enables the datum line on the shank to be located with reference to the requisite division on the drum. The datum line is embossed by soft-soldering a short length of wire in position. The gauge is opened to accommodate the object and the pointer rotated so that the one end is in alignment with the datum line, this being done by touch. The object is removed and the drum rotated to close the gauge, the number of times the pointer passes the thumb being recorded. The part revolution still to be decided is read off by the pointer at the edge of the drum. Thus if one complete revolution corresponds to 0.5 mm and there are x revolutions, the pointer being Iocated at division y on the drum then the distance is x/2 + y/50 mm.

This modification may be fitted to any type of screw micrometer (the drum has three screws forming a self centring attachment), also to a spherometer or any screw operated mechanism. Thus it can readily be used for measuring radii of curvature of lens faces or mirrors and can be used in determination of the coefficient of linear expansion of a rod.

There is however a more sophisticated version with the normal micrometer replaced by a much larger drum but this is a permanent attachment and cannot be changed from one instrument to another. Also it is not readily used by sighted persons.

Weighing to a reasonable degree of accuracy can be accomplished in various ways. The Butchart balance needs only the addition of an embossed scale. With a spring balance a lever is added to operate over an embossed scale and a magnification of 10 or greater is easily obtained.

In addition the scale may be graduated in pounds or grams. There are several balances with a rider moving along a bar and the rider clicks into position so that direct counting of clicks will give the required reading. A more sophisticated means is by modification of the beam balance, with electrical contacts which close when the beam is not horizontal, a differently pitched note being produced on either out-of-balance position. This is a simple transistor circuit but greater sensitivity may easily be produced by considering the balance pan as a movable plate of a capacitor as a basis of modification. The balance is fitted with a chain drum attachment which is brailled and this will weigh to the nearest 0.1 grm. For very small masses a torsion balance can be used but this is not of general application.

Although it is possible to adapt the standard stop clock by fitting an embossed scale which is used to "read" the second and minute hands using the probe, this is liable to errors due to both shadows and misreadings. The use of this type of clock even with sighted persons is open to errors. By using a synchronous electric motor, suitable contacts and an electromagnetic relay unit with brailled scales a clock indicating second intervals is produced, and this can also be modified to give one-tenth second intervals. The on-off mechanism is a simple press switch but the clock can be operated with make and break circuits. For very small intervals of time the make and break technique can be used with the standard electronic counter using the dekatron display. The light probe easily detects which electrode is glowing and all that is necessary is to attach an embossed scale round the display tubes.

Modification to the light probe by fitting an opaque cap renders the photocell non-operative and the cell is by-passed by two leads which are then used for physical contact connection. Hence in the case of a resonance tube where the length of the air column is required, the leads ends are attached to be coincident with the end of a metre rule and when touching the water level the probe will then emit sound.

It has been suggested that this same principle may be used to fill cups or other containers up to the required level especially if the liquids are very hot. With very little alteration it can be used as a rain indicator.

For the measurement of atmospheric pressure a J-tube type barometer is used, fitted with brailled scales suitably zeroed on a given datum line, the necessary levels being located by the probe and the pressure then being read as the difference between the two recorded heights.

Making use of 3 cm radio wave transmitter and receiver, the behaviour of radio waves can be dealt with directly and the information so obtained then used to illustrate the similar characteristics of light waves. Reflection, refraction, diffraction, interference and polarisation can all be illustrated very easily, and quantitative observations made; the behaviour of light can then be demonstrated with the light probe but measurements are now very much more difficult.

The use of the probe with a standard spectrometer will locate the D line of sodium with about 2% error so that the procedure can be illustrated. However to convert the visual scale to a brailled scale has presented many difficulties and it has proved impossible to date to measure angles with anything like the desired accuracy. The mode of operation can be demonstrated positively but precise operation is considered beyond the present limits. The location of real visual images can be dealt with adequately and if magnification is required the size of the object and image can be used by using the probe. With lenses this has proved satisfactory particularly if a good optical bench is available so that movement along a straight line may be made easily and accurately; but with mirrors, difficulties are encountered due to both object and image being on the same side of the mirror and some help is generally required in setting up the experiment. With virtual images by back-tracking of the rays the location of the image may be found but this is laborious and not particularly satisfactory, and the size of the image is also not capable of direct measurement.

The general nature (and behaviour) of transverse and longitudinal wave motions can be demonstrated by producing standing waves. With transverse vibrations the production of a standing wave in a string will illustrate the positions of nodes and antinodes, of which the nodes are easily detected by the probe. Using a helical spring and a suitable vibrator, by stretching the spring the nodes and antinodes can easily be located directly by touch. The two means of energy propagation can thus be illustrated quite adequately.

Having completed a series of observations in an investigation it is often necessary to plot a graph of these observations. The graph plotter which was evolved is both positive in action and simple to use. Based on a clip board principle a slider is fitted with one embossed scale, the slider itself moving along another embossed scale so that co-ordinates in two dimensions are thus possible. The fixed scale is attached to a rubber base on which is placed a melinex sheet. The co-ordinates are located by pins placed into the rubber base and a flexible rod can then be contoured to the pins, an ordinary ball-point pen being used along the rod to "raise" the graph on the Melinex. Using a straight edge in conjunction with the flexible rod a tangent to a curve can be drawn and gradients determined, but as with visual operation variations in accuracy and consistency will occur and tend to be rather wider with the blind student.

Another modification is instead of using embossed scales to use serrated edges so that measurements are recorded by the clicks heard. This is particularly suitable in the early stages of graphical work and development of the original idea is under way to make it more adaptable and quicker in operation. Furthermore another variation is to use a rubber pad in a sleeve of one side Melinex and the other side braille paper so that the completed graph is then easily dealt with for storage and any required information can be added to the braille paper in the normal way.

Volumes of liquids can be measured by using the probe with a pipette, the etched graduation on the pipette being easily located with a finger nail and the probe set up to that mark. A pipette-filler is used to introduce the liquid into the pipette and as the meniscus passes the graduation mark, the probe indicates this. With a little practice the meniscus can be precisely located at the graduation mark. A burette may be used in the same way but a larger error is introduced because the nominal spacing between successive 0.1 cm3 graduations is of the order of 1 mm whereas tactile differentiation is of the order of 2 mm. Remembering this source of error, experiments can be completed in a reasonably satisfactory manner. The ready availability of the hypodermic type syringe can overcome the above difficulty, by fitting a screw operated plunger whereby a small volume can be metered out with much greater accuracy. For larger volume requirements the usual measuring cylinder can be used directly with the probe or using the surface detector leads.

The need for a linear vernier is very apparent but is not easily solved because of the wide variety of interval lengths used on scales since they are arbitrarily produced, one burette having a basic interval of 1.2 cm and another of 1.1 cm yet both measuring 1 cm3. Much wider variations occur with measuring cylinders so that either a vernier is produced for each measuring device or the vernier must be applicable to all. The greatest problem to be overcome is the necessary observation of two coincident lines and translating this into a tactile form bearing in mind the minimum differentiation possible. In addition one must not forget the individual variations so that what is eminently suitable for one person may be near useless to another. The lack of a solution to this problem limits progress with the spectrometer which is capable of a visual accuracy of the order of one minute of arc but such a differentiation is completely impossible at the moment to the blind student. The unresolved D lines of sodium can be located using the probe in the telescope of the spectrometer but the probe will need modification before the lines of say the hydrogen spectrum can be resolved. With the very much more sophisticated apparatus such as the medium quartz spectrometer where the spectrum is photographed the resultant plate is used in a spectrum projector and the individual lines can be located by the present probe.

Since the emphasis throughout the teaching is for the student to complete the practical work unaided, or at least with minimal help, it is essential that time is spent initially ensuring that the student is conversant with each component of an experiment. In assembling various components and the understanding of the work it is imperative that such time is not reduced to the detriment of the student's progress. The approach made by the teacher is still essentially on an individual basis and success depends in a large degree on the personality of the teacher. The integration of the theory and the practical aspects must be given very careful consideration, the difficulties encountered on the practical side must be met and resolved. It must not be assumed that individual experimentation is always necessary, in many cases especially in the early stages working in pairs is to be encouraged thus enabling them to pool their ideas and help each other. But in this type of work careful watch must be maintained to ensure that each student is partaking to the full and that a dominant type is not doing most of the experiment.

When dealing with a complex piece of apparatus the maximum understanding of each component is self evident, as, in the case of the internal combustion engine, if the student understands the movement of the piston in the cylinder, the action of the petrol pump, the vaporisation of the petrol and mixing with air, the spark discharge of the plug, the resultant explosion and the conversion of the reciprocating motion into rotation, the final dove-tailing together of the individual actions makes sense. To compress the information too much results in it not being understood and appreciated but this is true in all cases and not applicable only to the blind. Thus good teaching methods are essential and the initial period of learning the separate items must not be reduced at the expense of laying the good firm foundation on which to build future learning.

In undertaking an experiment the direction and guidance of the student must be just adequate so that he uses his initiative to the full. An experiment which "fails" can be as important as one which gives the expected result and the former can be used to advantage in demonstrating important points of procedure. Although limitations of space, apparatus and laboratory staff cannot be easily overcome it should be firmly kept in mind that the student wants to get on with experiments so that delays in actually starting should, wherever possible, be avoided by prior organisation. Having to wait before starting a particular experiment can be to the detriment of the student as well as waste of his time. This then leads back to the importance of very careful build up of knowledge and experience linked with laboratory planning and teaching techniques.

It is not always possible, or desirable, for all students or groups of students to be attempting the same experiment and often it is advantageous for some to be doing the easier, routine, repetitive type of experiment so that another group can be guided in the use of more sophisticated apparatus requiring greater attention. Thus for a class of eight or ten students it is not good policy to try to teach a more complicated piece of apparatus to all of them at the same time, since the long gaps whilst each student satisfies himself with each component causes frustration. In this type of situation a selection of simple experiments will keep the class occupied whilst one group has maximum attention. The efficacy of the "class demonstration" type of experiment has very limited application and is of very little value in this work.

In the initial stages the methods of procedure are much more important than the attainment of high accuracy, since with experience and technique the accuracy will improve, which is also due to the more refined methods which are available at a later stage. Individual measurements must be supervised and checked in the initial stages to eliminate errors of misunderstanding or misuse and such checks will vary according to the work in hand and the experience of the student.

The usefulness of models in teaching must not be overlooked, provided that it is remembered that they are models; enlargements of small objects and diminutions of large objects can all play their part provided an adequate link is created between the model and its real counterpart wherever possible. An appreciation of the limitations of a blind student with respect to spatial references will indicate the use of models for the greater understanding of the world around us.

Turning to the problem of scientific literature, there is a near complete lack of adequate means by which the blind student may acquaint himself with work in science especially with modern progress. Very careful, serious thought must be given to this subject and research into the requirements in this field is imperative; it is felt that the mere transposing of sighted texts into braille form is not suitable. One consideration at least is the actual bulk of the brailled text, but what is more important is that the blind student cannot scan the text to get a quick overall idea. The format of presenting the information needs careful consideration and this will also include the desirability of the representation of diagrams and whether a coded system which would facilitate interpretation is the solution.

It must be remembered that most objects are three-dimensional and to represent these on a two-dimensional surface can lead to confusion unless some indication is given of the different planes indicated in the diagram. Thus a circle drawn on a surface may represent in actual fact a circular wire or a circular disc, or a solid sphere or part of a sphere, and to a sighted student who sees the whole diagram at one go the interpretation may be clear. The blind student builds up the various components and may have to retrace parts of the diagram if previous pieces are incorrectly interpreted. The use of different types of line, continuous, broken, dotted and other possible variations could be used to indicate different planes, and also types of "shading" could indicate surface shapes. Such variations are easily produced on the thermo-form braille copier but it would certainly lead to less confusion in the future if a system of identification were worked out so that it could be internationally adopted and could be extended with future requirements.

At present, programmed instruction is visual and this type of teaching could be used to advantage in this field where individual needs are so important. The necessary modification may be to use a tape-recorder to present the information orally and an additional "box", linked with the recorder electrically, using a punched tape, the questions being posed orally and the various answers incorporated electrically, so that on pressing the correct key the student can progress to the next step but on pressing the incorrect key passing on to the next stage is prevented. A wide field of research is open in this respect of presentation of material which could possibly be applied to sighted students. Also the increase in tape speed could allow a shorter time required for a given amount of information, but the dual difficulty of increased rate of information and change of pitch presents problems which ought to allow of solution. Much of the descriptive type of information could thereby be quickly scanned, leaving the more factual sections to be completed at the normal rate.

Turning from the pure physics to chemistry the reaction to this discipline is even more accentuated; that chemistry is too dangerous to let the visually handicapped student attempt it has been stated over and over again without any attempt at solving the difficulties. With an appreciation of what is required much can be done: the onset of boiling can be heard, effervescence can be heard and a "good nose" is also a good detector. Much of chemistry is now a semi-automated state and in particular titrations can be accomplished using a commercial titrator where the end-point is indicated by the pH value using a spot galvanometer. Work in physics has shown that this type of instrument is easily dealt with and thus the remaining obstacle is the means of accurately measuring small quantities of liquids. This can be done using the hypodermic syringe and operating the piston by a screw mechanism so that it is similar to the screw micrometer, and in this way successive additions of liquid can be made and the total volume found accurately. On a more elementary basis the sensor probe can be used in conjunction with colour filters to detect the end-point of titration by colour change, the choice of indicator being sufficiently wide to present little difficulty.

Qualitative analysis where specific colour changes occur in precipitation or flame tests introduces very much wider problems but as yet little positive work has been attempted on their solution. In general, the weighing of chemicals, measurement of volumes of liquids, determination of temperatures, precipitation techniques, collection of gases, and similar processes can be attempted with a reasonable degree of success. It must be remembered that suitable working surfaces, stable holders for apparatus, adequate protective clothing, convenient water taps and sinks, flint lighters for bunsen burners and such like are all very necessary for safety and, provided time, space, patience and good techniques are employed the student can then pursue his sense of adventure without too many restrictions or frustrations. Often the attitude of complete safety causes many a student to turn away from experimentation and so it is necessary to allow a little relaxation from the "play absolutely safe at all times" attitude to encourage and instil confidence in the pupil. Too often are the blind prevented from handling matches and lighting gas burners, and pouring boiling water into vessels but with control these are activities that they can learn to do safely.

Much of the necessary apparatus may require modification but the techniques in using the apparatus are often developed by the students themselves and these methods can then be passed on to other students. Sometimes carrying out an experiment in a dark room will help the teacher understand the difficulties of a particular technique and occasionally what appears relatively easy to do with one's eyes open turns out to be much more difficult when blindfolded.

Many of the elementary processes require no modification but time must be spent in the handling techniques such as pouring liquid into a beaker, a solution into a funnel, evaporating a solution to dryness and so on. The separation of salt from sand is elementary but is the process used in many organic separations and introduces the basic requirements of solution, filtrating, drying of filtrate, evaporation of salt solution. Separation of iron filings from powdered sulphur by coarse mechanical means using a magnet and then final separation using carbon disulphide as a sulphur solvent is an experiment which can be safely completed by the student. Heat treatment of a sulphur-iron filings mixture can follow to illustrate the difference between the ferrous sulphide compound formed on heating and the mixture components without heating. These are some simple experiments to give confidence to the student but at the same time are instructive and deal with underlying principles. The evolution of many of the common gases can be undertaken in the same way as with sighted classes but some of the tests may not be quite as simple to demonstrate. The formation of crystals from solutions of salts is fascinating albeit a slow process but leads to a sense of achievement. Likewise an estimation of the hardness of water and the use of detergents can easily be undertaken.

The present day introduction to chemistry by considering the structures of the atoms, molecules and crystals through the use of modules will incur little more difficulty than with the sighted student. These models are three dimensional and atom recognition could be easily solved by either a system of coding or surface texture. However the diagrammatic representation of apparatus presents the same difficulties as in physics but in addition a method of adequately dealing with chemical formulae must be given very careful consideration. The semi-micro analysis techniques will obviously produce difficulties in manipulative operations but larger scale work should be feasible. Much more work remains to be done in the chemical field.

In the teaching of biology very little has been attempted and this only at an elementary level, but everyone is interested at least in their own bodies so that the interest is there to begin with, although there are also many difficulties to be overcome. The human body is a complex arrangement of organs about which some knowledge is necessary in order to live a healthy life, whether the person is blind or sighted. Dissectible models of the torso are available so that location of the organs can be easily defined and then superficial examination of one's own body will enable identification to be made. The functioning and interdependence of the various organs should present little difficulty, and the heart, liver, lungs, kidneys and so on of an animal can be obtained easily from an abattoir. When one reaches the stage of molecular biology the usual models can still be used, such models as the cell, the D.N.A. molecule and others being obtained commercially.

Areas in which the blind student will not be able to work include dissection work and microscope examination of materials. Both these sections involve such fine detail that there appears to be no practical solution at the present and very unlikely in the future. However dissections have been generally criticised in the past on the grounds that biology is a study of living things whereas it is often introduced by the dissection of a dead animal.

The study of the growth of plants, effects of nutrients, the keeping of pets can be used as an encouragement to finding out more about oneself. A certain amount of work on genetics and hereditary factors can be undertaken and practical work could include the breeding of, say, mice so that verification of genetical factors is possible, the probe being used to give an assessment of the colouring and pattern of the fur, texture being dealt with by touch.

Here a word of warning, the adequate care of animals imposes a fairly rigid routine in terms of feeding, cleaning and other factors, and also that all members of a staff may not have the same inherent friendliness towards certain species of animals. With budgerigars these may be sufficiently tame for handling so that the student gets to know the feel of a live bird, its size, wing span, beak length and other dimensions so that comparison with a wild bird is then possible, if only by description. Bird songs will help identify different species so that a restricted amount of field work is possible.

On the botanical side seeds may be planted, study of germination is possible as is the development of the plant, and practical work will include potting up plants and general care. On a larger scale a small plot of garden suggests a possibility, certainly the herbs in a garden can be identified by their scents. For the students with a liking for this type of work this attempt at growing plants can be worth while but some persons may not seem particularly well disposed to this work and should not be compelled to do it.

Visits to local farms so that the domesticated animals such as pigs, sheep, chickens and cattle may be studied is another line of approach and a mixed farm could be visited on several occasions to evaluate the growth of plants and animals. But again initial preparation must be undertaken to ensure that the students are aware of what is taking place, an embossed diagram of the general farm layout will be an aid to direction findings, and the necessity of enclosures to prevent animals from wandering will help the students to follow the code of good behaviour whilst in the countryside. Zoos can provide some of the other animals not associated with the British habitat and in conjunction with a museum a certain amount of interest is engendered but there are great limitations when one considers any type of wild animal.

Finally the study of the individual, recording height, weight, lung capacity and so on gives direct meaning to measurements and by plotting graphs rates of development can be shown. Some observations as above are of necessity giving small rates of change but observations of pulse rate and respiration will give large rates of change in small time intervals and all that is required is the digital read-out clock. Body and skin temperatures can likewise be investigated before and after certain specified exercises to evaluate the effects of physical exertion.

In conclusion, although certain aspects of science are, at least for the present, out of range of feasibility for the blind student, much can be completed using modified instrumentation. For those with very low acuity of vision the aids for the totally blind can improve their achievement standards quite appreciably so that greater productivity in any work is then possible. It can only be emphasised that once there is an adequate appreciation of the difficulties a solution is much more likely to be achieved.

The Teaching of Chemistry in a School for the Blind

by

Dorothy A. McHugh

When one speaks of teaching Chemistry to the Blind, the first reaction of chemists used to dealing with sighted students is always to question its possibility - their minds jump first to "How can they tell when a colour changes?".

As all teachers of the Blind know - one never starts with what is difficult or impossible, but with what can be done and builds on that. My own recollection of my first science lesson was the excitement of seeing water boil in a beaker and then evaporating some seawater to dryness, and both things would be quite perceptible to a blind student. My recollection of the Professor of Organic Chemistry, E.A. Werner, under whom I worked as a research student, was of his coming into the laboratory, sniffing like a terrier to find out what his students were up to, and of his insistence that every chemist should have an "educated nose".

As a matter of fact, it is not beyond the art of modern man to devise a means by which the blind can detect colour changes audibly - such an instrument is now commercially available, and with the increased use of digital meters for all sorts of chemical tests, there is fundamentally no reason why a blind, or nearly blind, person should not be able to work in a chemical laboratory, as efficiently as a blind physiotherapist works in a hospital.

But I am concerned with laying the basis of scientific understanding and method, and for this one needs a minimum of special equipment, but good laboratory space, plenty of time, patience, and a cool head.

The special equipment I see as most necessary is (a) an audible balance - preferably several different kinds, for use with larger or smaller quantities and to various degrees of accuracy; (b) probes for determining the level of liquids and an easy means of attaching brailled scales. For the rest, room to work without crowding and to move apparatus without risk of moving it off the surface, access to supplies of apparatus without too much moving around the laboratory, though some is inevitable, and someone in charge who is prepared to take a few risks and give confidence to diffident students, for many come to school already imbued with a fear of handling liquids, lighting matches, and gas, which has been instilled into them at home for the best of reasons.

Generally speaking, the technique is not to think up how one would do an experiment if one were blind oneself, but by posing the problem to the class, starting with those well within the scope of all, to discover how the best of them deal with the situation and show the less able what these better ones have shown you.

The very simple process of learning to separate sand from salt can lead to practice in measuring small quantities of water, pouring, filtering, and evaporation. Once a pupil can pour water with some certainty, weak acids can be used and the separation of iron from sulphur gives experience of this and of recognizing the evolution of a gas, and a good example of crystallization is separation of rhombic sulphur from carbon disulphide solution. The smells are all rather pungent here and provide good material for nose education. Ferrous sulphide can be quite safely made in small quantities, and all pupils are aware of the intense chemical activity involved - an asbestos mat should be at hand to put the tube down on and thereafter the compound can be compared with the iron and sulphur mixture.

By the time these experiments have been performed by each pupil for himself, he/she will be ready to start the examination of diluted acids. Many who are technically blind can see the colour changes of the indicators - a probe will give some comprehension of them to those who see no colour. Very dilute hydrochloric acid can be safely tasted; and the action upon calcium carbonate is audible and that upon zinc, magnesium, aluminium reintroduces the gas hydrogen, always recognizable by the "pop" it gives with a glowing splint.

Thereafter, the course can lead on to the study of air, of water, of salts, in any order preferred by the teacher. I have found it perfectly possible to have classes prepare, collect, and test the following gases: oxygen, hydrogen, carbon-dioxide, carbon monoxide, methane, nitrogen, oxides of nitrogen, ammonia, hydrogen chloride, sulphur dioxide: to prepare specimens of MgSo4, CuSo4, PbI, Pb(NO3)2, NaCI, by neutralising an acid with an alkali, is not so easy and usually needs assistance. In this case, I get the pupil to do the experiment and if she cannot see the colour change, I tell her when it has occurred and also tell her when to stop adding the acid when enough has been run from the burette, when the experiment is repeated without an indicator.

In recognizing when to stop evaporation so as to get crystals, it is perfectly possible to test with a drop on a glass rod, held away from the experiment until cool enough to feel, when formation of any crystals will be gritty under the fingers, but in actual fact, since time is usually limited, evaporation has usually to be abandoned before very much water has been driven off - if left until the next lesson, the crystals will have formed. Enough space for the safe keeping of a number of dishes from one lesson to the next is essential.

Any pupil can determine when a gas jar has filled with gas by listening carefully to the sound of the bubbles: here is another reason for generous spacing, as a pupil dependent on sound must have his experiment reasonably distant from others. If he fails to realise that the jar is full, gas escaping round the sides will soon be evident to him.

While the titration of acid and alkali can be difficult, the titration of hard water with soap solution is more reliable on the audible than the visual basis, as the sound of a soap solution about to lather is quite different from its sound when not ready to do so.

In setting up apparatus, there should be a good supply of bent glass tubing and rubber connections and rubber stoppers that fit. Pupils can learn to assemble simple apparatus, provided the parts do fit and the normal techniques are observed. When moving apparatus during an experiment, a hand should be kept on the bench; in testing, vapours should be wafted to the nose, not the nose put into the vessel, and, similarly, those who want to peer must lift the tube to the face, not put their faces and heads down into the apparatus. It would be possible to enlarge indefinitely on experiments to be done and the means of doing them, but any competent chemist who puts his mind to it could work out a suitable set of experiments at any elementary level - sufficient certainly to give a basis of reality to theoretical work. I have not myself tried to carry the work beyond a fairly elementary level, but I believe someone with time and interest could well do so.

The underlying theory is no more difficult to blind than to sighted students. This must be based upon the electronic structure of matter, and an atom represented tangibly with spheres, or verbally described, is no further removed from reality than a diagrammatic representation in a good book. Admittedly, a chemical equation in braille is not quite the convenient shorthand that it is in letterpress, but it can be as intelligible.

I think the actual difficulties one meets in science teaching are more often due to the lack of the right educational opportunities in early life - the lack of experience of handling a variety of materials, and of training in symbolic representation which comes with early drawing and scribbling, rather than any innate incapacity in the blind for scientific study.

Biology for the Blind Student

by

G. W. Brooks

For several years Biology has been an integral part of the Junior science programme. As yet, for a number of internal reasons, it has not been followed through to “O” level, but I feel that this would present no significant problems, should it be attempted.

The aim of the course is simple, - to fulfil a natural demand for knowledge about the organic environment and our interrelationship with it. We have power over Nature, we have limitations within Nature and each individual, blind or sighted, ought to be aware of the fundamental facts of such a situation. The two-year span of the present course, in which Biology is taught alongside Chemistry and Physics, is insufficient for fulfilling this important need. Environmental knowledge is absorbed almost unconsciously by the sighted pupil, yet awareness is only fully stimulated by personal contact in the case of our boys. Obviously when one has to draw specific attention to each factor in the landscape, more time is required than if the landscape is scanned visually. The study of Biology is a basic educational necessity, but in a school for the blind it takes much longer than in a normal school. In any grammar school it is difficult to give to all children wide enough acquaintance with this subject.

The basic theme of the course has been one of human anatomy, physiology and hygiene. This seems to be the right approach in view of limited time. The obvious “visual aid” has been the student himself, - cheap and functional. Study of the “inner man” has been strengthened by the use of animal specimens, again cheap, obtained from local butchers, plus some models. Since real specimens are so easily obtainable it seems logical to continue, say, the study of respiration through to examining lungs and trachea; the study of food and its digestion through to examination of an alimentary canal, and so on. Little difficulty in terms of handling has arisen in this respect. Occasionally boys are rather “squeamish” but I have yet to find one who has failed, and in only a short time, to overcome this understandable hesitation to touch. In fact I would go further and add that far more could be understood by the sighted pupil if he handled material more thoroughly, instead of “just looking” and making “superficial examination”. Sheep and pigs offer organs of similar size and shape to that of man and so are most commonly used. As the life characteristics such as respiration, reproduction, movement, and so on, are studied, so cross comparison is made with other animals (at varying evolutionary levels) and with plants too.

Whilst models are used, their use is only occasional, since it is usually easy to find the real flora or fauna specimen. However, since the use of the microscope is impossible (though with the partially-sighted a micro-projector would be of great assistance) some compensation and detail is offered by examining models which represent material normally observed under a microscope, for example the alveolar structures so important in respiration, or the skin structure. Some parts of the body are too small or inaccessible for factual appraisal, so we use models for eye and ear structure. Models then are useful, but not essential and, if introduced, they must be closely related to the real thing in the student's mind. They may be expensive, especially if coloured, but with some ingenuity - and some glue - adequate specimens are easily prepared. Alternatively uncoloured specimens should be bought and then coloured to one's own requirement. Colour, it should be borne in mind, is of immense importance to the partially-sighted pupil.

We attempt to find a balance between laboratory and outside presentation of material, whilst at the same time endeavouring to link the two closely. In this respect it would be useful to set up vivaria, though the problem of looking after the creatures during school holidays is a significant disadvantage. A valuable activity is to grow plants under controlled conditions in the laboratory and compare them with similar plants grown outside. Such practical projects add interest and enjoyment for blind pupils as they do for sighted.

Our external programme is centred mainly on the College grounds. Size, shape and smell are an adequate basis for a system of plant identification; birds may be identified by their song and other features such as the finding of broken snail shell around a stone. Again factors affecting growth, soil condition, shade or exposure, cultivation, etc. are worth expanding.

Gardening would appear to be a worthwhile and rewarding venture, though in many ways difficult for blind students, but it really falls outside pure Biology and certainly cannot be fitted into our curriculum. However it could form an important extra curricular activity. Add to the above visits to museums of natural history, zoos and farms and I believe a widely interesting and educationally sound subject is produced. The cross links with Chemistry and Physics are numerous. For example, a study of muscles and muscle behaviour incorporates the physics of levers and the study of digestion incorporates the chemistry of enzymes.

The subject is basic and therefore important; it can be pursued without capital expenditure and run on a very low budget; it is wide open to the teacher's personal imagination and ingenuity and, what is most important, can provide much pleasure and excitement for the class.

The Science Laboratory in a School for the Blind

It is important not to design an unusual building or expect to use apparatus which is too special. Blind pupils must learn to work in the same kind of environment as sighted students, and sighted teachers and students should be able to feel at home at once in a Blind School Laboratory and with the apparatus used by blind students.

Yet certain modifications are desirable. Blind pupils need plenty of room to move and work. There must be adequate space for clear movement between the benches. These should be wider than usual to accommodate a Perkins brailler and braille book. Underneath there should be cupboards in which basic apparatus can be kept, systematically, in individual kits. The services on the benches should be normal, - i.e. gas with bunsen burners, electricity, water taps and sinks. The designer must expect that blind pupils will use these services for themselves. It would be silly to underplay the danger element and it could be wise to have a simple wire guard round bunsen burners and electric ignition, though blind pupils are quite capable of lighting a normal bunsen burner with matches and tapers. Asbestos mats or pads might be advisable. For a physics laboratory (or general purpose laboratory used for physics) it is useful to have low voltage AC/DC electric terminals on the pupils' benches, the terminals to be as simple as possible and with handy, but out of the way, fusing.

We have decided, with the approval of the Educational Inspector for Science, that there is no point in having a demonstration platform and bench for the teacher. He has to move about and work with the pupils on their benches. But he does need a special desk, perhaps in the middle of the Laboratory with the pupils' desks in an arc around him. This desk should have full services, including mains electricity (AD/DC) and probably a deep sink.

Bench space for twelve blind pupils is the maximum that is desirable for a single teacher. If all pupils are totally blind, ten pupils is probably the greatest number he can manage. We often split our forms into smaller groups of five or six for practical work.

Fire exits must be easy. There should be an asbestos blanket and proper fire extinguishers.

In our view it is better to have two laboratories, - one for Physics, one for Chemistry and Biology. We ourselves have a single, all-purpose laboratory, together with a small laboratory where advanced students can work on their own and leave apparatus out on the bench. We are a small school and, with larger numbers, there might be justification in having two main laboratories. It is difficult in a single laboratory to incorporate all that is required. I will explain why:

In a physics laboratory, as already said, there should be low voltage terminals on the pupils' benches: it is useful to have a galvanometer on a shelf with light beam and scale, to demonstrate small electrical effects: it is useful to have certain mechanics apparatus, including pulleys, permanently on the walls. There is need for accommodation to keep radioactive material in accordance with ministry rules. Distilled water apparatus is wanted. Blackout blinds should be fitted to enable light experiments, quite feasible for blind pupils using light probes, to be attempted.

In the chemistry/biology laboratory there should be a fume cupboard, a special store cupboard for chemicals (fire-proofed), and storage space for biological materials. The whole of one wall might be composed of a conservatory-type window, so that plant material is always ready to hand. In front of the window, at waist height, there could be a continuous sink for easy watering, with one or two narrow shelves above to carry smaller plants. We have found that blind pupils can obtain understanding and satisfaction from sowing seeds and growing plants under controlled conditions. There should be access to the outside, where there can be provision for gardening and keeping pets.

Both laboratories should have plenty of space for apparatus, braille books, material for making braille diagrams (very important) and a thermoform braille duplicating machine. It is essential that all such apparatus, books and material can be kept out of the way. It may be possible to dispense with the need to have two laboratories if there is a large adjoining store where braille books, notes, braille paper, material for making braille scales and braillon can be kept. But there should in the laboratory be sufficient storage space for apparatus to be kept really systematically and fully accessible to the teachers and, where desirable, to the pupils, sometimes in individual kits in addition to those under the laboratory benches.

If there is more than one teacher, it is useful to have two laboratories so that both can be time-tabled to teach at the same time. If there is only one laboratory, there must be at least one small room with services where a teacher can do his private work or take a small group.

It is difficult to give blind children experience of living creatures, physical features, machines, materials, which a normal child can see and more easily understand by seeing. There is a case for having a museum in a school, with models, sections of machines, stuffed animals and other specimens, - anything which the children can valuably handle. This can probably best be done in conjunction with the science laboratory, possibly by keeping one wall available for a display, which can be changed at certain intervals.

Manpower for preparing and clearing away apparatus, for making and fitting braille scales, for duplicating diagrams, for preparing notes and textbooks, for changing batteries, for clearing rooms is always a problem in a school for the blind. It may be wise to employ a laboratory assistant or at least somebody, other than a teacher, who can give a hand. If so he may need a room where he can work.

The laboratory or laboratories should have normal modern lighting, heating and ventilation, including extractor fans. The needs of sighted teachers should be considered: since they are likely to teach more happily and therefore better in an environment which is cheerful and smart, there should be plenty of light and the rooms should be full of bright colours and contain coloured diagrams and pictures. White coats should be available for teachers and all pupils using the laboratory or laboratories. There should be paper towel machine or roll of tissue for drying hands and mopping up; there may be more mess with younger blind children than there would be with their sighted contemporaries. It might help if the sinks were made of plastic, to check breakage of glass dishes. Alternatively plastic could be used for apparatus wherever possible instead of glass. It is certainly a good idea to have the floor and walls of a material which can easily be cleaned.

General Science - A Suggested Two Year Syllabus

The chief aims of this proposed course should be:-

a. to provide a "background" knowledge of basic science of general educational value.

b. to show some of the many applications and uses of science in everyday life.

c. Since Science is essentially a practical subject a main objective should be to make the work as practical, (i.e. in the experimental sense), as possible and to arrange this so as to enable pupils to discover for themselves, with guidance and, additionally, to improve their manual dexterity.

Some grounding should be given in concise methodical recording of experimental work and classes should be stimulated to make deductions from facts ascertained. It is also advisable to introduce classes into the interpretation of simple braille diagrams.

Presentation should be such as to stimulate pupils' natural curiosity into "how things work", "how animal bodies function" etc., using this instinct to enable pupils to learn useful and helpful facts of value to them in later life.

The content of this scheme of work, is here subdivided into "Biology", "Chemistry" and "Physics" for convenience in recording, but the subject matter should be taught as an integrated General Science course by moving freely from one section to another as the flow of the course dictates. It is not intended that the subject matter herein listed should be regarded as a rigid limit but rather that it should be used as a general guide.

Scheme of Work

Biology/Hygiene

As a foundation to a basic General Science course and also as a basis for further extension to other forms. A main emphasis should be placed on this section of work. The focal point is Human Anatomy/Physiology.

Varieties of living organisms including simple classification of the flora/fauna. Characteristics of all living creatures and organisms, (e.g. feeding, respiration, excretion, growth, movement, reproduction, irritability). How these differ in animals and plants generally.

Feeding in Man: Ingestion, digestion, absorption, defaecation. Function of the alimentary canal, lymphatic system, liver and blood stream. Types of teeth and dentition. Diet, including vitamins and trace elements. Production of food in plants. Osmosis and transport.

Respiration in mammals: Structure of respiratory system, gaseous exchange, inspiration and expiration - contrasted with respiration in insects and fish. Plant respiration. Excretion in man, plants. Lungs, skin structure and kidney structure. Water loss in plants and leaf fall.

Growth: cell structures and division. Abnormalities. Areas of growth/limitations.

Movement: Skeleton, nomenclature, relaxation and contraction. Movement on land, air and water. Limited. movement in flora.

Reproduction: in man, female and male genital systems. Development of the embryo and early development of the child after birth. Simple heredity/genetics. Pollination mechanisms and flower structure. Spore producing plants and asexual reproduction.

Irritability: Structure/function of nose, eye, ear, skin and co-ordination with the nervous system - brain.

Response - tactile and non-tactile stimulation. Tropisms in plants.

Chemistry

Mainly of water, air, soil, etc. - to tie in with Biology scheme of work but at the same time providing a good basic "'grounding" in this subject. Chemical laboratory apparatus should be introduced, explained and used in simple experiments.

Simple ideas of atoms, molecules, elements and compounds. Some of the more important symbols should be taught and their use in simple formulae indicated e.g. H2O, NaCI, etc. Main physical properties of some of the common elements and compounds. Basic differences between compounds and mixtures and simple methods of separation of mixtures, e.g. filtration, (mixtures such as salt and sand, iron filings and sulphur, suspensions like chalk in water etc.) Iron filings and sulphur to show compound formation. Basic ideas of solubility of gases and liquids, uses of evaporation to show, say, salt in salt solution.

Crystallisation and crystals: e.g. alum, copper sulphate, nitre etc. An indication of other solvents such as alcohol, CS2,(wax in benzene),etc.

Oxygen in air: approx. 1/5 (by expmt.) other gases in air.

Oxygen: simple properties, given off by plants, supports life, combustion supported, burning substances in air (e.g. carbon, iron, magnesium, sulphur). Oxides and oxygen. Nitre mercuric oxide (Lavoisier), and other sources of oxygen in lab. (Preparation of O2 in lab.),

Nitrogen: basic properties, nitrates and ammonia (latter as substances occurring in nature). Nitrogen cycle.

Carbon: carbon, carbonates and carbon dioxide in nature. Preparation and properties of CO2. Carbon cycle.

Water contains O2 and H2- electrolysis (no complex detail of process). Hydrogen - lab. preparation (acid on Zn etc.).

Fuels:- formation, occurrence, industrial preparation - e.g. coal, coal gas, oil, petrol, alcohols. Porosity of soil - types of soils, etc.

Basic ideas of atomic structure and different elements.

Heat

Sources:- gas flames (Bunsen), sun, coal, electricity.

Simple ideas of energy and energy transformation. Expansion of solids (e.g. ball and ring, bar and gauge). Everyday life effects of expansion: disadvantages, uses (e.g. railway lines, expansion joints, bimetallic strip as thermostat). Breaking of iron rod to show force exerted. (Rivets, etc.) Expansion of gases and liquids - simply shown. Molecular explanation of expansion. Construction and use of mercury thermometer. Scales of temperature - thermometric liquids. Clinical and max. and min. thermometers. Outline of other methods of measuring temperature (e.g. mercury in steel, bimetallic strip, thermocouple). Anomalous expansion of water.

Conduction of heat:- (molecules do not move etc.), comparison of different conductors. Good and bad conductors and insulation. Everyday life applications of good and bad conductors (e.g. soldering iron bit, metal saucepans, insulated handle, table mats, etc.).

Convection in fluids:- (molecules move), uses in hot water systems and central heating, winds, fire draughts, ventilation etc. Warming air by convection - convector fires (relate convection to expansion).

Radiation of heat:- in very simple terms, explain this noting strong temperature dependence - sources such as hot metals or fire elements, sun, etc. Term infra red mentioned. Reflection of radiated heat - electrical fires, etc.

Light

Very simple idea of light emission from luminous bodies - sun, flames, white hot metal, etc. Light travels in straight lines in effect (pinhole camera) - shadows and eclipses. Simple ideas of reflection of light and difference in intensity. Light in nature - photosynthesis, growth.

Sound

Vibratiqns and how sounds are caused. Simple sources of sound. Basic ideas of air being necessary to carry sounds to ear and very simple conception of waves.

Magnetism

Magnetic materials, attraction through materials, poles, law of attraction and repulsion. Compass (magnetic) property - N. and S. poles. Testing for magnetism. Basic idea of magnetic fields of regions of "influence". Outline of earth's magnetism. Very simple molecular magnet - explanation of magnetism.

Electricity

Simple ideas of batteries and simple circuits (bulb, switch, battery). Current flow and electrons. The electric torch-conductors and insulators and uses in everyday life, + - convention. House plugs, sockets, connectors, etc. - construction and way they function. Bulbs in series and in parallel - basic house wiring. Function of a fuse. Simple car electrics (no detail of a coil). Elementary ideas of A.C. and D.C. The simple electromagnet - (without detailed explanation).

Volumes and methods of measuring them for solids and liquids and gases. (Use of terms c.c., litre, ml.) Weighing and the simple balance, (gm. kgm.)

Idea of density - different elements and compounds combined.

Alloys.

Measurement and definition of density - solids and liquids.

Density of gas (air). Relationship (simple) between expansion and density.

Extension of springs and wires - Basic idea of Hooke's Law.

The spring balance (both types) and use to measure force. Stretching of wires - simple molecular explanation.

Elementary ideas about air pressure and barometers (mercury and aneroid).

Cause of winds.

Apparatus

It is considered advisable that the blind student should make use of standard apparatus wherever possible. Practical Science for the blind is limited, both by reason of safety and by the fact that apparatus is designed for handling and observation by sighted people. However, it is a vital part of the learning process and it is therefore desirable that the blind student should be able to undertake as much of it as possible.

The Nuffield aided study tackled the problem in two ways:-

a. Methods of adaptation of standard apparatus for use by the blind were developed, mainly by attaching tactual scales.

b. The design of special apparatus was encouraged where the use of standard proved impractical.

1. Standard Apparatus

Affixing tactual scales. This was achieved by the use of transparent Vito Embossing Foil, .014" total thickness (see Appendix 1) A pair of embossing pliers was made by adapting Rolcut Shears, with which satisfactory marks can be made on embossing foil, to which braille can also be added.

With this scale in position on top of the normal one, the position of the indicating needle or the liquid level can be ascertained by using a light probe. By and large the accuracy obtainable is not the same as if done by a sighted person, but at least an experiment can thus be carried out by a blind student, which might not otherwise be possible.

Embossing a scale. The required scale is traced on to the upper surface of the Vito foil by use of a fine black felt pen. The foil is then turned over (the marks can just be seen through it) and embossing marks made with the blade of the embossing tool. Braille can be added, where desired, by a writing machine or dotter, well rounded so that the foil is not punctured. After cutting the scale to size, nip through one corner of the upper surface with the inner edge of the embossing pliers, which are designed to cut through the upper surface only, then fold the corner back and peel off the removable back. The self adhesive underside is then ready for sticking down where desired.

Some apparatus (e.g. plastic measuring cylinders) is now made with embossed scales, which in many cases, with the addition of a few braille numerical characteristics, can be read directly by the blind student using the light probe.

2. Special Apparatus

Audible photoconductive light probe

This versatile instrument developed by the R.N.I.B. can be used in many situations in the school laboratory. It is a general purpose pocket size instrument designed to detect and convert light directly into sound, the frequency of which rises proportionately with intensity of light, i.e. no sound in total darkness, shrill whistle maximum illumination. The device uses an Ever Ready battery type D.23 available in Great Britain and Overseas. (see Appendix 1).

To use the instrument switch on and, holding the probe body in the hand, point the nosepiece towards the object or area you wish to examine, taking care not to cover the sound outlet holes. In this way the probe can be used simply to determine daylight from darkness, to spot a source of illumination such as a window or electric light bulb, to pin point signal lamps like those found on cookers and electric blanket controls and to identify dark and light clothing. More accurate discrimination such as establishing red and black on a typewriter ribbon, locating letter headings and following instrument pointers is considered possible, but when using it in this respect one must hold the probe vertical or at a set angle with the perspex lens in actual contact with the object being examined.

The user's own shadow can greatly influence the sound output and when the probe is used for accurate discrimination it is advisable for a blind person to locate first the source of other lighting, using the probe, (natural light is preferable), then sit down facing the light so that the shadows fall away from the source.

Light normally enters the lens through the sides and the tip, but for certain experiments it is advantageous to exclude side lighting and for this purpose a plastic clip-on lens hood is provided. A typical application with the hood in position is the determination of level of a liquid by pointing the probe downwards and listening for the change in note occasioned by the liquid covering the tip of the lens hood, which of course reduces the input of light.

Another method is to hold the Probe horizontal and in contact with a transparent glass or bottle containing liquid, the level of which can be located simply by moving the probe up and down the outside of the container. Use of the lens hood is also recommended where a blind user is trying to "watch" the magic eye recording level indicator on tape recorders.

Other uses, both in the house and in education, are expected to materialise in the course of practical use. (Figures 6, 7 and 8).

Prospective users should note that this aid had been designed as a short range instrument and as such is not suitable as a mobility aid; any attempt to use it for this purpose is strongly discouraged by the Institute.

Audible Thermometer

Mercury thermometers proved impossible for the blind student to use, so the R.N.I.B. were asked to develop a prototype dial thermometer which proved successful in use.

Electronic Thermometer (Prototypes)

The R.N.I.B. Technical Department has developed an accurate and easy to read electronic thermometer covering the range -6°C to +110°C, calibrated to within ±1% of full scale, for general school use by the blind.

The instrument is housed in a metal case size 4 ins. by 4 ins. by 1½ ins. and has a twin flex screened cable leading to a precision thermistor encapsulated in the tip of a thin metal probe. The on/off switch and battery compartment containing a Mallory Battery TR 126 or TR 126X, 8.4 volt, are situated on the side of the instrument case.

A 3 in. diameter braille scale is provided with single dot identification at every 2° and raised line divisions at every 10°. Braille characters have also been added at 0, 30, 70, and 110°C to assist identification. A central control knob having a well defined pointer rotates within the scale.

Temperature readings are taken by switching on, then inserting in or touching the probe against the medium being examined and adjusting the control knob until the out-of-balance sound completely disappears to a definite null point. The inclusion of a Schmitt Trigger in the circuit ensures a very sharp null and thus the usual gradual decrease in volume associated with null reading instruments is avoided.

No warm up period for the circuit is required but as a general rule 1 minute should be allowed for thermal response of the thermistor.

An indication of low battery state is a widening of the null.

    Note. The circuit used in the thermometer can be easily modified to suit various temperature ranges and furthermore can be used in conjunction with other transducers exhibiting a change in resistance, i.e. Photoconductive Cells and certain Pressure Transducers.

This instrument is made only to special order.

Chain Balance

Rough weighing proved practicable with embossing added to sighted scales. Accurate weighing did not, and an Oertling J 10 was modified by the R.N.I.B. Technical Department to give an audible balance point.

This makes it capable of being used by the blind student, but some practice and delicacy of touch is also required. The weights can have their values embossed on the bottom of the hole in the box in which they fit.

Chain Dial Chemical Balance

A few of these instruments, such as the Oertling Model J 10, have been adapted for use by the blind in Science at Schools by modifying them in the following manner.

Two hairspring switch contacts have been added either side of the mechanical pointer and, when the Scales are out of balance, contact is made between pointer and spring to operate a high or low tone depending on which pan is the heavier. When in balance the pointer hangs freely between the two contacts and there is no sound output, thus the silent null indicates the point of balance to the user. The audible information given in this manner enables the blind operator to select appropriate weights and manipulate the scales until the point of balance is approached, at which time final adjustments are made using the brailled Chain Dial control. This method allows readings to be taken by the blind to within .05 gram.

The transistorised tone generators and associated battery are housed within the base of the Balance and the on/off switch is situated on the side. The electrical path to operate the tone generators is made when the pointer, which is "live" with respect to earth, makes contact with one or other of the hairsprings and completes the circuit through a high Impedance gate to overcome contact resistance. This latter requirement is important as the pressure of contact between pointer and hairspring has been kept to an absolute minimum in order not to affect adversely the normal operation of the Balance.

Instruments of this type are modified only to special order.

Digital Clock

For small time-measurements, a standard Trumeter 1/10th sec. counter fitted with a stepping motor was modified by the addition of braille dots to the digit wheels. This can be either switched on or off by hand, or provision made for switching it electrically.

Speeded Cassette Recorder

Following the work of Dr. Emerson Foulke (Ref. "A Survey of the Acceptability of Rapid Speech, New Outlook for the Blind Nov. 1966") we attempted to make some of these facilities available to senior blind students of Worcester College, who were, at the time, integrated in a sighted class at Worcester Technical College.

They found it convenient to record notes of the lecturer in the class and edit and record in their studies at night.

A Philips EL 3302 was modified by fitting a variable resistance to the stabilising circuit originally designed to compensate for the battery fall-off in voltage during use. This speeded up the playback some 90% and allowed the student to re-read the material at an increased rate, while seeking the part he wished to re-record. It was felt that still further speeding would prove advantageous, but this proved not to be practicable without fundamental re-design of the circuit. Also, the modification was only capable of being used with the battery circuit and not when the mains converter was in use.

The accompanying rise in pitch, whilst not pleasant, proved acceptable with practice. (The Tempe Regulator, described by Dr. Foulke as increasing speed of playback without pitch distortion, costs some £1,400, and was, we felt, too expensive for the scope of our enquiry).

Messrs. Philips gave permission for the publication of the circuit of the EL 3302 Cassette Recorder and the modification, whilst not accepting any responsibility for any such alterations.

Avometer

This general purpose electrical measuring instrument has been available for some years with special embossed markings for the blind user. The position of the needle is found by locking it and then hunting delicately with an outside marked pointer.

The R.N.I.B. is currently producing a model with infra-red needled detection and consequently less liability to damage.

It has three raised line scales covering various AC and DC volts/amps and resistance ranges A metal pointer, until the sound emitted from the circuit (fitted in a tube on the front of the instrument) reduces to a null point The Avo 9 offers more ranges than the earlier Avo 7 and the modifications incorporated in this model allow for more accurate readings to be taken by the blind

Radionic Constructional and Experimental System

by

A. O. Pickles

The system is already in use in many Universities, Colleges, Schools and Service training establishments, both in this country and abroad, as part of the normal practical instruction in Electronics. It has received an enthusiastic review from "The Times Educational Supplement":-

"The ‘piece de résistance' which intrigued and astounded both experts and laymen alike was the six transistor superhet receiver, working effectively with all components positioned as in a typical theoretical circuit diagram."
"Its use is in complete harmony with the modern Physics syllabus in England."
"The progressive series of experiments is sound educationally and complies with the dictum 'progress from the familiar to the unfamiliar, from the known to the unknown', but also from the simple to the complex."

The system is a method of constructing radio and electronic circuits without the need for soldering, and circuits can be easily assembled, adapted, or dismantled without damage to delicate components.

Availability

The system can be obtained in the form of Sets One to Four. With Set Four, twenty-six radio circuits can be constructed. These progress from a crystal set to a six transistor superhet, in logical steps by enlargement and adaptation, and there is seldom need to dismantle before proceeding to the next. In addition, there are some thirty Electronic circuits dealing with devices ranging from light-sensitive controls to computers.

Electronic components can be bought separately, fitted with the Radionic Mountings. This means that any electronic circuit, simple or complex, can be quickly assembled, components rearranged as necessary, and dismantled when the construction has proved its purpose. All circuits are based on transistors, and can be handled with safety, since they operate on 3 or 9 volt batteries.

The firm has been most co-operative in adapting the system to enable the blind person to use the system unaided.

The system as adapted consists of:

a. A perspex sheet drilled over its whole surface with equally spaced holes;

b. Electronic components mounted on plastic bases. Their wires are soldered to screwed brass studs, which pass through the bases and fit into the holes in the plastic sheet;

c. A holed brass strip is used to connect the components. This is secured by nuts to the requisite brass studs. The nuts are tightened using a Radionic box-spanner, which prevents over-tightening, and makes for ease of assembly.

d. Braille notes giving identification of the components, the constructional details and theory of each circuit;

e. Braille blueprints and lists of components for each circuit.

Recognition of Components

Full details are given in the Braille notes ,but here is a brief resume:

Resistors and Capacitors

The components on their two-pin bases are covered with moulded plastic caps. On this three Braille numbers are formed. The dots are nearer to one edge to identify this edge as the top for reading purposes.

The coding for resistors uses the Braille numbers to denote the normal colour code, that is, the first two figures represent the digits of resistor value and the third the number of noughts.

The coding of capacitors uses the Braille figures to denote the colour code in pica-farads. A small notch cut in the end of the cap distinguishes them from resistors.

Some capacitors are too large physically to be encapsulated. These are recognised by their size and shape.

Transistors

These are mounted on triangular bases and are thus readily identified. Notches are cut in the base to differentiate the various types.

Diodes

On two-pin mounts the moulded cap has only a single Braille dot and a figure 4 (letter “d” for diode). The single dot identifies the positive end of the diode.

Coils

Are mounted on two-pin bases. Each lead has a colour and a number of loose sleeves. To differentiate between coils of similar appearance the number of sleeves is altered.

Other Components

These are identified by their shape, the base upon which they are mounted, and by cuts made in the base.

Construction

The Braille instructions assume that the user will wish to progress from circuit to circuit. Therefore, the notes for each new construction list the alteration that may be necessary to the previous circuit, and then the additional components which will be required.

Instructions are given by defining the column (1 to 16 from left to right), and the row (1 to 12 from top to bottom) in which a given hole is to be found on the board. The components are then inserted in the defined holes. For example:

"Insert 3.9.K resistor in 13-4 and 13-5".

The brass strip is packed in 15-hole lengths which are cut to the required size and fastened under the board.

Constructional details are given in numbered stages, for easy reference. For example, those to Circuit Number 18 commence as follows:

"(1) Run a 6-strip from 2-10 (nut down as earth connector) to 2-5.
(2) Nut down the block lead (1-sleeve) at 2-5 ......"

and end with the completed circuit ready to be used.

Blueprints

These are based on Lt. Day's four-unit code, details of which are given in the Introduction to the Braille Notes. The layout is identical in form to the completed circuit on the board, and therefore aids understanding of the blueprint.

The Braille blueprints are not an essential part of the Braille system and sets can be constructed without their use, but they do provide new opportunities to the interested person. With experience it becomes possible to "draw" blueprints on the Perkins, and hence to communicate and to discuss circuits with others, blind and sighted. Once the four-unit code has been understood, it is a simple matter for a sighted person to read, since it is purely a Braille transcript.

Conclusion

The Radionic System has been used with pupils of varying ability, with considerable success, for many years. Past and present pupils have obtained sets of their own and, using the Braille instructions, have assembled the circuits unaided. One pupil was further handicapped by having only one arm, yet he found sufficient pleasure from the system to purchase his own. It provides a leisure-time activity which can be pursued without calling upon sighted assistance, and therefore supplies the profound satisfaction that only independent achievement can give.

Much of the modern electronic equipment is based upon printed circuits which are plugged into place, and removed and replaced when a fault is found. There may be opportunities here for those able to understand blueprints.

Our pupils have the same interests in radio and electronics as the sighted. The Radionic System fulfils a need that is not provided by any other system. It gives a clear, basic understanding of electronics. With the aid of photo-electronic and thermistor devices used as an integral part of the system, accurate electrical and electronic measuring devices can be devised. The student can progress in practice and theory as far as his interests and capabilities will lead him. The system opens a new field of possibility, and the scope is unlimited.

Notes

(1) The price lists and sets are available from:

    The Sales Manager,
    Radionic Products Ltd.,
    Member of the E.S.L. Group of Companies,
    St. Lawrence House,
    29-31 Broad Street,
    Bristol, BS1 2HF.

(2) The sets are available as follows:

    No. 1: Circuits 1-16
    No. 2: Circuits 1-20
    No. 3: Circuits 1-21
    No. 4: Circuits 1-26

(3) When ordering, state that the set is to be adapted for use by the blind.

(4) If a set 4 is ordered, it is important that the firm be requested to include a Medium Wave Coil for use with the 298 pica-farads tuning capacitor, as this is not normally included in the set.

(5) The Braille instructions and blueprints for the 26 circuits are available in four volumes in thermoform from:

    The Students' Library,
    The Royal National Institute for the Blind,
    224, Great Portland Street,
    London, W1N 6AA.

    Volume 1: Introduction and Circuits 1-12
    Volume 2: Circuits 13-26
    Volume 3: Lists of Components for Blueprints
    Volume 4: Blueprints for Circuits 1-26

(6) Blueprints and Braille instructions for some of the electronic circuits are available from Dorton House School.

    The Royal London Society for the Blind,
    Dorton House School,
    Seal, Sevenoaks, Kent.

Mathematics at a Grammar School for the Blind

by

G. Jackson

In times past, it has often been thought that Mathematics was too difficult a subject for the blind. Certainly, the concepts of geometry do not come readily to a blind person, nor does the neat layout of mathematical textbooks have quite the same appeal to the blind as to the sighted, yet there is no overwhelming reason why a person of sufficient ability should fail to become a successful mathematician simply because he is blind. It is the object of this report to explain how this may be achieved.

A major report on the teaching of mathematics in these days cannot omit a discussion of the syllabus, especially with the question of "traditional" or "modern" mathematics. At Worcester College, if it is necessary to place the syllabus into one or other of these categories, it would have to be in the former. Modern mathematics in a secondary school is discussed elsewhere. Ideally, a combination of the better parts of both disciplines is likely to produce the more effective course; nobody wishes to spend a great deal of time on the arithmetic method of finding square roots in these days of calculating machines; on the other hand, to abandon the traditional skills entirely in favour of new topics is comparable to throwing out the baby with the bath-water. Most textbooks nowadays combine parts of both syllabuses.

Though the blind have been taught mathematics for over half a century, it was not until the advent of an upward writer that useful progress was made. Before this time, the only machine for writing braille produced dots on the reverse side of the paper; consequently, the Taylor frame was in much use. This apparatus, useful though it has proved to be, has definite limitations for higher work. The cubarithm is now generally recognised as superior to the Taylor frame, mainly because its cubes are in braille notation, so that a new code is not necessary.

Before discussing the various parts of the syllabus in detail, it is important to outline the equipment available. Most important of course is the upward writer. The machine now almost universally used in the schools of this country is the Perkins brailler. For elementary arithmetic, the cubarithm and the abacus are extremely useful tools, though the cubarithm is perhaps more useful in primary schools and the abacus, being small enough for the pocket, can act as the blind person's equivalent of the rough working a sighted person is able to do. Of the more expensive items, there can be no doubt that the graph and mathematical demonstration board - the graph board - marketed by R.N.I.B., is one of the most useful. As will be seen, it can be used in almost every branch of mathematics. The R.N.I.B. geometry kit allows the blind person to draw with reasonable accuracy, and this in turn will improve his ability to understand diagrams drawn for him. Elementary geometry can be assisted by the provision of a number of simple shapes. If these are cut from magnetised rubber squares, marketed by James Neill & Co., Sheffield, and used with a metal board, the blind child can examine properties of simple shapes without the inconvenience of these slipping. For more advanced work, there is a braille version of the Odhner calculator, which is capable of handling many problems in Statistics and Applied Mathematics. And also, of course, there is a large number of books available.

Of the four branches into which traditional mathematics is grouped - Arithmetic, Geometry, Algebra, Trigonometry -- it is natural and convenient to begin the discussion with Arithmetic.

Of the five fundamental processes of Arithmetic - I make here a distinction between short and long division - addition, subtraction and multiplication, both short and long, can be set out successfully in exactly the same way as that used by the sighted. Moreover, for intelligent children, who are likely to achieve a reasonable standard in mathematics, I believe it is most important that they should learn calculation by these methods. No evidence is forthcoming that other methods produce better results with intelligent pupils, and there are clear advantages. A sighted teacher can more easily cope with a familiar layout; more complicated arithmetical problems, such as are encountered when solving trigonometric problems with logs, are much easier to handle in columns than in rows. Short division is likewise straightforward, a line being drawn underneath the original number to separate it from the answer as in the example given:

Sum: 23924 divided by 7 = 3417 remainder 5

It is with long division that the difficulties traditionally arise, and for some very good reasons. The sighted child also often experiences much difficulty in understanding the procedure. The problem is that it is impractical to keep moving the carriage up and down the paper; a possible layout is given, whereby the answer appears in a column on the right hand side of the problem.

Sum: 106572 divided by 43 = 2478 remainder 18

Directed numbers can easily be introduced in much the same fashion as that described in book 1 of the School Mathematics Project, the children walking forwards or backwards to represent the operations of addition and subtraction, and facing in one of two opposing directions to represent positive and negative. In this way, it is possible to remove most of the mysteries associated with directed numbers, which arise not from a lack of appreciation of the mathematics involved, but from the ambiguous use of the words "plus" and "minus" to mean both the operation of addition or subtraction and the quality of the directed number. This in itself can then be demonstrated on a number line with a graph board.

A topic such as binary numbers can easily be taught with the aid of a chess board, where a piece is either in a square - representing 1 - or not in a square - representing zero. In this way, a sounder appreciation of the denary number system can be obtained.

The graph board is a piece of apparatus to which the children should be introduced as soon as possible. To be able to describe accurately and efficiently the position of a point to another child who must place his own pins in that same position can lead to some very stimulating discussions, and it can easily be made into a game. The traditional game of "Battleships" provides an excellent introduction to coordinates.

Geometry is not a subject which should be started in the secondary school; some experience in the primary school is almost essential. The blind child will suffer greatly in this respect if geometry is merely ignored. His knowledge of the world, and practical objects in his own environment is too limited to give his ideas much opportunity. We have found at Worcester, however, that many of our boys know very little geometry, so that we have been compelled to start from the very beginning. Two things must be done as soon as possible; the child must be taught to draw, beginning with how to handle the equipment, and he must learn some basic geometrical properties.

Now that suitable equipment exists, the first problem is largely one of continual practice; even so, there will always be the blind child who finds it almost impossible to produce a satisfactory diagram. Mention has already been made of the magnetised rubber shapes. Many simple shapes can be made, and, if suitably done, these can be made to fit together in various ways to produce whatever properties it is desired to illustrate. Rapid progress can be made with these shapes. In addition, the relative ease with which rectilinear shapes can be made with a graph board shows how valuable this piece of equipment can be. With it, it is possible to demonstrate quite simply the formula for the area of a triangle, a rectangle or a parallelogram, the geometrical properties of various triangles, the properties of a parallelogram, etc.

At this point, a few comments on the value of formal proof are in order. The present tendency is rather away from formal geometry, though it is significant that many experienced teachers are by no means convinced that this is a good thing. For my part, I am in favour of formal geometry, though in a school for the blind, it must not be overdone, especially if a class shows itself rather poor at the skill. It is the only experience a future mathematician will receive of mathematical method, i.e, developing a subject from a few basic assumptions and the rules of logic. However, if introduced too early, formal proof is worse than valueless; it is essential that the child believes what he is trying to prove. Here at Worcester, we do not attempt any formal proofs until the third or fourth year, though we encourage drawing and measurement, so that the child may verify certain properties. I believe this is the only way.

Of the four main branches of mathematics under discussion, much the most straightforward to teach is algebra. Here there are usually only the same problems as those encountered by sighted children, i.e. the understanding of what algebra is all about and why it is so useful. Algebra can perhaps be most easily introduced by means of the graph board once again where, beginning with a study of coordinates, the letters x and y can be introduced naturally, and not as something artificial. Concrete meaning can be given to equations, and the study of simultaneous equations is not out of place.

Special emphasis must be made at the very start of algebra on layout. If a blind child is ever successfully to master the complicated algebraic manipulations required at a higher level, he must be able to organise his work so that he can find certain parts of it quickly. The labelling of equations must be done effectively, ideally with dots across the page from the end of the equation to the number which labels the equation. Individual equations should start on a new line. English and equations should not share the same line of braille. Though this does lead to a certain wastage of braille paper, we have found here that layout does not come naturally to the blind; they prefer to write algebra as if it were English prose. Such a method makes it extremely difficult to understand later.

Care must also be taken at the very start with the correct notation. Wrong notation ought to be pointed out to a child; it should not merely be tolerated by a teacher saying it is obvious what was meant. For example, the child that writes xy instead of x2y - i.e. the lower B is missing after the ING sign, - should have this error pointed out, together with an explanation of why it is incorrect. Only by being scrupulously accurate in the early stages can the necessary accuracy be later achieved.

The above three branches should not be considered as separate entities, though it is convenient to discuss them as such. They can be developed through the school in parallel; each has something to offer the others and, as has been shown, the graph board can act as a valuable unification. Trigonometry, on the other hand, cannot be developed until a child has become proficient in certain basic facts, in particular, ability to use tables, and knowledge of Pythagoras' Theorem. Tables are available, and the blind should experience no extra difficulties in using them. The theorem of Pythagoras is so essential to the development of higher mathematics that it becomes quite vital that a child learns the theorem, whether he can prove it or not. Nevertheless, a proof is desirable, but not the traditional "square on the hypotenuse" proof. This proof (though having the merit of perhaps being the original proof) has a diagram rather too complicated for a blind child. The neat similar triangles proof is acceptable, except that Pythagoras' Theorem is likely to be encountered before similar triangles. I would suggest that one of the simple dissection proofs be used. It is quite straightforward to make models which can be assembled in two different ways to demonstrate the theorem.

Diagrams for trigonometric problems are most efficiently produced by means of a graph board. This apparatus has the great advantage of having squared paper with right angles already made. The one disadvantage of using a graph board for diagrams is that such diagrams cannot easily be lettered. With simple diagrams, this will not matter; more complicated diagrams can perhaps be drawn with the geometry kit.

So much for a brief discussion of the topics to be found in a traditional mathematics syllabus suitable for a secondary school. It would be in place to discuss the few points for which less satisfactory solutions can be offered.

As an exercise for its own sake, accurate geometrical construction is impossible for the blind. Not only is the equipment itself less accurate, but the sense of touch is so inferior to that of sight in this respect, that any results obtained by the blind could not fairly be compared with those obtained by the sighted. The elementary constructions - bisecting an angle, constructing a right angle, etc. - are useful exercises, both to improve drawing ability and as theoretical exercises, but an involved construction, such as constructing the common tangents to two circles, is valueless.

Three dimensional diagrams cannot be supplied in the same convention as that adopted for the sighted. Perspective diagrams are entirely a visual concept, and the congenitally blind child has no effective means whereby he can acquire this concept. On the other hand, it is possible to teach three-dimensional work and the properties of solids by drawing plane sections of solids and constructing solids. For construction, I have found the simple device of straws, joined together by pipe cleaners, a very useful method. This allows the child to get inside the solid to examine it, and it does not matter if the solid becomes damaged. If the facilities of a workshop are available, properties of spheres, cylinders and cones can be examined by making these solids on a lathe.

No report on the teaching of mathematics at a grammar school would be complete without a discussion of work beyond O-level. The above should be enough to demonstrate that it is possible to teach mathematics to the blind child; success or otherwise will depend on whether the child has sufficient ability to understand the subject. We must also consider the relatively few children who possess particular aptitude.

At A-level, mathematics is one of the harder subjects for the blind. The main reason for this is simply that working in braille is far slower. Time and time again at Worcester, we have seen boys embark on the A-level course, only to find that there is insufficient time to get through an A-level syllabus in two years. Thus, it is only fair to say that a blind child ought to possess genuine ability before he embarks on an A-level course. An average sighted boy may embark on an A-level mathematics course and obtain a low grade at A-level; an average blind boy is likely not to succeed at all.

Paradoxically, however, the blind boy with aptitude will find that there are fewer technical problems at A-level than there were at O-level. The work is largely algebraic and, provided he has been taught to master the notation and set his work out tidily, there are no more hurdles. He must, however, be prepared to put in rather more time than his sighted counterpart, since he is compelled to work at a slower pace. The problems which bedevilled the A-level course in the past - the lack of textbooks - are being rapidly solved.

In order to show what is possible, it is worth while at this point quoting some of the results obtained at Worcester over the past decade, though it must be stated that these were obtained with very talented pupils. At A-level, one boy obtained two A grades with scholarship in each, one an A and a B with scholarship in each, two boys each obtained two B grades, and one a B and a C. Of these five, two obtained First Class Honours in Pure Mathematics at university, and one an upper second. The other two read Physics, obtaining a First and a Second class honours degree. Five years ago, the O-level form consisted of eleven boys. All passed Elementary Mathematics, and seven out of eight passed Additional. Two years ago, all twelve entries at Elementary Mathematics gained a pass.

"Modern" Mathematics in a Secondary School

by

Audrey M. Sims.

Once I had become moderately familiar with using Braille methods for Mathematics and compared my pupils with those in sighted school, I found three main differences.

a. The speed of calculation was far slower, except for work which could be done mentally; and interest in a problem was lost as time went on.

b. Some girls appeared to have very little ability to comprehend even a simple diagram, all had difficulty in reproducing it, and even when successful there was little accuracy.

c. Most girls were more willing to learn facts and techniques parrot-fashion than to think logically.

About five years ago I started introducing more practical work, aiming to obtain ideas by discovery rather than by formal proof - especially in the first three years - and to build up concepts of pattern in number and shape rather than concentrating on manipulation and calculation, tying this work up to an appropriate “O” level syllabus in the fourth and fifth years.

This method is now being followed all through the school, the group who followed a very "mixed" course and suffered many of my worst mistakes having just taken the alternative syllabus - (Oxford 0.52) in “O” level.

Apparatus

The abacus is now used for all calculation, the speeds being attained by those who have used it several years being comparable with "pencil and paper" rough work. Some pupils are familiar with its use on entering the school and the rest start at once, and I find that, although some never reach great speed and certainly not 100% accuracy, the general standard is higher than by other means. The use of an abacus can be learnt once the basic number bonds have been firmly established and has its place throughout the secondary level.

The main deficiency of the abacus is the absence of working notes by the time the final result is reached. Partial answers can be noted as needed, but the main reason for keeping all the working notes was for examination purposes; with the introduction of multi-choice questions and the allowance of a slide-rule in the public examination, this argument loses much of its point.

Most of the shape work is done using pins and elastic bands on a cork or rubber surface, often with a sheet of plastic graph paper. (Varying grids can be made using a thermoform machine), and the use of co-ordinates is one of the first ideas learnt. Besides actual graphical work, area, etc. the graph paper gives automatic right angles for many diagrams. I have not found a geo-board any help as the unused pins confused many girls.

The pupils use this apparatus to make diagrams which they can comprehend while learning to use geometry instruments on plastic film, which is a slow process and the result produced by many girls is poor in comparison with their "pin and band" diagrams.

Straight line diagrams and statistical graphs can often be made using the Perkins, and use is made of standard school apparatus, peg boarding, etc.

Syllabus

Together with a more practical approach to Mathematics, a reduction in the amount of numerical calculation, algebraic manipulation and pure geometry studied, several new topics have been introduced into the syllabus.

a. Statistics:- Many of the girls who find diagrammatic and space work hard have had greater success with statistical work, coping with the graphical work and gaining a two-dimensional concept. Data for group work can be obtained verbally and this appeals and gives confidence to the less practical pupil.

b. Set Theory:- The ideas of "a set" are no harder for a blind than a sighted child and this topic can be followed at about the same rate for both. A simple Venn diagram can be made by using a metal ring and a piece of filter paper, or drawn and the areas numbered rather than the usual shading.

c. Co-ordinate Geometry:- As I find graphical diagrams are more readily understood than other types, it seems reasonable that if a logical system can be built up using this method, greater understanding is reached. This system may not be rigorous but it does lead the pupils to discover for themselves many of the properties of plane figures. Starting with knowledge of Pythagoras and the slopes of lines (parallel and perpendicular properties) which have previously been found practically; and using numerical co-ordinates, (for example; the vertices of a triangle,) geometric properties can be built up.

d. Matrices, Vectors and Motion Geometry:- When a pupil has mastered the use of matrices (introduced by making codes) I feel it is an indication that she has moved into two dimensions on paper and is not tied to the linear Braille - a stumbling block to some. Matrices as applied to Geometry can again all be done graphically (as C above).

e. Elementary Computer Science:- A brief introduction to the power of the computer is, I feel, necessary for all school children today as they will be living in the "computer-age". This is just as true for blind pupils as sighted.

In introducing various of the above topics to the first year I find that a number of problems arise. Firstly, nearly all the usual text-book illustrations are based on vision, i.e. coloured and shaded charts, ink-blot symmetry, 3-dimensional pictures. Secondly, as the pupils have come from different backgrounds and have different ability it is useful to start on some common ground.

All the girls have one thing in common, Braille is their natural medium, and all have a Perkins. With this most of the problems can, at least partially, be met, e.g. reflection patterns (m and sh), symmetric shapes (ice), complements (k and w), collecting sets of signs with different properties, finding the number of these sets etc.

Braille is also a binary code, as in each of the six positions there either is or is not a dot. This can lead into binary arithmetic, punch card information, etc. Here, at least, the blind student may even have a slight advantage over her sighted counterpart.

Text Book

At present there is no standard textbook being used in the school, for the order which I find fits the pupil's development best is not that of any book I have yet found; but many have been invaluable to me in developing this course, the main ones being:-

    SMP texts. (C.U.P.) including the recently published book, A B etc. designed for those working toward C.S.E.

    Contemporary Mathematics - St. Dunstan's booklets (Blackie);

    Exploring Mathematics on your own - (John Murray);

    Learning Mathematics – Heritage - for the Shropshire Maths project (Penguin) - (Book 1 in Thermoform).

    Scottish Modern Mathematics Texts - (Partly Brailled);

    The Abacus - Dr. Davidson - (American Printing House for Blind).

Mathematics for Primary School Blind Children

by

F. H. G. Tooze

The work we have carried out at Sheffield in connection with the above project has not been sufficiently disciplined to be called research in the true sense of the word. It has been more in the nature of experimentation and continuing enquiry concerned with:-

a. the problems of recording Mathematics,

b. the development of apparatus to enable blind children more actively to pursue their own enquiries into mathematical relationships, and

c. the extension of the "discovery approach" in classroom activities.

We have not been able to check our innovations scientifically neither have we any statistics to support the conclusions we have reached. Nevertheless out of all this activity certain ideas have been born and new techniques evolved which appear to be valid; they have spread into other schools and, as far as we have seen, have been successful.

As I mentioned in my interim report in July, 1967, we had been affected by the Nuffield Research Programme Project operating in Sheffield before we were linked with the programme organised from Worcester College. We had at least become aware of some of our problems when we started the enquiries which are reported below.

Recording Techniques in Mathematics

At the beginning of our enquiries the recording of mathematics was extremely cumbersome. It could either be done on the Taylor Frame or on a Braille Frame (or Stainsby Writing Machine). The Taylor Frame has been in use for nearly a century. Metallic square pegs with a bar projection at one end and a “two dot” projection at the other were fitted into lines of octagonal insets. Eight different positions were possible so that when both ends were used sixteen different signs would be recorded on the board. The symbol for each number was the bar projection in one of the first eight positions round a star shaped inset. This was quite different from the symbol used in Braille. Braille numbers are identical with the first ten letters of the alphabet and are preceded by a special sign in Braille. This meant that the young child had to learn two symbols for each number. When a child attempted to record arithmetic on the Braille Frame it was necessary for him to reverse his paper in order to read what he had written. This made it extremely difficult to record mathematics in Braille.

The invention of the Upward Braille Writer, in our case, the Perkins Brailler, made it possible for pupils to write Braille from left to right - the way in which it was also read. Now we were able to record mathematics in Braille. The tendency was to continue recording mathematics in very much the same way as was done by seeing people in ink print without due regard to the suitability of such a method for blind children. We therefore felt our first area of inquiry should be into more efficient ways of recording Mathematics in braille.

Cubarithm Board

My own inquiry was centred on the possibility of replacing the Taylor Frame with some device which would enable even the youngest child to record numbers in Braille notation from the beginning. I have examined several devices and finally concentrated on the plastic cubes and plastic board produced at the Paris School for the Blind, metallic cubes and board made available to me from the American Foundation of the Blind Office in Paris, and, finally, some adjustable cubes which came from Italy. After several months of experimentation I decided to utilise the metallic cubes from the American Foundation for the Blind and the plastic board from the Paris School. With this combination the equipment proved easy to manipulate and, most important of all, the metallic cubes stayed undisturbed in their sockets on the boards even when touched by the children. The plastic cubes from the Paris School were not so rigid in the plastic board. They were too easily displaced.

The Italian adjustable cubes were too cumbersome to use. Moreover the cube used six small dots which seemed rather unnecessary in view of the fact that numbers in braille are in what we call the "upper cells" or the top four dots of the Braille cell.

We tried out this system using metallic cubes and plastic boards for some months at the Sheffield School and similar trials were made at the St. Vincent's School for the Blind, Liverpool. The results seemed very satisfactory indeed. Some publicity was given to this apparatus at various meetings of teachers organised by the College of Teachers of the Blind and the two cubarithm items were eventually accepted by the R.N.I.B. as pieces of apparatus they were prepared to stock.

One of the early criticisms of this cubarithm device was that it would be much slower in operation than the Taylor Frame. Once the children had learnt how to manipulate the board this proved to be untrue. We have now discovered that young children can operate the board quite as quickly as they operated the Taylor Frame. The great advantage which has never been disputed was that the same Braille symbol was used to denote a number both in the "new" Arithmetic board and in the Braille notation.

When the board began to be used in schools other than our own it became clear that some literature on the use of the board was necessary. I was asked by the R.N.I.B. to prepare such a pamphlet. The resultant manual gives detailed instructions in the use of the cubarithm board. Pierre Henri who developed cubarithms in the Institut National des Jeunes Aveugles de Paris was very interested in its wider application. I felt the need to produce a simple manual so that all schools could use the cubarithms the same way.

In the preface to the booklet, I did emphasise that the cubarithm board was primarily for the use of young blind children and that it would be replaced eventually by the Upward Brailler and possibly the abacus as the child moved on to more advanced work. After using cubarithms for nearly four years we begin to feel that, though it is invaluable to younger blind children, its usefulness decreases rapidly to children (of at least average ability) after the age of seven. It is invaluable to young children when they are trying to express their first number concepts in some written form, but its disadvantage is that it does not provide a permanent record of more advanced work.

The Abacus

We began our enquiries into the use of the abacus for blind children about four years ago. While we were still at the stage of learning how to use the abacus ourselves and examining the various kinds of abacus that we were able to obtain, I paid a visit to St. Vincent's School for the Blind where I saw a teenage boy demonstrate his ability to use the Cranmer Abacus. He was continuing his education with seeing children and used it to work out mechanical problems very much as seeing people do with a pencil on the back of an envelope etc. I noted at the time that this student was fast and accurate using all four rules in numbers. I was not able to test him further. There were other able students too but this boy was exceptional. Before we introduced it to our own children we examined several kinds of abacus, all of them bigger than the Cranmer Abacus including one where the lever was spring loaded but, as far as we were able to estimate, they were no more easy to work than the Cranmer Abacus which used beads sliding up and down a wire rod against a felt underlay. They were certainly much more expensive.

I may have been biased by the demonstration I saw but we decided to purchase a number of Cranmer Abaci to introduce to our children on the grounds that they were equally efficient, small enough to go into their pocket and fairly cheap to purchase. In order not to interfere with the Mathematics programme of the school, we decided to introduce them to a class of ten year olds, the majority of whom had mastered recording in Braille. They had lessons in the abacus for a whole year and the more able among them achieved marked efficiency in addition and sub- traction but far less accuracy in multiplication and division. During the year this group of children spent little time recording mathematics in Braille. When they moved up into the next class we examined their general ability to record mathematics in Braille and found that the group as a whole had lost some of their ability to record mathematics in Braille. When they were attempting to set out problems or state mathematical relationships, they appeared to be far less mathematically literate than we would have expected. They were certainly able to make mathematical calculations fairly easily but they had lost a sense of form in setting out mathematical problems. We tried the experiment a second time with another form, reducing the time spent on learning the abacus and increasing the time spent on recording braille. At the end of the year the results were again rather a disappointment. Many of the children were able to add and subtract using the abacus but found difficulty in multiplication and division. Their recording in braille was also below the standard they should have achieved.

We discussed this carefully in a Staff Meeting and finally decided to restrict the use of the abacus to "marginal" work in addition and subtraction. Moreover, as far as ten year old and eleven year old children were concerned, we would encourage them to concentrate on recording mathematics in braille.

Originally we had decided to introduce the abacus lower down the school as far as the seven year olds were concerned - the equivalent of first year in junior school. In view of the damaging effect this experiment seemed to have had upon the child's ability to express himself mathematically in braille we have discontinued this experiment.

There is still a place for the abacus with primary school children but our feeling, at the present moment, is that it should be restricted to addition and subtraction much more than to complicated numerical problems. Primary school children need to be able to read the work they have recorded to help them with their own discovery techniques. Three of our children are continuing their education with seeing children and they use their abacus primarily for just "marginal" work. They seem to find it useful.

We have obviously not solved the problem of when the abacus should be introduced or how far it should be employed but this remains to be investigated. It may well have a value in the 7 - 9 year group along with other apparatus like Dienes etc., in helping children to establish a sense of "place" values. The only thing that has been proved is that the Cranmer instrument is a very effective form of the abacus that can be used successfully by blind children from 10 years upwards for computation.

Graphical Representation

Experiments in representing mathematical relationships pictorially and graphically were entered into by children of all ages from 5 to 13 years. This has been one of the most exciting and rewarding sectors of development in connection with the project. For the purpose of this report the activities are described more or less as we now seek to stimulate them in our children from early years onwards.

Pictographs

These were and still are most successfully made by children approximately 7 years of age. Younger children make "play" Pictograms but they need considerable help from the teacher. In the early attempts children were asked, for example, to find out how many boys and how many girls were in each class. They then had to record this pictorially. At first rough torn pieces of Braille paper were glued in groups on a piece of cardboard -- with perhaps one size for boys and supposedly another size for girls. Some children used "sorting boxes" to demarcate class from class. Improvements were rapidly made as the ideas spread. Primitive "pipe-cleaner" figures were adorned with paper skirts or hair for girls and the boys were unadorned or perhaps given long trousers. At this time we were producing a variety of tactile forms of graph paper and a simple version was printed for the younger children ruled off in large rectangles. This introduced form to the recordings and was used in a variety of ways. Pictures 4 and 5 show how model cars were used to depict how many families had cars. These were pinned down by the children to make a more permanent record. Developments have continued in many ways including that which led on to a tactile version of Histograms.

    [Digitiser’s note: We regret that it has not been possible to reproduce the photographs and diagrams of the original print on the Internet.]

Histograms and Block Graphs

Once the children discovered they could represent mathematical relationships in the form of a block graph or histogram they started to do this in many different ways. One way was by using Colour Factor blocks. At the beginning of our project we magnetised several sets of Colour Factor blocks and the children found this was a quick and easy way of making a histogram. In their first attempts they put in a bottom line (later to be identified as an axis) and then they represented their quantities by clipping on the Colour Factor blocks vertically. Picture 6 shows how the blocks were mounted though the example in the picture was an illustration of symmetry exhibited by a relationship based on x = y. (The lines scored across the panel were from a previous experiment in graph making. This particular piece of apparatus was later discarded.) Picture 7 shows how the child used a piece of commercial apparatus with slots to record his findings using colour factor. This was his own idea and many other examples like this could be quoted. In Picture 9 a girl is recording the result of her enquiries into the diameters of heads of children in her class. Instead of using Colour Factor she decided to use Stern apparatus. When confronted by the difficulty of recording half inches she used pink blocks from the Colour Factor set to go with the Stern blocks. Picture 8 shows the actual practical work proceeding.

When we had sufficient supplies of "planners", P.V.C.1 sheets with magnetic backing, we were able to produce a large number of square inch planners for use on what we called a magnetic board. The children were shown how these could be used much more accurately in constructing block graphs provided a vertical and horizontal axis were inserted, again using a strip of P.V.C. with magnetic backing [see section on Structural Apparatus]. This proved to be extremely popular. It was deliberately encouraged by the staff because, at the time, it seemed to us to be one way of leading the children into the use of line graphs.

It was in connection with the use of “mini-planners” that we carried out experiments using different sized squares ranging from square centimetres upwards. Generally speaking we found that the children were able to record easily with inch squares and had a lot of difficulty with anything smaller than this. For a while we gave up using the square centimeter “mini-planners” until we ourselves produced moulds on the thermoform based on the commercial vertical box type histogram boards. Picture 10 shows a girl using one of these moulds and recording her findings with square centimetre “mini-planners”. There is a tin panel underneath the mould to which the magnetised planners are attracted. Picture 11 illustrates the commercial models which led us to think of the plastic moulds. In the commercial model a girl is recording her findings on a 3 dimensional Demonstration Board (GALT).

    [Digitiser’s note: We regret that it has not been possible to reproduce the photographs and diagrams of the original print on the Internet.]

Line Graphs

We spent many months trying to find out ways in which children could construct some graphs when they were ready for this new adventure. Picture 12 shows a girl who has recorded some findings on a peg board and knotted them together in string. This was a clumsy attempt to see a continuing relationship. We tried to use the magnetic board to record our findings with a whole variety of magnets. Picture 13 illustrates some of the material we used. Some of the very flexible magnets appeared to make it possible to create graphs but the very slender string-like magnets were not sufficiently resistant to touch. We had some stud magnets made through which we threaded a string-like magnet as in Picture 14. This certainly made a more permanent record of our findings but only a very few children were able to thread the string magnet through the small tunnel at the base of each stud magnet. Though the magnetic board would prove its worth illustrating graph formations it was obviously too impermanent to record for our work.

It was at this stage that we began to experiment with a variety of graph paper patterns on the thermoform, eventually producing the type of paper seen in Picture 15. Here the squares were raised and separated from each other by troughs. The troughs ran vertically and horizontally around half-inch squares. The corner of each square was indicated in the trough by a circular depression. Axes could be inserted anywhere but we usually indicated these by the lines running along the edges of the raised squares adjacent to the margin. Graph paper was pinned to a piece of Sundeals board. Scales and definitions could be pinned along each axis in the same way. Children then made their graphs by sticking in each pins with blank heads in the appropriate places on the graph. Where necessary the pins were fastened together using string or elastic. The graphs indicated in Picture 16 are those based on varying speeds worked out by the children. Several graphs are plotted out on one piece of paper and the appropriate statistics are in the braille book lying on the board.

This particular piece of graph paper was evolved in its present form by Mr. Whittaker but he still felt that it was too crude a way of making graphs for the increasingly complex mathematical relationships the children were discovering. Eventually he made the graph machine seen in Pictures 20 - 23. The first model was constructed out of square parts but the important thing was that the principle embodied the use of the child's sense of hearing for the more exacting plotting of graphs. Using a simple ratchet system the movable upright axis clicks along the base axis giving an audible click every one eighth of an inch Similarly when the necessary point on the axis has been established another ratchet moves up the verticle axis making an audible click every eighth of an inch. The point is centred by a small arm which sticks out of the upright bar and is registered by the insertion of an inch pin. This all recorded through a sheet of melinex over the top of a rubber backing. When the child has finished plotting his points a piece of flexicurve is placed round the pins and pinned in position. He then runs a stylus or pen along the flexicurve and records a continuous graph. This is seen in Pictures 22 and 23. The paper can be inserted back in the machine accurately; if necessary another graph may be made on it to find out points of intersection. These can be read “backwards” using sound. The melinex record can be filed with any other recordings the student has made.

    [Digitiser’s note: We regret that it has not been possible to reproduce the photographs and diagrams of the original print on the Internet.]

This has proved to be an extraordinarily useful piece of apparatus. It was demonstrated at the International Conference of Mathematics at the Perkins School in 1967 and American teachers were very interested. They asked for the model to be left but it was the only one in existence. The difficulty now is to get it produced commercially. Arnolds of Leeds have examined this piece of apparatus. Though they admire its ingenuity they feel it would not be of sufficient commercial value to them. At the present moment Dr. Butler of the University of Sheffield is working on this piece of apparatus seeking to evolve a more sophisticated machine which by using electrical impulses will emit different sounds at specified intervals down to one tenth of an inch.

This is certainly one piece of apparatus that is worth developing, Attached to this report is a copy of an article written by Mr. J. Whittaker on “Graphical Representation” for publication in the “Teacher of the Blind”. This contains a record of other enquiries made at the time and illustrates very vividly both our aims and problems when we were endeavouring to develop a way of recording graphs. Mr. Whittaker's work was very successful and the article makes reference to other devices tried at the time as, for example, use of the Perkins both to produce a straight line and curved graphs. The machine referred to at the end of the article is the one that I have described above.

Structural Apparatus and Materials

    [Digitiser’s note: We regret that it has not been possible to reproduce the photographs and diagrams of the original print on the Internet.]

During five years of enquiry into the development of means whereby blind children themselves could be actively engaged in discovery work in mathematics we have examined scores of pieces of commercial apparatus in addition to devising apparatus of our own. Before commenting first on the commercial products we have introduced to our children, it would be helpful to make a clearer reference at this stage to the magnetic material that we have obtained from James Neill and Company, Napier Street, Sheffield.

Magnetic Material

Mention was made of this under the section on “Histograms and Block Graphs” under the name of P.V.C. sheets with magnetic backing. Mr. Pickles first discovered this material and on one of his early visits to Sheffield I went with him to Neills and obtained supplies of the material to use throughout the school. Neills had made a compound of rubber and fine permanently magnetic powder. This had been mixed together and then either extruded into "bars" or "strips" or calendered i.e. rolled out into sheets. From this basic material, the firm marketed "planners" which were coloured P.V.C. squares backed by magnetised sheets and "tiles" which were rolled strips of magnetic rubber sheeting one side of which was covered with an impact adhesive. At that time the extruded bars (rather stiff rubber strips) ranged from 1/8" in width to 1/2", all being magnetic. Through the years they have developed this material considerably and the range now includes very fine magnetic string and a whole variety of widths both of magnetic strips and stiffer rods. The magnetic tiles with their adhesive side can now be bought in pieces as large as 48" x 18½". More recently they have added a series of small metal magnets; some of these are illustrated on Pictures 13 and 14. The magnetic planners can be cut very easily into any desired shape. Neills actually produced for us a supply of planners one inch square and one centimetre square.

We equipped ourselves with the steel boards which the children called "magnetic boards" and used these as a base on which to place our magnetised shapes. When later reference is made to magnetising shapes on blocks it means that we have fastened a magnetic tile onto whatever shape we wish to use.

In addition to its uses in Mathematics, magnetic "tiles" and "planners" have now been extensively employed in making Braille apparatus and maps.

Commercial Structural Material

    [Digitiser’s note: We regret that it has not been possible to reproduce the photographs and diagrams of the original print on the Internet.]

Colour Factor

The most dramatic material to be introduced into the school was that known as Colour Factor. At first we used this without attaching magnets and "played" with it throughout the school. We introduced it in fact in 1964. After experimenting with it for six months with children of all ages we decided to use it systematically in the Infant and early Junior phases. We even encouraged parents of pre-school children to let their children play with a box of Colour Factor at home. We noticed incidentally that the children were able to identify the differences between the shapes with remarkable ease. When five and six year olds were ready to accept a measure of direction in the play we introduced them to the moulds seen in Pictures 25 - 27. The plastic moulds were made for me by Mr. James who had a moulding machine at Lickey Grange School, Bromsgrove. These have been used since by many other schools in England and Overseas.

When the children began to make patterns and eventually to develop number concepts we devised a special L square with a slide to keep the bricks together. The present supplies were made at Hethersett Assessment Centre. With this apparatus the children were able to go through a whole range of activities that sighted children can enjoy when using this material. Amongst the many attractions Colour Factor material had was the fact that it was possible to record simple computations using Colour Factor blocks themselves. In addition we even devised a system whereby we could illustrate numbers up to and beyond hundreds in a tactile form.

It seemed logical to magnetise the blocks and use them on the magnetic boards and this we did. This turned out be of more value to children who have some difficulty in locating the blocks on the board. They much prefer to use an L square. The uses to which Colour Factor blocks can be put are many and various. Picture 7 shows Colour Factor blocks being used to make a Histogram. We also made a number-line board to fit Colour Factor blocks although we did have considerable difficulty in trying to write numbers in braille along the top of the board. In the end we recorded numbers in multiples of five e.g. 0, 5, 10, 15, etc. Picture 1 shows a blind child at Liverpool working out a problem with his Colour Factor then recording it with cubarithms. This was a child of five who was able to handle number concepts more easily because of the material at his disposal. Picture 6 shows magnetised Colour Factor blocks being used on a magnetic board to make a block graph.

Dienes

We bought a set of Dienes material, base 1 to base 10 from E.S.A. and also Arnold's Tillich Blocks which embody the same principle. We found the children could handle these without much difficulty although they needed a lot of space to work in. We sometimes had difficulty in grouping the blocks. We only used them for setting out and grouping and as an additional experience to Colour Factor. They were much more expensive than Colour Factor material.

Stern Apparatus

We obtained a considerable amount of Stern apparatus from E.S.A. including Stern unit cubes, Stern histograms boards and unit blocks both 3/4" and 1 centimetre. All this was easily used by the fairly able blind children. The apparatus is easily controlled by blind children. The units fit together and are rigid while the boards keep the unit blocks neatly and safely in place. The 1 centimetre blocks offered difficulties to the children with any degree of spasticity but apart from that, they were able to identify them and use them. The number strip board was easily managed by the children though the staff had difficulties in adding braille numbers when necessary. The child in Picture 9 is using Stern apparatus and Colour Factor to make a Histogram.

Moulds

Even before the project was started we were aware that there was a tremendous amount of commercial material that could be used by blind infants. The biggest problem always was introducing some means of helping small children to control apparatus. In the Infant Department we used a series of straightforward mould which helped children to make sets and compose numbers. These we obtained from Mr. James of Lickey Grange School, Bromsgrove.

Miscellaneous

We tried out a wide variety of mathematical balances both plastic balances (provided by E.S.A. and Invicta) and the simple balance (provided by Arnolds) with two tin containers at either side. Sometimes we had to adapt them slightly to enable the child to know when the balance was level, but apart from this they were and still are freely used by our children as in schools for children with sight. There was no difficulty in obtaining domestic scales of various types commercially and the children were able to use these in their discovery activities.

The Unifix apparatus has been used in schools for some considerable time and we merely developed it with the 5 and 6 year olds side by side with Stern apparatus and Colour Factor as an additional medium.

There was a wide range of simple aids like trundle wheels that were made audible, wooden sliding callipers (Arnold's) and weights and measures generally that needed only the addition of braille labels to become usable. Apparatus like Geo-Strips (Invicta) were immediately available. It appeared to us that it was much more easy to find apparatus to suit the needs of the children from five to ten than it was after that age when their discovery techniques had become much more improved and sophisticated.

One other range of apparatus which we found of interest was that devoted by commercial firms to illustrating fractional parts and the relationship between shapes of different sizes. All of these were utilized though we had to adapt them slightly as for example in Gait and Sons "Primary Shapes". This is a series of pieces of apparatus which encourages the children to find out for themselves qualities of different shapes and the relationships between the areas of different shapes. We magnetised these shapes and then produced a braille book with closed questions for the children to answer. Further-reference is made to the adaptation of this apparatus in "The Magnetic Board, 2D Shapes and Area" below.

One final piece of useful commercially produced apparatus we are still using is the drawing apparatus produced by "The Quickdraw Company Limited". Used with a Melinex sheath and pad, it enables the student to draw accurately geometrical shapes and, with its fixed base, is invaluable in drawing diagrams in for example, Directional Geometry at the secondary school age, See also section on “Geometry Apparatus” below, where this apparatus is further developed.

Specially Produced Apparatus

After the project had been under way for just over a year we thought it was necessary to devise Number Line Boards for every age group. The Stern number strip had proved useful but we wanted longer boards properly brailled that would range up to 100. In addition to demonstrating to the child how numbers grew, we sought to make it possible for the children

a. to practise number trios e.g. a three-strip plus a seven-strip equalling a ten-strip etc.

b. to be able to see the relationship between 10 + 2, 20 + 2, 30 + 2 etc. and

c. to generally practise the discoveries they had found in number relationship using other structural apparatus.

Eventually we standardised a number board where the numbers were marked off at one inch intervals with each board having a set of strips increasing in number value. Here, as elsewhere, it seemed to us that the length of one inch was easily discernible by young totally blind children. This was the conclusion we reached when deciding on the most efficient size for small "planners" for use on the magnetic boards. These were one inch squares. Since then we have discovered that after the children have had two or three years' experience with this tactile apparatus they are able to work just as easily with smaller lengths. Our earlier assumptions have been proved incorrect. One class has made a number line board marked off in centimetres and it seems to be acceptable to the children though once again the units are only brailled units of five. Picture 35 shows a girl using a number line board graduated in inches.

The Magnetic Board, 2D Shapes and Area

The magnetic P.V.C. "planners" proved an ideal vehicle for introducing children to discovery problems based on 2D shapes and area.-Picture 36 shows a child working out a problem on the conservation of area using blue magnetic tiles on steel board that has been painted green: In Pictures 37, 38 and 39 a pupil is again making discoveries both about area, shape and the characteristics of various shapes using a box of primary shapes based on Galt's material. These are directed questions and he has his course plotted out for him in a braille booklet printed on the thermoform. In Pictures 40 and 41 an older boy is working with a set of shapes produced at school which enables him to make more advanced discoveries based on the shapes in the thermoform book at his left-hand side. After he has made his discoveries he writes up his findings in braille. In Pictures 18 and 19, the child is endeavouring to find the number of rectangular shapes possible, with a constant perimeter of 22". He is using one inch planners from which he collects the data for his graph.

These are some of the ways in which this particular piece of apparatus has enabled our blind children to make discoveries for themselves and its applications continue to increase.

Magnetic Table - Polyhedra

It has long been possible to make solid polyhedra for the blind to feel. We tried to revive the children's interest in this field by using some of the commercial three dimensional shapes. We examined Galt's apparatus (items N463, N462, and N598) using which the child builds rectangles, triangles and squares respectively but only on a “base tray”. Our children were not able to feel any particular polyhedron as a whole neither was it possible to carry out exact enquiries showing, for instance, that in a perfect cube the six sides were exactly the same shape and size in area. We used some of the solid geometry equipment produced by E. J. Arnolds -- perspex, mathematical models. These certainly excited the children's interest and helped them to appreciate the appearance and characteristics of 3D shapes included in the equipment. In addition the set of heavy duty volumetric models were of great help when comparing the volume of various kinds of prisms.

Nevertheless we still felt that until a child could build a shape for himself he would not discover all that was waiting for him in solid shapes. It was with this in mind that we asked the adviser at Neills if it were possible to construct a table with a magnet underneath that would project a magnetic field in which we could assemble metallic shapes. He thought this was quite feasible but, in point of fact, it was Mr. Pickles who supplied the first models. With these he supplied metal shapes from which we were able to construct cubes, rectangles, tetrahedrons etc. Picture 42 shows one of the early models with a hollow cube fitted together over the magnet. Picture 43 shows a later model in which the magnet is covered by a plastic strip over the magnet. The girl has just constructed a tetrahedron using metallic shapes. Picture 44 illustrates the tetrahedron-like shape made by the same girl using ball bearings.

This has proved to be a very valuable piece of apparatus but it could be improved still further by producing a stronger magnetic table which could be connected to the mains. Apart from being able to build bigger models it would be possible to switch off the electricity created in the magnetic field so that the component parts could crumble into 2D shapes. Several engineers have been asked to produce this more sophisticated piece of apparatus.

Cardboard Polyhedra

After the introduction of the magnetic table into our scheme, several members of the staff tried to devise a way whereby the children could make different kinds of polyhedra as we noticed children did in schools for the sighted. After many failures a colleague, Mr. Pointon, came up with a workable solution. He made a large assortment of regular polygon in cardboard from plastic templates purchased from A. Brown and Sons, Hull. The equipment was called "Poly Shapes". On the side of each shape was a tag which secured to a matching tag on the side of the adjacent shape inward and we re-designed them so that the elastic bands slid on and off more easily.

The children were able therefore to make polyhedra whose outside plane surfaces were realistic and whose final shape was valid and complete.

We were concerned at first that the manipulative problems this apparatus posed might frustrate the children. Fairly extensive tests were made with the following results:-

a. able children without manipulative disabilities could build the polyhedra

b. speed of assembly did appreciably increase with practice

c. the final shapes frequently had gaps between sides but the children seem to accept these defects

d. the tags had a limited life and were the first parts to “wear out” when used constantly in assembling new shapes.

The children have been able to build polyhedra for themselves and Pictures 45, 46 and 47 show them doing this in a project which sought to discover and verify "Euler's Law".

Apparatus involving the Measurement of Time

When we began to direct children towards discovering their environment we came up against the necessity to measure intervals of time with increasing accuracy. For example we might want children to be able to compare the time taken to walk, hop, run and cycle over a defined distance. For quite a while we were unable to obtain or produce any apparatus that measure time intervals with any accuracy. We assumed that it was not true discovery work if a blind child had to be told time intervals by a teacher who might be using a sighted stop watch.

Measurement of Time

We experimented with the "Timers" produced by the Royal National Institute for the Blind. They were of little value when it came to measuring varying time intervals. Several commercial firms had interesting little gadgets which indicated time intervals but again they were of little use where variations occurred. Most devices only measured a set time interval. We bought “seconds timers” both from Arnolds and Galts and removed the glass on the front of the clocks. These were not able to stand up to usage by the children! Perhaps one of the most helpful improvisations was the use of a metronome with special attachments. Here again, the individual child was not able to measure an interval of time exactly. It was necessary for someone to count the number of ticks by the arm of the metronome.

We explained our difficulty to Dr. Leonard of the University of Nottingham and after a short time early in 1967 he produced a most efficient electric “stop clock”. This was made for us at the University of Nottingham. It consisted of a braille meter like the speedometer of a car which was driven by a power unit and linked up to the mains through a transformer. Each little panel on the meter was brailled and it became possible for our children to read time intervals up to 1/10th of a second. Sometime later the Royal National Institute for the Blind came out with a similar instrument which has been commented on elsewhere.

The only drawback both to this particular piece of apparatus and that produced by the Royal National Institute for the Blind is the cost. Nevertheless the “stop clock” made for us at Nottingham proved to be an extraordinary piece of apparatus. We had hoped that a portable version of this could have been produced for us so that children could take it more easily out into the grounds and into the streets but so far a second piece of apparatus has not been forthcoming.

With this instrument we were able to devise other pieces of apparatus which enabled the child to carry out experiments involving the recording of time. Pictures 48 and 49 illustrate this development. A railway track was fastened to an inclined plane which was fixed at one end and elevated at the other by adding one inch blocks. A small railway truck was allowed to run down the plane and the child in Picture 48 has her hand across the track at a fixed point so that she is able to record the time taken by the truck to run down the plane. As the angle of elevation increases she is able to note the time taken. Later on this particular piece of apparatus was further adapted so that an electrical contact was fitted at the top and bottom of the board and connected to the stop clock. As the truck broke the first contact the indicator on the stop clock began to record tenths of a second. When the truck broke the bottom contact the clock was stopped. It was possible to carry out experiments both related to the variation of the angle of elevation and to the variations in the weight carried by the truck.

Another valuable piece of apparatus devised by Mr. Whittaker can be seen in the film which has been made in connection with this project. Here again a closed railway track was wired up to the stop clock, movable contacts made it possible to record the time taken by a train to move a distance of one foot, two feet, three feet, etc. Again the load could be varied and comparisons made of the time taken to cover distances. This experiment again did not depend upon manual control; the clock was switched on and off as the small electric train passed through the first contact and the second contact. The children incidentally used this piece of apparatus in different ways to collect statistics for making graphs.

The stop clock was used to a limited extent outside by fitting long extensions to the mains.

Geometry Apparatus

The three pieces of apparatus mentioned below were designed originally to help pupils continuing their education with seeing children.

1. In “Directional” Geometry it became necessary for the children to draw exact diagrams involving angles. Mr. Whittaker purchased plastic triangles that fitted the rectangular inset of the "Quickdraw'" apparatus, five triangles in one set. Along the hypotenuse of the first triangle insets were cut to make angles at the base at intervals of 5° beginning at 0° i.e., 0°, 5°, 10° .….. etc. The second triangle was notched to give angles of 1°, 6°, 11° …... etc., the third triangle gave angles at 2°, 7°, 12° ...... etc. the fourth triangle at 3°, 8°, 13° ...... etc., the fifth triangle at 4°, 9°, 14° ...... etc. - By moving the base of the rectangular inset of the "Quickdraw" on to a line bounded in use by two pins, any angle could be located using the appropriate triangular "protractor" and another pin inserted in the inset. The "protractor" was then removed and the new course drawn between the base pins giving the required angle. This is a difficult operation to describe but a fairly speedy and reliable one to perform.

2. The modified protractor in Picture 52 grew out of discussions between Mr. Whittaker and representatives of the Association of Teachers of Mathematics. Each degree is cut out to allow the marking of points by pins (on Melinex). The arm is secured by a screw when the correct angle has been registered. The new direction is marked by a pin placed along the arm extension. The protractor uses the principle of "equal opposite angles" and is used in the position indicated in Picture 52.

3. The device shown in Picture 53 is notched up the left-hand in degrees so that the two arms can be secured at required angles. It enables the pupil to draw regular polygons quickly where the angles between sides are the same.

The Discovery Approach in Children's Activities

In 1965 when we embarked as a school upon the project we decided to ignore the rather rigid syllabus that we had followed for several years. Each member of the staff was encouraged to start with his children to find out the mathematical patterns that existed in the world around him. It is true that at the beginning we agreed that with the younger children we would accept the direction imposed upon us by following a course in Colour Factor. It is probably true too that we have only slowly come to a stage where we can let the children work out the rules of number for themselves. Nevertheless from the beginning we did try to face our children with a graded series of problems that would lead them to make discoveries for themselves and here we used the material in ink print that we saw being used in some of the more progressive Sheffield schools around us. We learnt a lot more from visiting these schools and attending courses run by the Local Education Authority. Every member of the staff was able to attend one or several such courses. Some of these courses were led directly by Miss Biggs, H.M.I., and we owe a great debt to her.

None of the ink print text books used in seeing schools was in Braille. Series like "Facts to Discover and Learn", "Using Mathematics" by Sealey or "Making Sense of Mathematics" by Watson and Quinn were full of useful studies for the children but not accessible to them. Many such books were examined by the staff who then produced a series of "cards" in Braille which individual children or groups used in making their own discoveries. This involved all teachers in a tremendous amount of preparation for many months. The "questions" or "directives" were very simple and “closed” at first. Some of the questions posed to the Children at 11 years of age eventually left all the planning to the child.

Picture 54 shows a girl carrying out a line of enquiry which has necessitated her measuring the height of most children in the school before trying to find some relation between height and age. The piece of apparatus she is using is something we have failed to have reproduced by commercial firms although it is a very simple piece of equipment. Each of the larger lengths of wood are a foot long and the smaller blocks are an inch long. They slide down the centre pole so it is possible for a blind child to measure fairly accurately the height of her subject. Picture 55 shows two children carrying out the sort of enquiry that sighted children are interested in. Most of many enquiries resulted in the creation of Histograms, see Pictures 3, 5, 8 and 9, or of Graphs as in Pictures 18 - 24, an experiment which is concerned with the conservation of perimeter.

    [Digitiser’s note: We regret that it has not been possible to reproduce the photographs and diagrams of the original print on the Internet.]

Pictures 56 and 57 show 6 year old children playing a game devised by Mrs. Davenport, one of the Infant Teaching staff. The game can be played by two or more children, one of whom is the "Banker". Competitors pick up thermoform shapes from a pile, identify them, and ask the "Banker" in turn for a cardboard reproduction to fit into one of 9 squares. The children are constantly identifying shapes and creating composite shapes.

This is an example of the "Play" approach creeping into the unlikely field of Shapes and Area.

As I mentioned in the interim report we were able to run a three day course in the teaching of mathematics for blind children in Sheffield in June, 1966. This was led by Miss Biggs, H.M.I. It was noticeable that all schools in the country sent representatives to this gathering. We were all able to take part in "Environmental Mathematics Workshop".

After four years activities we have felt more able to draw up a much more productive scheme for teaching mathematics in our kind of school and this we have now proceeded to do. At first we used a scheme based upon "Mathematics in the Primary School" but during the last six months we have begun to devise a “model” scheme aided by the Association of Teachers of Mathematics. The local Secretary of this Association is both a Mathematician and a parent of one of the children in the school. He and two local lecturers, members of the A.T.M., have met several times with the staff. Together we have produced the first draft of a programme for teaching mathematics to children in the first case up to 11+. The new element in this development is that we are trying to produce a scheme of work which embodies all that is best in progressive schemes for seeing children. We are very anxious to keep our children on the same level as the best we see in our local schools. This would certainly not have been deemed possible before the Nuffield Project was launched at Sheffield.

Our combined activities with the A.T.M. has led to a new impetus to the production for apparatus for our children. At the present moment we are concentrating on apparatus that can be used by those of our children of secondary school age who are following a mathematics course at a nearby comprehensive school for sighted children.

Reference has already been made to a film being completed on the subject of Teaching Mathematics to Blind children. Its title is "Voyage of Discovery" and we are glad to acknowledge that this film would not have been possible without the support given by the Nuffield Trust. The film itself is an illustration of the way in which discovery is possible for blind children and it does show the increased amount of apparatus now available to them.

This report would not be complete without some tribute to the staff of Tapton Mount School, Sheffield. Over the years, all my colleagues have been completely involved in the project; each one of them has made a real contribution. I am grateful to them for their tolerance under difficulties and their unwearying efforts. All of us are indebted to Mr. J. Pickles of Worcester College for his invaluable help in supplying materials and equipment. Without him, our achievements would have been very limited.

The project is still continuing and new ideas are already forthcoming. This is to be expected. However full of shortcomings our work undoubtedly has been, the experiences we have shared together here have stimulated an interest in Mathematics that will continue for many years to come.

Simplified Cubarithm Manual

Adapted from the original of Pierre Henri

by

F. H. G. Tooze

Introduction

In an interesting booklet published in 1955, Pierre Henri of the Institut National des Jeunes Aveugles de Paris traces the invention of the Cubarithm back to 1886. The latest development was in 1953 when the American Foundation for Overseas Blind brought out a larger plastic base board consisting of fifteen rows of twenty sockets each, and a lighter plastic cube. This board is much more useful than previous smaller boards though the original metallic cubes (an alloy with a lead base) are still more effective when being used by young blind children. Henri's Manual is divided into six sections of which the second gives advice on using the Cubarithm device; some of these hints are included below. Sections three, four and five are devoted to an exposition of the various ways in which he feels the device can be used in Arithmetical calculations, in representing Geometrical figures and in concrete Number Work. It is well worth reading, but the development of the Perkins Brailler, the increased use of the Abacus and, more recently, the Magnetic Board tend to satisfy, more easily, the needs he so cleverly anticipated.

We are greatly indebted to the pioneer work done on developing the Cubarithm device at the Paris School, but in introducing it for use in English Schools today it is necessary to relate its usage both to the recent new devices for recording Mathematical ideas mentioned above, and to the even more recent standardisation in the United Kingdom of a unified Mathematics Code (see book shortly to be produced under the title "Braille Mathematics Notation"). We have moved towards having one Braille system for Mathematics, and the values attributed to the Cubarithm signs must conform to this where possible.

It is probable that the function of the Cubarithm device at the present time is to afford young blind children a means of performing simple Arithmetical calculations closely allied to the Braille system which they will eventually use more fully on the Upward Brailler. The Cubes themselves bear Braille signs and, with practice, are easy to manipulate. In the early years, therefore, when the child is acquiring Number Concepts, the Cubarithm device is, at present, the obvious medium. When the child becomes adept in the use of the Upward Brailler he will use this more and more, with less reference to the Cubarithm Board. Furthermore, if he learns to use the Abacus, he will use this instrument increasingly for "marginal" work rather than the Cubarithm device even though some may still find a place for it in this field.

It would appear, therefore, that any scheme for using the Cubarithm device should take note of these considerations:

1. It should be related to the new Unified Maths Code.

2. It should be easily understood by young blind children.

3. It will be replaced (in varying degrees with different individuals) by the Upward Brailler and Abacus as the student moves on to more advanced work.

4. In Geometry, Algebra and concrete Number Work there are other devices now that are more effective than the Cubarithm Board.

It is against this background that the following experimental manual is offered.

Number Signs

Signs for the numbers 1 to 9 and 0

These are the same as the Braille Number Signs for 1 - 9 and 0 and are all Upper Cell signs.

Operational Signs

The Braille Notation for +, -, X and + all involve Lower signs in the New Maths Code. It is necessary to use other signs with Cubarithms because they are all Upper signs. To avoid confusion by using signs in Braille Notation for which there already are values, the above four operational signs are represented as follows:

Signs for mathematical operations

The full code for reference, therefore, is as follows:

Signs for numbers and key operations.

    *Dots apply to full cell though only the upper cell, Dots 1, 2, 4, 5, are represented on the Cubarithm.

Rules

1. The operational signs for +, -, X, +, are written close up without any space before or after.

2. The signs for = (dots 2, 5; 2, 5) and "is to" (dots 2, 5) are preceded by a space.

3. The signs for brackets are written close up to the number they enclose.

4. Fractions. Obviously the use of the lower cell signs is precluded with Cubarithms, so that fractions are written as follows:

Examples for fractions.

    Mixed numbers are written leaving a space between the whole number and the fractional part, so

Examples for mixed fractions.

4. Examples

(a) Vulgar Fractions

Examples for 'vulgar fractions'.

(b) Decimals and Brackets

Examples for decimals and brackets.

(c) Money

Examples for money.

Using the Cubarithm Device

Part II of Henri's Manual is headed "Hints on using the Device." He has in mind developing the Cubarithm Board for more extensive use than is now necessary with the popularisation of the Upward Writer, but his advice on first stages is still of value.

4. He emphasises that, first of all, the cube "should be thoroughly studied." His detailed suggestions are perhaps not so important as the general principle. Young children should be encouraged to play with the cube in order to get to know it before using it for recording numbers. For example, they can put cubes in at random over the board to represent children scattered around the playground; later, lines of "dot 1." or dots 2, 3" etc. can be inserted to represent the children "lining up" in different classes. They enjoy making patterns and shapes with the cubes and, all this time, they are getting familiar with it.

5. When using the cube to represent numbers, Henri says it is desirable "to familiarise the beginner with the procedure of passing rapidly from one sign to another by rotating the cube around its axis. In this way the cube will never be completely removed from the baseboard: it will be taken out just enough to make rotation possible."

6. In order to obtain proficiency in handling the cubes, he further advises, amongst other things, the following:

    (a) When the cubes are to be used they should be loosely packed in a container so that they can easily be picked out.

    (b) The cubes should not be taken out one by one as required, and the child should not use both hands to find the desired number. (One hand - the best reading hand - "must always remain free to read the data already in place on the base board.") He continues: "If, for example, the right hand is the best reading hand, a few cubes (two, three or more, according to the size of one's hand) should be held in reserve in the left hand; the fourth and fifth fingers will retain them in the hollow of the palm, from where the thumb will take them one by one. If the cube is felt the index finger will easily find the desired number. It must be noted that if the tip of the middle finger rests on the 7 and the flat part of the thumb on the bar line, and if the cube is pivoted between these two points, all the numbers (except 7) will come naturally under the index finger.

    This is a good habit to adopt. We realise that there are other ways of doing it and that the best procedure is the one which the operator is in the habit of using. But the important thing is to use only one hand to find the desired number."

It may well be argued that the above suggestions (in particular holding several cubes in one hand) cannot apply to young blind children, whose manual dexterity is far from developed, but Henri's advice has been included here to indicate possible developments in actually handling the cubes.

Teachers who wish to read the whole of Henri's Manual can obtain a copy of it in French from the American Foundation for Overseas Blind, Inc., 4 Place De La Concorde, Paris 8. It is called "Le Cubarithme."

Graphical Representation

by

J. Whittaker

Immediately the above phrase is used, most of us would remember labouring to produce that delicately poised pencilled shape the meaning of which was somehow bound up with the fact that y = 2x +x2 - 5, or some equally specific vagueness which the maths master appeared to determine for want of something better to do. My own efforts almost always were returned with the comment "'too messy", written in a faultless handwriting in red biro, together with just a sufficient number of exclamation marks to make me believe that it really must be so.

This produced within me a critical attitude of any steps towards inflicting such things upon the blind, indeed I began working from a point of view that such “sighted” devices as graphs were a very unlikely need in a classroom for blind children. This point of view is now no longer held, graphical representation has a great deal to commend its use with blind children, the benefits of such work extending beyond the value of the actual mathematical content of the project.

Some problems associated with the use of graphs with blind pupils.

One of the early doubts which ranged around the mind was whether or not the labour needed to produce a curve would be justified by the child being able to appreciate first of all the shape itself, and then in some cases the implications of the shape. The doubt was there that this would not be a sensible demand to make upon a blind person; and this thought has found expression many times in conversations heard and taken part in. To continue with such opinion is only to underestimate the ability of some of our pupils. They have shown themselves quite capable of understanding what shape has resulted, and are sometimes astonishingly accurate in predicting the shape which will result even before the plotting of the points has commenced! Again, the degree of astonishment is only the measure of the degree to which their ability is underestimated. Proof of this ability was demonstrated on the day when two of the children examined a straight line graph in connection with speeds, and related the early part of the line to its time and distance and evolved the speed of the vehicle, and then proceeded to explain in m.p.h. the meaning of increase in angle of slope of the second part of the line. From this point the first doubt began to be less imperative.

The second group of worries were - assuming the children could appreciate the result - how could they ever

a. record accurately to a scale comparable to that available for sighted pupils?

b. produce a result which was permanent, and not restricted by the use of elastic and pins?

c. manage to produce a curve free from irregularity and error?

The achievement of these three points results from experiment with various apparatus - and the methods of using Stainsby and Perkins machines will be outlined later. The only need at this point is to state that blind pupils can achieve such results, and without too great a difficulty.

Throughout the consideration of this as a suitable skill for blind pupils there also lurked the difficulty that would be present when trying to read information back from the graph achieved. There seemed little point in labouring to produce a graph if only the information plotted was available as a result - such information was surely better kept in braille and available for examination in that form. The development of the means to read back from the graph additional information becomes an increased spur in attempting to solve the difficulties in the way of producing suitable graphs, and more detail about the point of reading a graph is included later.

These were the main doubts which accompanied the development of the methods, but there was also one other - namely that there might be some other method - much less troublesome for blind pupils - of recording the information achieving the same results. The methods used for graphical representation had, therefore, to be as free from trouble as possible, but with this achieved it becomes the positive aspect of the techniques that assumes importance, and the benefits which are only to be derived from graphical representation make themselves very clear.

Some advantages of using graphical representation in classes of blind pupils.

Obvious amongst the special advantages of using graphical representation is the fact that this allows the children easily to investigate any acceleration in the statistics collected, e.g. in speeds or in temperature etc. Such increases, or decreases, are quite readily examined in graphical form by our children, but such particulars are not so readily obvious when contained within the statistics recorded only in braille form. Any such investigation demands a sensible use of hands and fingers, and this attitude is one to be encouraged. The teacher is able to direct and develop manual skills, and certain older children have demonstrated their ability to discern and interpret even a change in the rate of acceleration or deceleration as represented by a greater or lesser gradient on the graph. Even the youngest children can be asked to find out information from the resulting chart. Graphs used in this way present very clearly to the children the idea that some changes in a situation may be sudden and marked, and others may develop gently.

The idea of change being suitably represented by graphs as described above leads to the development of a further concept. The children can discover that two dimensions of a shape or of a solid may each change their size, but do so in such a way that their change is related.

Graphical representation allows the changes in size of the individual items to be recorded but also illustrates clearly the relationship linking them. The existence of this fact can be developed well by the use of graphs throughout a whole range of studies. The orderliness of these changes of length, and area, and volume can be made apparent. Such orderliness is not always, of course, appreciated by some blind children, and study of it is worth while, aimed towards a better understanding of the connection and interchange of some facts, ratio, and a greater tidiness of thought when considering the world around them as they feel it. When a study of “a” and “b” are seen to have a relationship in a graph, and then later the-same relationship is noted during a study of “c” and “d”, then this tidiness is being presented to them. Refinements of this tidiness are also available for consideration, and our children have been able to comment - "The graph is the same really except that ......" They were appreciating the connection of y = x, y = 2x, y = 3x, etc.

The latter part of the above paragraph is noted in activities which investigate in many forms what we all recognise as number tables, and such work in graphical form offers the child opportunity to study how the numbers are related as an alternative to “chanting” or memorising what could remain without meaning. Such work which produces the straight line allows the introduction of the idea of

a. the extension of the line beyond the statistics used to build it.

b. drawing information from intermediate points upon the line produced. i.e. an introduction to the conversion graph.

The orderliness of this idea may not be readily apparent to a blind child, and its promotion is of value.

The ability to use a graph for the extraction of information is dependent, of course, upon the talents which the child possesses, but this holds true for all activity in school. Graphical representation encourages from an early age the use of fingers and mind towards that end, and is also a valuable lead into abstract recording of information. Numbers themselves are such abstract representations, and their true values are not always immediately or easily associated by the children with the braille. Understanding of such symbolism needs to be developed carefully, and graph building from an early age encourages the mind towards this.

So far it has not been methods of graphical representation which have been referred to, but rather some mention of the ideas that can be presented to the child through the use of a graph. The ideas encourage the child to

a. search for a relationship amongst the data available around him - to recognise when and why there is a relationship present - and to be aware that in some cases no relationship can be there.

b. to develop from the above work a tidiness of mind which the blind child may further relate to his environment through skilful use of his hands.

c. to accept the use of symbolic representation with a greater understanding, and to relate this more readily in the mind with the reality. (This latter being a difficulty for many children in connection with arithmetic.)

Graphs are used frequently by seeing people and blind children also may derive much benefit from a knowledge of and the building of them. The aims outlined above lead the children through work upon a project which involves thinking, activity, movement, creativity, and accuracy.

The advantages of using graphical representation apply equally to all the children whether they work with straight-line, or curved, or intersecting graph; or whether they work with simpler representations using boxes, or blocks, or rods, or actual models on the graph. All the children develop their abilities at their own standard in this work as they do in all other work in school.

What follows is a summary of the sort of study which can be tackled, and some indication of the apparatus which can be used to good effect.

Simple representations

At first it will be a one to one correspondence which is used and one actual model will represent one actual detail in the study - e.g. one model car will represent one real car in the project, or one model doll will represent one child in the project, etc. Such representations will be used by the very youngest children engaged upon a simple project, which could be, for example, the finding out of how many cars are owned by parents of class 1 children, and class 2 children, and class 3 children etc. For each car owned, 1 model car will be displayed on the graph. The building of such pictographs engages the children upon a whole range of activity and purpose additional to the mathematical content. Such activity demands co-operation, thoughtfulness, carefulness, accuracy, movement, creativity; and these points are relevant also to the projects referred to later although it would be tedious to have them stressed each time. When suitable for the children, the idea of scale is introduced at the time when 1 model car is used to represent 2 real ones in the project. Such pictograms may be built covering a variety of subjects, and their making is a valuable contribution to the child's understanding of the use of symbols.

The building of pictograms as suggested above relates to activities suitable for the very young children, and the apparatus itself should be suited to their understanding, i.e. it should feel correct in itself, and not be meaningless to the touch. Plastic model cars, boats, trains, dolls, etc. can be purchased in bulk, and provide suitable cheap material.

As the child's understanding progresses more abstract representations may be prepared on the thermoform so that pictures in diagram form may take the place of the models on the graph. Representations of boys, girls, cars, bottles, televisions, radios etc. can all be devised, thermoformed in stiff plastic, and used in place of the real models, but only if the symbolism is obviously no difficulty for the individual who is using it.

As each graph is built, and when it is completed, oral discussion between teacher and children is necessary, and the value of the graph can be illustrated by requiring the children to use it to answer questions posed. Sensible use of hands is thus promoted.

Histograms, and Column Graphs.

The children must be led towards the use of square, or block, or dot, to represent the detail of the project, and this stage needs time to be allowed for them to work through many topics so that the symbolism may become thoroughly accepted by their minds. The square, block, or dot does not resemble the reality it represents, and much work is necessary for the establishment of the correct concept by the child.

Use of shoe boxes, match boxes, and unifix cubes provides links between the use of actual models and the use of flat square shapes backed with magnetic material. The first three materials mentioned will create 3D histograms, and the last will achieve a flat representation. Many topics are available for illustration, including the numbers of children in the various classes in school, the numbers of boys, or the numbers of girls, the sizes of shoes worn by children in school, the numbers of different types of pets owned by the children's families. etc.

The use of the individual columns for the extraction of information is again desirable.

Some materials which are suitable for this type of representation have been referred to, others include the use of the 3D board, colour factor, and other structural maths apparatus. It has been useful to have thermoformed paper, guide-columns into which prepared magnetic squares may be placed, whilst the whole rests upon a flat metal base. The paper guide permits of easy writing of details on the axes, and assists any child in building vertically.

The foregoing gives rise to a vast area of activity and uses a wide range of apparatus; both of which aspects would be presented to the children according to their suitability under the given circumstances of the moment. An easy study might be represented by large building bricks which are often available in classrooms for younger children; whilst a more ambitious study, for example about distances, might be represented by other materials more suited to the older age of the children.

The children could be led on to the use of Perkins braillers for the achievement of a more permanent graph upon which the children discern the values as they are represented by braille dots placed in a row. Use of this machine, of course, permits of easy writing upon the graph, the heading, the axes, etc.

Jagged-Line graphs.

The previous representations have been of simple studies of information not closely related. Time comes, however, when it is necessary for the children to observe information which is more closely related, e.g. the changes in temperature, the rise and fall in savings, etc.

The first method of achieving this is by using pins pushed into a softboard base at the relevant points upon the graph-grid which can be prepared by using a spur wheel upon a card sheet. The pins are connected by straight pieces of wire or string facilitating easier study of rise and fall in statistics. This method is well-known and serves valuably in the early stages when a class record is the aim; and larger size is of lesser importance.

At a later stage the children may again be led back to the use of their braille machines. Both Perkins and Stainsby are suitable for this work. Thermoformed graph-grids are prepared with information printed on the axes, and horizontal guide lines for the finger to follow across from the point being read to the information on the left hand axis. The vertical guide line for the finger is put on to the grid by the machine dots to the height required by the statistics. The confusion of too many guide lines on the graph-grid is thus avoided. The thermoformed grids are prepared accurately so that dots are placed by the machine in the precise position automatically as the child writes in the usual way, and the resulting rows of dots correspond with the reference points printed on the axis.

The thermoformed graph-grid is put into a cellophane and braille paper sleeve, and the whole is placed into the machine and a column of dots printed. After this is complete and the graph has been removed from the machine, a piece of rubber sheeting is inserted beneath the "Melinex" so that the tops of the dot columns may be joined by biro and straight edge, thus producing a “raised-line”, rising and falling according to the information plotted. This raised line rests against the thermoformed backing grid and permits of reading by touch. Once the thermoformed grids are available the graph becomes quite simple for the children to achieve, and is a more personal and permanent piece of work.

Relationship graphs.

The progression to the building of graphs about statistics which are more closely linked is not to be rushed, for this is a vital point in the presentation to the blind pupil of the ideas on relationship, interdependence of properties and shapes and solids, ratio, constant rate growth, and increasing rate growth. These ideas are often denied to the blind child's casual observance, and sensible presentation of them is going to have value not only in the context of the work of the moment, but also in affecting the observations which a blind child makes of his environment. A new awareness of points of detail may be encouraged.

The range of topics to be studied is very wide and includes the links between numbers themselves, number tables, conversion graphs, speeds, how springs stretch according to their load, perimeters of x squares in comparison with their side, circumference of a circle and its diameter, the number of turns of a wheel according to the number of turns of the pedal on a bicycle, comparisons of different speeds, the area of a square as against its side, etc. The relationships represented here are not of the same type, and discussion of the mathematical work is not, here, relevant. The whole range of work here indicated depends upon finding the means to record the information.

The greatest barrier in this section was the problem of scale. Sighted graph paper is squared off in tenths of an inch. Blind children could not use a grid to so fine a detail. To very greatly increase the size was to defeat the integrity of the work, and to produce large wall-sized representations whose results may remain valid for examination by the eye yet less effective when considered under touch. Means other than touch were necessary to enable blind children to work to a smaller scale.

The first consideration of relationship graph will probably arise from some group study when a graph has been produced by two or three children working together upon some project. Such group records are made to a scale of half inch squares using a thermoformed grid-paper devised so that a pin may be drawn up along a narrow channel over a number of depressions which are counted so that the pin may be pushed into the relevant one. As the pin goes over each depression a distinctive sound can be heard and, of course, a pronounced movement of the pin can be felt. The resulting positions of the pins are connected by use of elastic bands. Much work has been done successfully by the children using this paper which minimises errors caused by straying fingers from one grid-line to the next when plotting the points, because in this case the pin is fairly secure in its travel up its grooved guide line. Many relationships have been illustrated by the use of this apparatus in group work.

For greater freedom in individual work, two systems have been devised allowing the blind child to achieve a graph by use of mechanical apparatus.

The Perkins machine can be used to produce both straight-line and curved graphs by making use of the spacings of the writing head, dot positions, and roller winding. When working to the larger scale the spacings across are counted according to the scale chosen for that axis and the number of times the space bar is pressed. Working across, therefore, gives rise to no worries. In order to represent the positions up the graph, the keys for dots 3 and 1 are counted as points 0 and 1 respectively. When the paper is rolled into the machine for one space, points 2 and 3 are now represented by keys 3 and 1. When the paper is further rolled in, keys 3 and 1 give the positions for points 4 and 5. So the fixing of points up the graph becomes a simple matter of counting upon keys 3 and 1 as the paper is rolled further into the machine. The required point is represented by a dot caused by the depression of either key 3 or key 1. This scale allows 35 positions along the “x” axis, and 50 along the “y” axis. Thus the graph is plotted mechanically, and the positions are recorded by dots.

    (A smaller scale can be achieved by inserting a stop-screw into the groove on the Perkins machine beneath the line spacer knob. This allows the use of key 3, key 2, key 1, followed by the partial rolling in of the paper by depressing the line spacer as far as it will go, and then further use of key 3. Thus 4 dot positions can be achieved close together within one range of the roller movement as compared with 2 on the large scale as outlined above. The small scale allows 34 recording positions along the “x” axis and 95 recording positions along the “y” axis).

The other machine which will allow blind pupils to work to a very fine scale has been devised and hand built specially for the purpose. It depends upon the use of sound for movement of a "y" axis across a "Melinex" and braille paper sleeve inside which a rubber sheet has been inserted. The "y" axis is moved mechanically and its position above the graph paper determined by counting of the required number of “clicks” which occur after each movement of one eighth of an inch. The "y" axis can thus be placed in any of 900 positions along the "x" axis. Similarly any of 68 positions up the "y" axis may be fixed by sound, and a pin inserted through the graph paper and rubber sheet. A series of points is thus recorded by pins correctly positioned mechanically and by sound, to a very fine scale.

In each of the two previous paragraphs, graph points have been plotted accurately to a fine scale without the burden of using touch upon a very delicate graph-grid.

If the Perkins machine is being used then the "Melinex" sleeve has to be laid upon a base so that pins may be inserted at the points indicated by the dots, although this, of course, is dependent upon manual skill whilst use of the graph machine is not. Thus both systems arrive at the same point, namely a "Melinex" sleeve having a rubber sheet inserted and pins pushed through at points arrived at by mechanical and auditory means.

The children have next used a piece of “flexicurve” as supplied by E. J. Arnold and secured it according to the shape determined by the pins. A biro then outlines the shape formed by the flexicurve on the cellophane, and a raised line graph results.

The writing of this section has involved the description of new techniques and apparatus, and the explanations have of necessity obscured somewhat the simplicity of the operation, The children have worked quite successfully, and have achieved very satisfactory and accurate graphs.

Information can be read back at intermediate points on the graph, and this has been adequately achieved by the children. If the graph has been made upon the Perkins, information can be read back using a thermoformed "y" axis accurate to the scale and made in rigid plastic. This axis slides across and over the graph to the point required along the "x" axis, and then the graph line can be felt at that point and its value read on the scale. If the graph has been made on the graph machine, it can be replaced against the guides, and the processes for extracting information are, in effect, the mechanical reverse of plotting it.

The use of the above methods has allowed the children to study and make observation and comparison amongst a very wide variety of environmental mathematical topics whose nature was formerly less keenly investigated, and remained only superficially examined.

The methods outlined have presented much work for the children, and it may not be out of place to stress again that the activities have promoted co-operation, thoughtfulness, carefulness, movement, and creativity. Not all children succeed equally well, but many have been surprising in their abilities.

Raised Diagrams

by

W.J.Pickles

I. Drawing for the Blind

1. Validity of the Concept.

A question frequently posed is: "What is the use of embossed drawing to a blind child?". For the purpose of this report we shall not consider its possible aesthetic value, a subject examined thoroughly by Revesz in his book "Psychology and Art of the Blind" (see Appendix 4) but answer simply that it is important as a means of communication. Embossing may be used in conjunction with bright colours to help children with residual vision, who form a considerable part of the total numbers in the schools for the blind. Raised line is interpreted tactually without too much difficulty by children with visual memories. The real problem is to explain embossed diagrams representing three-dimensional objects to children who have been blind from birth and have therefore had no opportunity to form spatial concepts through vision. These formed at the time of the Nuffield aided project about 30% of the pupils in two schools for the blind, Worcester and Lickey Grange.

While in teaching it is vital to bear constantly in mind the needs of all children, whatever their degree, if any, of vision, our main task in this paper is to set out the steps we took to make diagrams meaningful to those dependent on touch alone. This is not to say that we limited our research to the congenitally blind, still less that we were concerned only with specialised means for the totally blind. This would have been utterly wrong in view of the need for the blind to communicate with and be integrated into the normally sighted community. Our aim was that all pupils, whether using touch alone or both vision and touch, should be enabled to understand diagrams and discuss their meaning with fully sighted people who could, apart from braille symbolisation, interpret them equally easily through vision. Ideally blind and sighted together should be able to handle and discuss laboratory apparatus and consider the diagrams which are produced to show its design or working.

2. The need for training.

It was not to be expected that blind children would take readily to a training in interpretation of raised line, since the concept is alien to their understanding and so little has been done to help them with it in the early stages of learning. Several pupils expressed their hostility by condemning a study whose value for any purpose they doubted. We for our part generally avoided research into embossed pictorial representation, but it is clear to us that understanding of raised symbolical diagrams is vital to a full study of Science, Mathematics and Geography and that ability to interpret an embossed map can be of great help to a blind person in improving orientation and mobility. Some information indeed, particularly in Mathematics, cannot sensibly be presented in any other way.

This proposition has not been accepted by all teachers, particularly those engaged in the difficult task of instructing younger congenitally blind children of low intelligence. They feel that it will be sufficient if only the brighter children learn to interpret raised diagrams, and that later. But it is not known how early in life a congenitally blind child can start valuably to learn this. Experience at Worcester has shown that graphic illustration taught and used from as early an age as possible (twelve years) has proved an important teaching aid. It has also shown that some children never achieve real understanding. But we do not know whether these might have done better with an earlier start and more experience on the part of the teacher. Nor do we know if less bright children can valuably be trained. But the opportunity for experiment has now been made a great deal easier by the installation in most schools of the Thermoform 55 vacuum forming machine, on which plastic copies of embossed drawings and maps can quickly be made.

3. Characteristics of drawing for the Blind.

Before discussing in detail methods of producing raised diagrams, it is as well to stress the principle that, whereas sighted people learn from an early age, often unconsciously, to interpret pictures, drawings and plans, to a congenitally blind child this symbolisation is much more artificial. He cannot, for example, learn naturally the conventional use of a line to mean a boundary between two surfaces or a change in plane. He has consciously to learn the conventions which, because of the importance of communication, should be as nearly as possible the same for him as for sighted viewers.

Our first task was to discover which textures and types of embossed line could most clearly be recognised by blind students. We decided that it was better to rely on the judgment of blind pupils with some experience of raised diagrams than on that of novices. Our panel consisted of a number of pupils about eighteen years of age who had used line diagrams continually in their education for at least seven years. These were asked to express a preference for certain types of line on grounds of (1) clarity; (2) comfort in reading; (3) ease of differentiation from other lines; (4) distinguishability from adjacent braille.

Our findings may be summarised as follows:

(a) Line Texture.

A rough line is more readily distinguished than a smooth one. This fact does not imply that smooth lines should not be used. They are valuable for marking secondary or recessive features and were so used by Dr. Leonard at Nottingham and by Dr. Wiedel at Maryland on orientation maps to depict "The side of the road you don't walk on". But lines can be rough in different degrees. If the texture is provided by strings of dots these can be so close as to be indistinguishable, they can be set apart as widely as five to the inch. We found that a line of twenty dots to the inch was very successful. A line of ten dots to the inch was satisfactory, but was too close to the conventional braille spacing. There is a case for standardisation of texture for clear definition of particular features in maps. This means also some measure of agreement about tools for producing embossed lines. But more will be said later about tools.

(b) Line Relief.

It was difficult to experiment accurately with height of line, as we had no optical measuring device. But while practised readers could clearly pick out relief as low as ten thousandths of an inch, particularly if the paper was on a hard flat surface such as a desk, it was found that a height of twenty thousandths of an inch was generally better. In our experiments we were aware that discrimination was affected by the thickness of the line and the sharpness of the crest. We had to take note of the fact that certain shapes flattened more quickly under the finger than others. Good lines were produced from fine string, 25-35 thousandths of an inch thick. The best solution was found to be a line formed by taking Thermoform copies from designs made from .045" solder wire rolled out to give a triangular section of vertical height .035". A round crest was less easily distinguishable than a sharp, but was useful as an alternative.

(c) Useful size of diagram.

A large plan cannot be understood as a whole by touch in the way that it can by vision. In fact the eye does use a scanning glance to distinguish shape clearly, but this movement is much more immediate than that of the fingers. Probably a diagram six inches square is as large as can be taken in as a whole by the fingers of one or both hands, with the heel of the hands placed at the bottom of the diagram and the fingers moved in rotation. Yet with a large plan some 3ft. square some general impression was given to blind students by movement of both the arms and the fingers together. With such very large diagrams lines as thick as ¼" can profitably be used and many plans are indeed made using lines of this size by teachers in schools for the blind, on table tops or on wall boards. We believe that children should learn to interpret from all methods and materials in use and that there are opportunities for learning such interpretation now as never before.

(d) Perspective, Plan, Section, Scale.

The blind pupil can learn to appreciate plan and section drawing, even perspective. But there are greater difficulties, particularly with representation of circular and spherical objects. The problem to the blind of distinguishing scale is more complex than for sighted people. For the latter, clarification is assisted by magnification. Stereoscopic vision provides the impression of distance. Rapid, often unconscious eye movement gives the required restimulation of nerve endings. But with tactual drawings clear definition disappears when details get much closer than 1/10" apart and magnification is not always successful when the size is increased beyond the 6" square, even if the drawing is broken into a number of manageable sections. It is rash simply to magnify printed illustrations and present them in embossed form. When a complex piece of information has to be put over, a series of drawings may with advantage be used, provided that each emphasizes a single point which leads on to the next.

Large embossed maps, one of which must be provided for each reader, can however have their use as a depository of related detail to be examined sequentially and for ease of handling and storing. Yet it may well be that information of this kind provided on a large map can be presented more readily in booklet form. The scale will be smaller and each sheet will carry only a small amount of information For example, when it is desired to relate coalfields to waterways, both sheets can be examined simultaneously if the scale is kept the same. The nearest parallel to this system is that of the lift-up colour drawing on transparent paper often used for Biology lessons and consisting of a series of related drawings lying one on top of the other.

(e) Relief and Texture.

We have already mentioned the question of line height and degree of roundness. We experimented also with various methods of producing different kinds of relief and texture and were concerned to find out the effectiveness of each for a blind reader. Low relief with rounded edge was satisfying visually, perhaps because of light shading effects, and produced beautiful copies on the Thermoform machine. But it did not communicate information satisfactorily to a blind reader. A delightful series of books with low relief published in East Germany proved to have only a limited usefulness. Similarly, reproduction on the Thermoform machine of low objects like leaves was effective only if they were thick or pasted onto cardboard before vacuum forming.

We experimented also with entirely flat relief, and found a tendency for the material within the edge, say, of a flat relief map to press down, so that the reader lost the impression of height and felt only a line, sharper on one side than the other.

A better performance was obtained with thicker plastic (.007" Flovic) and this material was useful for teaching line to inexperienced pupils. For making the relief on the master sheet we found self-adhesive linotile (.050" thick) to be effective, using manilla paper as a base.

There is room yet for much experiment in reproducing different tactile textures on Thermoform copy. Too strong a texture dominates the attention, too weak is lost. Detail can only be simple. A blind student cannot possibly cope with all the convolutions of a normal map depicting for example coal and iron fields. A cut-out area of suitable material glued on to the manilla paper to give increased height, as described above, will give effective results on the Thermoform machine. Scrim, wire gauze, perforated plastic sheet, open-coat garnet or emery paper are all useful, but, though differing on the master copy, will, apart from the perforated sheet, be almost indistinguishable on the Thermoform copy. We found that a line limiting the texture area helped to define the area, provided it was not too highly raised.

(f) Coded Symbols and Lines. Braille Labels.

It has already been suggested that for embossed maps there could be standardisation of line and symbol, as there is for a sighted person on an Ordnance Survey map. Nothing of this kind at present exists. Printing houses have designed their own symbols, one suspects sometimes for the convenience of the transcriber rather than user. A blind student may find the reference to differing keys a source of confusion. Furthermore, whilst he is trying to recognise the meaning of a line, he is also engaged in tracing its course. His powers are in any case limited. Important as it is to give him as wide definition as possible, the coding must be kept simple and the symbols few .

Maps must somewhere include braille titles and instruction; yet some difficulty has been found in distinguishing lines and braille, particularly as the braille, if it is to be recognised as such, has to be read either from left to right or bottom to top. When experimenting with neighbourhood maps we at first caused utter confusion by putting names in the middle of streets. As has been said, difficulty is accentuated if lines are composed of dots with the same spacing (1/10") as braille and unfortunately the Duplatt Taylor machine used by the Royal National Institute for the Blind is structurally incapable of embossing dots closer together than this. We found that the reader is helped if the height of line and braille is different. This is easier to achieve with vacuum forming, as on the Thermoform, than with embossed printing, where everything is geared to a height of .018" and any increase results in flattening. Probably the best course when preparing a Thermoform master copy on manilla paper or aluminium foil is to stick on it a previously brailled label. If Twinstik transfer tape is used, the backing can easily be stripped off with scissor point and the label affixed without further application of adhesive.

We tried the experiment of removing the braille label altogether from the drawing and putting it on another sheet immediately underneath in the corresponding position. The reader could then feel the braille with one hand and the drawing with the other. Another variant consisted in putting the braille label on the back of the drawing. Results were not very conclusive. Readers were perhaps given insufficient training in these techniques. It is certainly true to say that they found interpretation of the map easier when the braille was removed, though they were worried to find it elsewhere, even though in related position. Again, we did not really test whether these uncertainties could have been removed by training.

(g) Conclusion.

We came finally to the conclusion that interpretation of embossed maps and diagrams by blind readers demands not only skill but intelligence. There appears to be an intelligence level below which raised diagrams are not interpreted clearly, or at all. Even some bright children may fail for lack of tactual ability. Reading of braille, essentially by a scanning movement with the finger, is achieved only through a long chain of communication and individuals differ greatly in their speed of reading, not necessarily in direct relation to their intelligence. Interpretation of line demands a greater ability to master spatial concepts than the reading of braille and blind children with visual memories will, as we said earlier, find this easier than the congenitally blind.

Despite these difficulties we have become convinced that, with good teaching, intelligent blind children can learn to interpret diagrams and maps. This diagrammatic understanding is highly regarded by successful students and is vital in some studies, particularly Science, and certainly also in learning to get about.

4. Production of Drawings and Diagrams.

(a) By Printing Press.

Embossed diagrams are either impressed by hand or by a machine which will emboss dots and characters (RNIB) or lines, characters and dots (American Printing House, Louisville). The character of the line or dot must be determined by the shape or pointedness of the tool and the thickness of the zinc sheets between which under normal printing methods the manilla paper is pressed.

We are led to ask in what position in a printed book diagrams can best be placed. The obvious place is alongside the text which refers to it. Yet this arrangement presents problems to a machine operator. The braille transcriber is often a blind person writing to another's dictation; the diagram embosser has to be sighted and works a different machine. A high degree of co-operation between them is needed. The page position of the diagram can be calculated accurately in advance, but even so it takes longer to emboss a diagram than to fill an equivalent space with braille, so that co-operation in timing is also needed. From a printer's point of view it is more convenient to place all the diagrams in a section at the end of the book. This idea is violently opposed by blind readers who point out that the need for constant reference to another part of the book is annoying and distracting.

The least objectionable choice is to publish diagrams in a separate volume. This means yet greater congestion on a school desk, but some teachers do not object, pointing out that the book of diagrams can be kept open on the knee and referred to with one hand, while the other is reading braille on the top. Yet there is a risk that with this method reference to diagrams tends to be avoided. Reference of any kind is immensely harder for a blind reader than a sighted, since he cannot rapidly skip over pages and columns.

We should consider whether there can be better methods for producing books with good, properly placed diagrams. The Solid Dot machine of the Royal National Institute for the Blind has not been used for diagrams. All over the world organisations for the blind are using vacuum formed diagrams and relief both in sheet and bound book form. A beautifully illustrated book of insects is produced by Mr. Okamoto in Japan using screen-printed dot-line diagrams, but this process had made little headway elsewhere. There will be an ever greater need for textbooks, - of Mathematics, Geography, Physics, Anatomy, - containing diagrams. We have already indicated the difficulties incurred by the printing houses when using traditional methods of embossing manilla paper, on which in any case the diagrams will tend to be pressed down through storage and use. Perhaps plastic coated manilla would help for the diagrams, but it would be a nuisance to transcribers to have to select special paper for this. In any case the normal size of British braille books is 13" x 10½'', large enough to demand the use of narrative as well as diagram on any one page, if diagrams are to be incorporated in the text.

An answer may be to use vacuum forming for diagrams. This method allows greater flexibility in production and the resultant diagram wears better. For this purpose we have found that FIovic is tougher than Braillon and, as we have said, that the thicker type of Flovic, .007" rather than the .004", the thickness suitable for braille lettering, affords the best results. It forms well, remains firm when used as a single sheet and binds well experimentally. It is true that the master diagrams have to be made by hand. But this may be an advantage, since it avoids the use of a special machine. There is one problem concerning size of page. The Thermoform machine can take a sheet only of maximum size 11½" x 11", which means that for normal size British books the taking of copies from a master diagram can be done only on the commercial type vacuum forming machine possessed by the Royal National Institute for the Blind and the Scottish Braille Press. The Royal National Institute for the Blind Publications Department has been asked to experiment with this method.

(b) Within the School.

The established method of making lines on manilla paper or on aluminium foil by using a spur wheel on the reverse side has a first advantage, that several copies can be made simultaneously, though there is the disadvantage that the drawing has to be executed in mirror reverse. The American aluminium foil, .005" thick as used by Recordings for the Blind Inc., was found superior in use to the .003" thick foil supplied by the RNIB. We found a compromise - .004" - to give adequate results. Aluminium foil will emboss readily with a variety of tools. Lumps can be raised on small areas and pencils will make a smooth line, though they break easily, except for a carpenter's pencil. We found that the Teflon end of the Howe Press's new slim dotter worked well for this purpose. The aluminium has to be laid on a resilient surface for embossing. The thick geometry mat (R.N.I.B. Catalogue No. 9281) was very suitable for deep embossing but the R.N.I.B. mats Catalogue Nos. 9177g and h with their thinner rubber surface gave a much more even depth in spite of variations of tool pressure. Aluminium sheet is not readily available with a matt surface and the normal shiny surface gives it poor vacuum-forming properties. This can be improved by puncturing it lightly with a pin, especially in the hollows. For Thermoforming we intentionally used sharp tools, which always punctured the sheet except when making a continuous line. For direct use, since puncturing could scratch a user's finger, we employed tools with more rounded ends.

In our experimental work with aluminium foil we compared notes with Mr. Jasha M. Levi "Recording for the Blind" and Professor Joseph W. Wiedel, University of Maryland. The recordings for the blind operators use aluminium sheet to accompany Technical Instruction records and therefore keep to a standard size of 7" x 7". They use an optical reversing projector to project the image of the drawing on to the back of the sheet, on which tracings can be made directly with embossing tools, and both seem to use coarser lines of relief. Fine lines however allow for more detail and take up less space. But their interpretation requires greater skill in discrimination.

In testing tools on manilla paper we felt clearly that a careful distinction had to be made between tools and materials to be used for the blind and those capable of being used by the blind. Some can be used for both purposes with different degrees of efficiency. Manilla paper, especially the thick kind, remains the best all-purpose material for embossing lines. We collected as many existing tools as possible, then designed a series of wheels and points with many different characteristics. We decided that the best plan was to make a single tool with a number of detachable heads, ensuring at the same time that the detachable heads would fit into one leg of a pair of compasses. We looked for a fixed spur wheel of simple type and were lucky to find a commercial tool, the Millward Tracing Wheel, sold by needlework shops at about 20 pence and preferred unanimously by the blind to the R.N.I..B. embossing tool Catalogue No. 9083, price 45 pence.

Another method, using a deposited line to make a diagram set directly in relief on a suitable surface, from which copies are taken on a vacuum forming machine like the Thermoform, is attractive to both maker and reader. The aim, of course, is for the blind reader to feel the plastic copy, not the master diagram.

A variety of materials and textures, as has been suggested, will commend themselves to the ingenious teacher - felt, cord, glass paper, lino. The self-adhesive lino tile has proved useful. It is .045" thick and can easily be cut with scissors and avoids the messiness of direct application of adhesive. Other complementary materials used were Twinstik transfer tape, thin string or fine cotton twine, thicker string for very bold lines, ballotini glass powder for dusting the adhesive, fine spherical glass balls used for reflective signs.

The master drawing is prepared on a background 1" shorter in length and width than the Thermoform frame. Embossed master drawings can be laid directly on to photographs, blue-prints and actual drawings. If it is desired to retain the drawing intact, a sheet of spoiled X-ray film (0.007" thick) (easily obtainable from a hospital) can be laid over it and the embossed drawing mounted on the film. The whole area is then covered with Twinstik and the release paper peeled off. The majority of this paper should be replaced, with only a small blank space left for working.

String can either be laid down with tweezers or be fed down the barrel of a felt pen case. A sharp knife is held in one hand to press down and cut the string as required. Texture or raised area and braille is then added. Surplus stickiness is removed from the surface by powdering it with grade 13 ballotini powder. This improves the air-bleed from the surface during subsequent vacuum forming and enables very sharp reproduction to be made. Finally the whole sheet is laid centrally on a full-size sheet of heavy grade manilla paper, allowing a border of ½" at each edge. The reason for the backing paper and border is to give consistent conditions at the rubber clamping seal whatever the variations of the drawing. A line is drawn round the edge of the central sheet, that is ½" in from the edge of the backing paper, with a spur wheel downwards over a rubber mat. This makes a series of fine punctures at the borderline, improving the vacuum forming characteristics of the master.

Vacuum formed copies are then taken from this master. The special plastic developed for the Thermoform machine - Braillon - has a specially grained matt surface on both sides. We found that blind diagram readers preferred a matt surface; the fingers tend to slip on a shiny surface. It is also known that vacuum forming is more efficient if the matt side is placed downwards, since it allows a more rapid escape of air, which is essential for good vacuum forming. Hence plastic vacuum-formed prints for use by the blind are best matt on both sides. On the other hand a matt surface dirties quickly, so that school notices, for example, are better done with a shiny surface. This problem of the dirtying of plastic sheet which has to be fingered often is a very real one. Static electricity is readily generated on the surface and this also attracts dirt. A practical compromise is to use I.C.I. Flovic .004" sheet, which is shiny on one side, matt on the other.

In this section it now remains only to mention alternative apparatus which may be used in the absence of a Thermoform machine or when only a few prints are required, such as one-off travel maps. Plastic prints can be made from aluminium embossed in reverse on a rubber mat and then placed on a mould. Details of apparatus needed are shown in V Sundry Items, A. To form the mould, a wood frame is made up simply by panel-pinning the ends. The frame and the diagram embossed on foil are laid face down on a table top. The tray formed is now filled with dental plaster mixed with water to a thick pouring consistency which sets in a few minutes. The surface is skimmed off absolutely level. As it sets, plywood is laid on top and panel-pinned through to the sides with a Rampin tool (the use of a hammer is not recommended). As soon as the plaster is set, the whole can be turned over and the aluminium fastened down on to its plaster bed by stapling every few inches round its edge. The completed mould can then be left a week or so to dry out; if this is not properly done, steam will lift the foil when it is heated.

With this apparatus any vacuum forming plastic can be printed. The whole mould should be heated in a domestic oven set at 200°C. Above 200°C the wood starts to burn. 200°C is above the temperature at which suitable plastics like Flovic soften (90° - 130°). But we found that some extra heat is needed in the mould to carry it over the handling time after removal from the oven. Assemble the mould on a block in the order: wood, mould, rubber, wood. Clamp the whole lot tight and cool thoroughly (with cold water in a sink if desired) before loosening.

At the end of this section on making raised diagrams and maps we will repeat our assertion made at the start that there is a real place for these in the education of the blind. We were concerned of course particularly with their use in teaching Science, mainly Physics, and Mathematics. But we also made up maps of the school buildings and, with Dr. J. A. Leonard of Nottingham University, experimented widely with the use of neighbourhood maps for teaching orientation and mobility. We are not sure how far full understanding of geographical maps can be taught to a congenitally blind person. Sighted people tend to accept the shapes delineated in such maps as real, whereas in fact they are highly symbolical, showing views and projections which will not in practice be seen even by an astronaut. However, the continuing practice for the blind child in the use of embossed maps and plans widens his experience and increases his ability to interpret material of this nature.

II. Drawing By The Blind

It is an agreed educational principle that children learn best by doing things. Drawing is an activity of this kind. Should the blind learn to draw, even if the result, by sighted standards, is very low? Teachers, particularly at primary level, doubted the value in itself of learning this skill and still more its ultimate usefulness. The blind have so much to master and inevitably there is this marked stress on vocational need. Yet we felt that there must be three valuable purposes to be served: (1) the stimulus of trying something oneself; (2) the learning of manipulative skill: (it was found that many blind people had no notion of a pencil grip and much preferred a hammer grip); (3) the use of a skill essentially the same as that of sighted people.

We wondered whether sufficient had been done to find tools suitable for the blind themselves to use. So many of the existing tools are heavy and, because of round handles with an embossing wheel at the end, cannot easily be directed. Furthermore, nearly all the tools emboss downwards, necessitating reversal in drawing and turning over of the paper before the work can be felt. Some senior pupils can manage spur wheels, particularly the Millward Tracing Wheel, which gives a good, clean line, capable of variation if certain points of the wheel are cut off. The R.N.I.B. upward embossing spur wheel is hard to control, but, if used with a thick rubber mat, produces a coarse line satisfying to a blind reader. We experimented with rubber mats. It was certainly easier for the blind user, as earlier noted, to control depth of embossing with the thinner rubber mats in the R.N.I.B. Geometry Set (Catalogue Nos. 9177g and h). Similarly it was easier for him to draw on aluminium foil on this mat, provided he uses pencil or, better, the Howe Press tool already mentioned.

Our main endeavour was directed towards experimenting with drawing on thin plastic film over a rubber sheet, giving a rippled line on the same side. This principle is used in the American Sewell Embossing Set, R.N.I .B. Catalogue No. 9173..We found certain disadvantages. The paper clips, even if extra are used, do not hold the film well and buckling occurs. Application of pressure sensitive adhesive instead of paper clips improves anchorage. But the best method proved the simplest, - a few drops of water under the sheet! We found that the film supplied split easily under pressure of the ball point on the ⅛" rubber mat of the Sewell Kit. This happened less with the 1/32" rubber mat now supplied in the R.N.I.B. Geometry Set. Nevertheless the film (.001") was still too flimsy to handle and store conveniently and was not suitable for direct braille embossing.

The solution to finding material suitable both for use and storage has been found in the R.N.I.B. Geometry Outfit, in which a sheet of plastic film is attached to manilla paper in the form of a sleeve, so that a slightly smaller rubber mat can be slipped inside it. When the mat is removed after drawing, the film and manilla sleeve can receive braille together and are firm to handle and store. The best tool for drawing has been found to be a black ballpoint pen, the Scripto. The presence of colour helped both the student with residual vision and the teacher. The fingertips of the blind user become slightly messy, but this pen stains less than most coloured pens

As the Melinex/manilla sleeves of the outfit are rather expensive, a simple rubber-faced drawing board was developed for practice work. (R .N.I.B. Cat. No. 9328). This enables embossed drawing to be done using Melinex film held firm to the board by water adhesion.

We looked at Geometry kits from several countries before recommending the R.N.I.B. Geometry Kit. In the Bonham Geometry Set, still extensively used, manilla paper is pressed on a narrow sawblade fixed in a board or rotated over a spur wheel. The device is efficient and in expert hands several copies can be made simultaneously, but is difficult for the less skilled blind pupil and hard to teach with. In an East German set, a hollow rim-wheeled tool is used for drawing over paper with wires set underneath, and this produces upward drawing. A Russian outfit employs the method of making channels in a waxen substance with a blunt instrument.

Before the start of the Nuffield-aided scheme we had begun to try out different kinds of film, as well as the original Sewell Kit film, Melinex, an I.C.I. film of grade S, thickness .001", was found very suitable. Grade E 10, a P.V.C. coated variety .00105" thick was later preferred on grounds of slip and feel, but due to manufacturing hold-ups the recommendation for the adoption of this material was deferred. The best proved to be a P.V.F. film called Tedlar marketed by Du Pont, in a .001" and .002" thickness and coloured white. Unfortunately, though it is tougher, has better slip and gives a better visual line, it is at present much more expensive than the transparent Melinex film of which the R.N.I.B. carry stocks.

It is difficult for a blind student to use drawing instruments and observe tactually at the same time the progress of his efforts. Standard drawing boards and T-squares caused difficulty. The pantograph drawing frame, though promising, was not finely enough made, - a frequent problem with choice of equipment for blind users. At the time when the Nuffield-aided scheme started we favoured the Thornton Drafting Set, which was a drawing board with a sliding bar across it. Then we heard of the Quick Draw Drafting Set, similar to the pantograph board, but commercially produced and much better finished. Both of these were converted into film drawing units, the Thornton Board by merely covering it with a 1/32" rubber sheet, with the intention of using it with sheet Melinex. The Quick Draw Set, with very slight modification readily agreed upon by the manufacturer, took the larger sleeve of the R.N.I.B. Geometry Set and the plastic/rubber faced mat with corners cut off.

All of these devices were tried out under a methodical scheme. First, permanent work by the teacher (illustration and demonstration, based on manilla): second, temporary work by either teacher or pupil (based on Melinex Sheet): third, permanent work by the student, based on Melinex manilla sleeves. On its own at the end came the Thornton Drawing Board, using Sheet Melinex. A number of experimental projects were undertaken under this scheme.

Surface Representation Study 1966.

Proposed Integrated Drawing System for the Blind.

Table: Proposed Integrated Drawing System for the Blind.

III. Experimental Projects

1. Illustrated Primary Readers

Despite our doubts about embossed pictorial representation, we tried out an illustrated primary Reader, the "Janet and Jane" book. Coloured drawings were copied in simplified form using an embossed line made from soft solder, .048" high. Braille and pictures together were bound into a booklet 5¾" x 5½". The line was judged too high and smooth, the drawings, though simple, were not easily interpreted by blind children. "Why", one asked, "was an aeroplane sticking out of Janet's left ear?" We would not at this stage accept the criticism that the whole experiment was unrealistic and artificial. All drawing to an extent is unrealistic and artificial and experience of this kind gained by the blind child may be important for his understanding. We tried again with four little booklets, with the line made from twisted wire giving a height in the embossing of .026". Teachers commented that it would have been better to use double spacing for the braille.

We hope this will not be the end of the experiment. Children's books in braille which omit the sighted child's pictures and diagrams are that much the duller. Direct copies do not help with progressive learning of braille which, with its contractions learned from the start, has a different progression from normal spelling. For reasons not fully proved yet, but possibly connected with visual memory, or the use of contractions, blind children are apt to be poor spellers.

2. Drawing with Blind Children.

Two experiments were carried out: by Miss Audrey Slater at Dorton House and by Mrs. Maureen Pope at St. Vincent's. Children found little difficulty in learning to hold a pen, though they often had to be shown how to use more pressure when drawing. All children showed interest and enthusiasm from beginning to end of the experiments. They recognised their own pictures when the collection was put on a table. Details of the experiments are given in V Sundry Items B and C. It may be significant that neither teacher has renewed the experiment!

3. A Training Programme introducing Diagrams.

A training programme aimed at bridging the gap between reality and representation by Mr. M. R. James of Lickey Grange School is described in V Sundry Items. This makes use of diagrammatic material prepared by a commercial size vacuum former, but similar results could be obtained by using the Thermoform machine. This programme illustrates the transition of ideas from the known to the unknown.

4. Basic Geometry with pupils of selected intelligence.

Geometry has always been considered a difficult study for blind children. At Worcester, from 1961 onwards, we attempted to give our twelve and thirteen year old boys a better understanding of practical geometry. Although it preceded the Nuffield aided study, although instruments at that time were less satisfactory, we were convinced now that a much more methodical perceptual training of blind children should be given from infancy. From this can come experience with models, houses made out of bricks, etc. Growth of spatial experience will, in normal progression, lead to diagrammatic representation of it.

The first step was choice of tools and practice in handling them. The boys were given simple exercises in use of an embossed ruler for measuring and drawing. For a compass it was found that a spring bow, with thread locking mechanism, was needed because the boys could not with a normal compass observe changes of radius during use. They had to learn the practical employment of geometric terms. It proved difficult for them to master the meaning of the word “angle”, though they became used to measuring angles with a protractor and right angles with a set square. Then came the triangle, the circle and subdivisions of figures and lines. Students who took this course expressed the feeling later that it provided a vital stage in the process of understanding and a foundation upon which they could build their later work.

5. Basic technical drawing with pupils of selected intelligence.

In 1963 the course on practical geometry was followed up with one on basic technical drawing. The aim was to improve understanding, not to vie with sighted students. Orthodox drawing instruments proved valueless and the work resulted in the development of the Drawing Aid and later the Thornton Drafting Set with a rubber surface. Drawing was executed on sheet Melinex .001" thick, with a ball pen and compasses. Simple block shapes were made in wood, capable of being handled, and a model of intersecting planes. Plans and elevations were drawn from the shapes. These were followed by drawings of an open topped box.

Geometrical shapes, cylinder, sphere, cube, cone, were attempted, but the execution of sections of these proved a failure. However, the understanding created by related demonstration and explanation proved valuable.

These students, interviewed much later, thought that this short course had improved their understanding of diagrams, particularly representation of sections and spherical shapes.

6. Diagrams for advanced students.

In September 1965 three boys, two blind, one partially-sighted, started to study advanced level physics at Worcester Technical College. The textbook specified was “Intermediate Physics” by G. R. Noakes, a book of some nine hundred pages of close text interspersed with about the same number of diagrams. The transcription of this into braille presented a formidable problem, so the written text was read onto tape. The diagrams were presented in embossed line very much as they occurred in the inkprint copy. Only those with pictorial appeal, such as the photograph of a famous scientist, were omitted. Even three-dimensional ones were attempted. This three-dimensional representation presents an enormous problem to the blind reader, but in this case understanding of the drawings was reinforced by the provision of solid models. An example of this was a model showing the effect of a diffraction grating on beams of light. Because of the use of models we were not able to conclude whether or not the three-dimensional drawings could have been understood in their own right.

To make the diagrams for this project, as only three copies were required, three sheets of Braillon were stapled to a sheet of thin manilla. On the back of the manilla the diagram was copied in pencil in reverse, leaving room for braille to be added. The diagrams were then drawn in reverse with a felt pen and next a heavy impression was made through all four sheets onto a rubber mat. Braille was then added with a stylus and long arm writing frame. The nine hundred diagrams were completed in this way and bound into ring binders, with each sheet reinforced by adhesive washers at the ring.

7. Perspective Drawing.

We were approached by Mr. C. N. Vincent of Birmingham College of Art who felt convinced that he could teach the practice of drawing in perspective to the blind. Very few teachers of the blind would have given Mr. Vincent much hope of success, yet he persevered and attempted trial assessments with single pupils. The theory and practice of perspective is a purely visual concept, using tightly defined conventions. Mr. Vincent's practical system was clever enough to be simple. His sighted students used either a T-square on a drawing board with three concave edges or lined up a straight edge with a grid at the edges of the board. In either case they achieved a drawing in a three point perspective with a minimum of worry or difficulty. As a result of these trials the perspective grid was produced in embossed form on 1/16" rubber sheet some three foot by three foot square. This was stuck down onto a large board and the sheet of film held in place in the centre by water adhesion. Experimental teaching programmes were devised with step by step instructions and diagrams for the drawing of simple objects, a model boat, a table, a reading lamp. These were tried out at the Queen Alexandra School for the Blind, Harborne, Birmingham, with students at the engineering school. It was hoped that some form of drawing might be understood which could be useful to them in their intended work as workers in engineering.

8. The Rolls Royce Design Project.

In Britain there are two braille printing presses, one at the Headquarters of the R.N.I.B., London, the other in conjunction with the Royal School for the Blind, Edinburgh. The R.N.I.B. uses a machine for making master diagrams on to the zinc plates used in printing braille, developed by Duplatt and Taylor in 1930. The Scottish Braille Press had no such machine, diagrams were rarely included in text, and then had to be hand punched.

By fortunate chance we learnt that the firm of Rolls Royce was seeking design projects for a group of graduate trainee engineers. We suggested that they should consider designing a diagram-master making machine, specifications were drawn up and the proposal accepted. The design team, with a budget of some £ 1,500, completed their project within nineteen weeks and handed the machine formally over to the Scottish Press without charge. The machine has been put to work immediately, producing embossed drawings to accompany a text on Modern Mathematics.

Not only have Rolls Royce Ltd. donated the machine, but they have made the drawings available to approved organisations or firms wishing to copy it.

IV. Abandoned Projects

If only to avoid others wasting time on fruitless experiments, a number of processes tried and abandoned are described briefly hereunder.

1. Pressure printing of embossed diagrams from etched blocks.

2. Similar to the above, with the co-operation of Rank-Xerox Ltd., using Xerography instead of photography.

3. Thermographic Process Plastic powder is melted on to wet printed lines.

4. Screen printing.

5. Chemically treated papers and inks.

V. Sundry Items

A. Apparatus required for making Plastic Prints.

2 pieces of block-board or ply 12½" x 11" x ¾". Number of pieces of wood 12½" by 5/8" by ½". Number of pieces of wood 11 in., by 3/8" by 1/2". Number of pieces of thin ply 12½" by 11" by 4mm.

Panel pins 1 in.

Panel pins ¼ in.

An office stapler

4 "G" cramps 4 in.

1 Rampin tool.

Bag of dental plaster

Aluminium Foil .004" x 11½" x 11" for making diagrams

Rubber mat (R.N.I.B. Geometry Mat) for making diagrams

B. An experiment in "drawing" with a class of young blind children.

Spring Term 1967, and Summer Term. Dorton House School.

(Owing to a measles epidemic there was considerable absenteeism resulting in lack of continuity).

Pupils with some sight were given "sighted" materials, including felt pens. Those without used ball pens on "Melinex" sheet over rubber surfaced boards. The boards were made with sticky edges to prevent the film from slipping.

There was very little difficulty in teaching the correct way of holding a pen. Some children had to be shown how to use more pressure when "drawing".

All children showed interest and enthusiasm from beginning to end of the experiment. Children recognised their own "pictures" when the collection was put on one table.

13/1/67 Children given the opportunity to draw a "picture" of their own choice.

20/1/67 Toilet articles which are handled every day.

27/1/67"My Dormitory". A discussion first as to what could be included. Children encouraged to use all the space available.

3/2/67 A picture of "Myself".

10/2/67 Percussion band instruments. These again are objects which are frequently handled. An attempt to rule lines.

17/2/67 Tracing around various shapes - circles, squares, triangles.

24/2/67 Own choice of picture.

3/3/67 Map of road walk. Preliminary to this, mobility lessons had included this walk. The walk had been made with bricks and with lengths of wood on the classroom floor.

10/3/67 Plan of hard playground area. (This is frequently used).

17/3/67 Tracing shapes (domestic animals). Holiday.

21/4/67 Own choice of picture.

28/4/67 An attempt at some repetitive pattern.

5/5/67 Various fruits.

12/5/67 Cuisenaire Rods (of varying lengths).

19/5/67 A trident aircraft. This was suggested after a visit to Heathrow Airport, where the children had the opportunity of boarding the aircraft and of "looking" at wings, undercarriage, etc.

16/6/67 Tracing around "mosaics".

23/6/67 Own choice.

30/6/67 B.B.C. "Stories and Rhymes" story "illustrated".

14/7/67 A further attempt at a pattern.

The work of four pupils was selected for study, not on grounds of ability, but because their work ran in a continuous series and all were totally blind. These were:

Johanna G., b. December 1959. I.Q. above average. Uses hands extremely well.

All Johanna's work was realistic and had meaning. Her human figures were all "stick men" in front elevation. These were drawn quite happily "on the floor" when included in a room. Her orientation was obviously related to the drawing of "a walk", as was her drawing of a friend's house, which was done as a ground floor plan. Her drawings of common objects were easily recognisable.

Paul R., b. December 1958. I.Q. average + Uses hands extremely well.

All Paul's work had meaning, especially drawings of common objects and local orientation. With some optional subjects he set himself rather grand subjects (beach and sea, with liner and motor boat and whale). Any resemblance of his drawing to these must have been in his imagination. His drawing of a Trident aircraft was most interesting (as were the others). The pupils had been shown round this plane on a school trip. Their drawings amounted to sequential plans of the features they had examined (e.g. cabin seats and landing lights) and bore no resemblance to our conception of the appearance of an aircraft.

Peter W., b. October 1958. I.Q. above average. Uses hands extremely well.

His work was very similar to Paul's and his execution improved with practice. He was more realistic with optional subjects, although these were treated very simply, and he was possibly filling in the rest in imagination. Miss Slater writes "It is interesting to note that Peter's early pictures of vehicles are "upside down". I realised that this was how he "saw" them. The top of the vehicle was, to him, nearer than the bottom and therefore he has represented them in this way on his sheet of Melinex. Note, too his pictures of animals of June 23rd. Also, when Peter was tracing round shapes, he would hold his shape firmly in one hand, and, with his pen in the other, would walk round the table to achieve the shape on the Melinex."

Paul L., b. February 1959. Average to below. Very poor spatial concept. Poor use of hands.

Paul could trace round shapes, but did not succeed in creating outlines with any obvious connection between them and what they were reputed to represent. His drawings without exception appeared to be random lines wriggling across the page (other than the tracings). No understanding of the concept of an embossed drawing appeared to have been achieved. Miss Slater writes "Except where some guidance has been given, most of Paul's efforts at "drawing" have a left to right movement (connection with reading movement?)".

C. An experiment in drawing with 10 - 12 year old blind children. St. Vincents School.

All the pupils were given the same instruments, ball pens, Melinex and rubber faced boards. The boards were made with sticky edges to prevent the film from slipping. Mrs. Pope's approach might be described as more geometrical than Miss Slater's. She used largely commercially made tracing shapes consisting of geometric and model shapes. Only one of her drawings related to the child's surroundings.

Name

Age

Blindness

I.Q.

Jonathan

12

  

(107)

Eammon

12

  

(106)

Leslie

11½

 

(102)

Richard

11½

T

(104)

Frank

11¼

T

(111)

Andrew

11

  

121

James

10¾

 

132

Mark

10½

T

135

Pat

10½

  

116

Neville

10

  

(100)

Bernadette

12½

 

(104)

Kathleen

11¾

T

(116)

    (T for totally blind)

Drawing Scheme

Paper I. Practice drawing round various shapes - lids, boxes, geometric shapes - triangles, polygons, etc. tracing shapes.

Paper II. Free drawing of

1. T.V. set on legs

2. man pushing a wheelbarrow

3. garden tools

Paper III. Each child given (from the mosaic shapes) a large and a small triangle and an oblong. Use them to make any pattern he likes.

Paper IV. Given choice of large geometric shapes and rules as above.

Paper V. Mixed all the shapes together and let them choose.

a. 5 chose to draw free hand including 2 totally blind (Frank & Richard).

b. Rest chose a vehicle shape (bus, plane etc.) plus 2 or 3 larger geometric shapes.

All the class very keen and getting great enjoyment out of it.

Paper VI. Using wire shapes, including arrow, ellipse, spiral, etc.

Paper VII. Using a ruler and biro only draw these figures.

1. a square of side 1"

2. a rectangle 2 x 1

3. a circle at size of a penny, a half penny

4. an equilateral triangle of side 1"

5. an isosceles triangle

6. a spiral

7. an ellipse

8. an arrow

Triangles, spiral and ellipse were found to be most difficult.

Paper VIII. Drawing around cubes of different sizes and shapes to try and get the children to understand area, plans, etc.

The work of the four totally blind children, Richard, Frank, Mark and Kathleen was examined in detail. This is hardly a surprising observation, but in the diagrammatic drawing, the correlation between I.Q. and representational ability was striking. The other drawings did not reveal much information; they represented the child's acquisition of mechanical skill and factual knowledge rather than representation of capability.

D. A Training Programme introducing Diagrams.

The teacher can start with the classroom, strips for walls and movable blocks for furniture (magnetic rubber strips and rectangles on a tin-faced board can be used effectively). The scope can then be widened, the garden and paths added, then a plan of teacher's house or other less familiar place.

A sense of expectancy should be encouraged: "Is the window opposite the door?”, “What lies behind that wall?”, “How do I get to so-and-so?" etc. This should demonstrate the purpose behind diagrammatic demonstration and exploration. The diagram is also an aid to organisation as well as a scaled down form of representation.

Next comes the jump from the familiar to the unfamiliar, from the house-plan to the Neolithic hut, from the plan of the village to the mediaeval village. The same principles can be applied to ecclesiastical and military architecture.

The series illustrated shows ground-plan developments in church, house, hut and castle, through a logical understanding process. It was designed and used as a series of exercises using quasi-visual material, not necessarily representations as we usually understand them from a sighted point of view, but rather the presentation of symbols to hang information on.

The outlining of features in bold black lines also enabled those pupils with some sight to make use of it to the best advantage. It also provides an introductory series leading up to the use and interpretation of maps.

Appendix 1: Apparatus and Suppliers

Apparatus mentioned in the foregoing pages can be obtained from the following firms:-

R.N.I.B., 224-6-8, Gt. Portland Street, London, W.1.

    Vito Embossing Foil (Black Cat. No. 9035, White Cat. No. 9036)

    Light Probe

    Embossing Compasses Cat. No. 9347

    Multiple Head Embossing Tool Cat. No. 9346

    Flovic, .004"

    Melinex, .001" Packets of 50 sheets, cat. No. 9173b.

    Braillon, .004" and .007" Packets of 500, 100 sheets.

    Drawing Board 11" x 8½" Cat. No. 9328.

    1ft.and 30cm Rules, Embossed

    R.N.I.B. Geometry outfit Cat. No. 9177

To order only, from R.N.I.B.

    Audible Thermometer

    Chain Dial Balance, modified

    "Trumeter" Digital Timer.

    Avometer, modified

duPont (U.K.) Limited, 18, Breams Buildings, Fetter Lane, London, E.C.4.

    Tedlar P.V.F. Film

From retailers or Philips Limited, Century House, Shaftesbury Avenue, London, W.C.2.

    Cassette Recorder

    Electronic Engineer Kit

Radionic, St. Lawrence House, 29-31, Broad Street, Bristol, BSL 2HF

    Radionic Kit

Evode Limited, Common Road, Stafford

    Twinstik Transfer Tape

Jencons Scientific Limited, Mark Road, Hemel Hempstead, Herts

    Ballotini

From retailers of dress materials.

    Millward Tracing Wheel

Thermoform Corporation, 8659, East Slauson Avenue, Box 125, Pico Rivera, California, 90660.

    Thermoform Vacuum Former

    Braillon

To order only, from British Thornton Limited, P.O.Box 3, Wythenshawe, Manchester 22.

    Thornton Drafting Unit, Modified.

To order only, from Quickdraw Co., Ltd., 10, Beechdale, Winchmore Hill, London, N.21.

    Quickdraw Drafting Set, Modified.

James Neill Limited, Napier Street, Sheffield, 11.

    Magnetic rubber tiles

    Magnetic Tape

Magnetic Applications Limited, 323, City Road, London, E.C. 1

    Magnetic tables

E.S.A. Limited, Pinnacles, Harlow, Essex.

Philip & Tracey Limited, Fulham, London, W.6

Invicta Plastics Limited, Educational Aids Division, Oadby, Leicester.

Taskmaster Limited, Clarendon Park, Leicester.

E. J. Arnold & Son Limited, Butterley Street, Leeds, LS10 1AX.

    General Educational Apparatus

Chellwood Precision Machining, 24 Chellwood Road, Chellaston, Derby, DE7 1SJ.

    Embossing Pliers

Ever Ready Battery Co. (Great Britain) Limited, Wolverhampton, Staffs.

    Type D23 Battery

The Torsion Balance Co. (Great Britain) Limited, 694 Stirling Road Trading Estate, Slough, Bucks

    Torbal Balance

Fisons Scientific Apparatus, Bishop Meadow Road, Loughborough, Leicestershire, LE11 0RG.

    Fi-Monitor

R.S. Limited (Components), P.O. Box 427, 13-17 Epworth Street, London, EC2P 2HA.

    Electronics

Griffin & George Ltd., Frederick Street, Birmingham, B 1 3HT.

    All Biology, Physics and Chemistry Apparatus

(This firm has Branches all over the world)

Appendix 2: Bibliography of Science Books

"A” Level Physics

Text: *"New Intermediate Physics"
G. R. Noakes (abbreviated in 25 volumes - see article)
pub. Macmillan

Practical: "A Laboratory Manual in Physics"
F. Tyler
pub. Arnold

Practical: "Sixth Form Practical Physics"
E. Armitage
pub. John Murray

Extra Reading (“A” Level)

"Advanced Level Atomic Physics"
G. M. Mossop
pub. University of London Press

"Modern Physics"
Caro, McDonnell and Spicer
pub. Arnold

"Nuclear Energy"
L. A. Redman
pub. Oxford University Press

"O" Level Physics

*"Ordinary Level Physics"
A. F. Abbott
pub. Heinemann

"General Physics"
C. W. Kearsey
pub. Longmans

General Science Books

**"Chemistry" (General Science)
A. W. Wellings
pub. John Murray

**“Physics" (General Science)
W. Ashurst
pub. John Murray

**"Biology" (General Science)
Mary Green
pub. John Murray

Biology

**"Biology for General Science"
W. R. Barker
pub. Longmans

**"General School Biology"
Brocklehurst and Ward
pub. English University Press

FOR MORE UP-TO-DATE WORK (Sighted only ).

Chemistry (for "O” Level)

"A New Certificate Chemistry"
Holderness and Lambert
pub. Heinemann

Biology (for “O” Level)

"A Concise Biology"
Barker and Springthorpe
pub. Heinemann

Braille Books

Those marked with asterisks are available in brailled form.

    * = available with most diagrams brailled

    ** = available mainly without diagrams

Appendix 3: Bibliography of Mathematics Books

The following represents a useful list of mathematics books. All are in braille unless stated.

O-level books

New General Mathematics, by J. B. Channon, A. McLeish Smith, H. C. Head, published by Longman. (Braille book without answers, 1970 code).

Mathematical tables. Tables of logs, antilogs, squares, square roots, the six trigonometric ratios for degrees and minutes are published by R.N.I.B.

Tables of reciprocals, logarithmic trigonometric tables, Napierian logs, tables of ex and e-x, sinh x and cosh x, degrees to radians, various statistics tables are available in thermoform at Worcester.

Note also: Modern Mathematics for Schools, prepared by Scottish Mathematics Group, published both by Blackie and by Chambers. Published in braille (five books, four volumes to each book) by the Scottish Braille Press, Craigmillar Park, Edinburgh, EH 16 5NB.

A-level books

Pure Mathematics - a First Course (Second Course), by J. K. Backhouse, S. P. T. Houldsworth (B. E. D. Cooper), published by Longman. (Braille book in 1970 code).

Higher AIgebra and Higher AIgebra for Schools, by W. L. Ferrar, published by Clarendon Press, Oxford. (Braille books in 1955 code).

An Introduction to the Infinitesimal Calculus, by G. W. Caunt, published by Clarendon Press, Oxford. (Braille books in 1955 code).

Geometry for Sixth Forms, by C. O. Tuckey and F. J. Swan, published by Longman. (Braille book in 1955 code).

An Introduction to coordinate Geometry, by A. Barton, published by University of London Press. (Braille book in 1955 code).

A Shorter Intermediate Mechanics (1949 edition), by D. Humphrey and J. Topping. (Braille book in 1955 code). Book written in British units, with g = 32 ft/s2.

Books of past examination papers of the Oxford & Cambridge Schools Examination Board, in thermoform at Worcester.

The Midlands Mathematical Experiment (not in Braille) by Cyril Hope. Published by George G. Harrap & Co. Ltd., 182, High Holborn, London, W.C.1.

Mathematics available in Thermoform

CLARKE, L. H.
Ordinary level Mathematics.
Heinemann Educational, 1958

CONTE, S. D.
Elementary numerical analysis; an algorithmic approach. (Series in information processing and computers).
McGraw-Hill, 1965

JOHNSON, D. A.
Curves.
(Exploring Mathematics on your own, 14)
Murray, 1966

Probability and Chance.
(Exploring Mathematics on your own, 15)
Murray, 1966

LINDLEY, D. V. and MILLER, J. C. P.
Cambridge elementary statistical tables.
C.U.P., 1968

NORTON, M.S.
Basic concepts of vectors.
(Exploring Mathematics on your own, 16)
Murray, 1966

Finite Mathematical Systems.
(Exploring Mathematics on your own, 17)
Murray, 1966

SCHOOL MATHEMATICS PROJECT
Advanced Mathematics, Book I: metric.
C.U.P., 1970

Advanced Mathematics, Book II: metric.
C.U.P., 1970

Advanced Mathematics, Book III: metric.
C.U.P., 1970

Appendix 4: Bibliography of Books on Drawing

G. Revesz.
"Psychology and the Art of the Blind"
Longmans. First published 1950.

Moji-yo Konchu zukan
”An illustrated book of insects, for use by blind children”

General Supervisor: TORII Tokujiro
Supervisor: TANIGUCHI Magoichi
Editors: OTA Osamu, SAKURABA Osamu
Braille Printing: SUGIMOTO Kyuichi
Illustrator: Okamoto Yozo

Published privately at Kyoto. No date.

Appendix 5: Current Research into the Teaching of Primary School Science

by

S. O. Myers

A Science Teaching Project has been initiated by the Research Centre for the Education of the Visually Handicapped, School of Education, University of Birmingham. This project has two interests: the teaching of science to primary school children aged 5-11, and also to secondary children aged 12-16. The primary school children have the full range of intelligence and ability, but, where the Science Teaching Project is concerned with, secondary school children, it will concentrate on the needs of children of average and below average ability.

The Research Centre wishes to stimulate the active interest of practising teachers so that the Teaching Project will have some of the features of a consumer research enquiry. Mr. S. O. Myers, Senior Research Associate of the Research Centre, who, at present, is developing the Science Teaching Project, has initiated a first phase programme based on co-ordinating existing ideas and practical teaching schemes. Meetings of teachers have been held and the Research Centre has printed and circulated copies of ten articles contributed by teachers describing a variety of science teaching activities.

The co-operation of head teachers and teachers of science having been readily gained, the way is now clear for development of the Science Teaching Project. To date it has involved Schools for Blind Children only, but the range of activities should be extended to include Partially Sighted Children. Also, from the consideration of science teaching schemes already in existence, we should begin a study of the number of newly developed science projects for seeing children. With the co-operation of practising teachers it will be possible to examine such schemes and consider their relevance for visually handicapped children and possible revisions and adaptations. In addition, the Science Teaching Project would like to initiate discussions and investigations from the point of view of the special needs of the children in order to consider whether it is necessary to develop some special curricula.

The Research Centre therefore is now initiating two lines of enquiry for its Science Teaching Project. These cover the whole range of visually handicapped children considered to be the Project's responsibility. Although there are considerable differences between the two enquiries, there is the fundamental common factor of the pupils’ understanding in a practical way of their environment.

1. The first project concerns primary school children and will be an investigation of the Science 5/13 Project which was sponsored by the Schools Council, the Nuffield Foundation, and the Scottish Education Department. The books for the 5/13 Project are being published in 1972 and 1973 by Macdonald Educational, St. Giles House, 49 Poland Street, London W1A 2LG, and are based on children's discovery and exploration of their environment. This approach is particularly relevant to the needs of handicapped children, particularly the visually handicapped. After preliminary discussions it is hoped that the Centre's Science Teaching Project will initiate field trials of certain parts of the 5/13 Project reporting back on any adaptations, revisions, omissions and replacements which would make the materials and methods of presentation for visually handicapped children. Since much of the work is environmental study and since the books are addressed to teachers urging them to select work which is suitable for their own classes, the whole scheme seems most attractive for teachers of the visually handicapped and a challenge to them to adapt it for their children. The Science Teaching Project would help by centralising and circulating opinions of teachers in many schools, who can easily feel themselves working in isolated conditions.

2. To date, a single scheme for seeing secondary pupils does not present itself as suitable for such enquiry and adaptation for visually handicapped pupils comparable with the 5/13 Project and primary school children. Therefore, the Science Teaching Project suggests that attempts should be made to formulate a statement concerning the areas of science of which school leavers should have knowledge and experience, bearing in mind always, of course, the needs of adolescents of average and below average intelligence and ability.

Appendix 6: Further Notes on Teaching Science to the Blind

by

S. C. Stephenson

The original article in this publication contains much that is still relevant with regard to the teaching of Science at this College, but there have been some developments since it was written. It is the purpose of this report to bring the story up to date.

We have now confirmed our earlier view that brailled diagrams are extremely useful, (indeed, almost essential), in Science teaching here. They are valuable aids to comprehension to replace blackboard and textbook diagrams. (Developments in embossed diagram work are reported elsewhere). We now have textbooks for the G.C.E. Ordinary Level and Advanced Level examinations in Physics which carry a good complement of diagrams in embossed form and, in addition, we have built up a library of braille master drawings from which copies for every pupil are duplicated on our Thermoform copying machine. We find that diagrams should be introduced at a suitably early age in a pupil's school career - at a time dependent on the degree of maturity of the particular class - and one must be prepared to start by teaching diagram interpretations. By the third year, at least, most pupils are fairly adept at reading new diagrams. The diagram is, of course, only an adjunct to verbal explanations and the use of models, experiments and demonstrations. Needless to say, direct copies of sighted textbook diagrams are not always very useful; one must be prepared to draw one's own diagrams - sometimes using several, each to illustrate one aspect of a sighted drawing, bearing in mind the special perceptual problems of blind persons.

More brailled literature in Science is now available and we have “O” and “A” level Physics textbooks with diagrams in braille form. I have had to abbreviate the “A” level textbook in order to have it brailled, but, even so, it amounted to 25 volumes! We have braille literature for Biology and Chemistry containing teaching material up to General Science “O” level only, but this is almost completely devoid of diagrams.

We are using more magnetic tape recordings to which the pupil can listen in his own time. It is better if these are specially prepared by the teacher than to buy school tapes intended for sighted persons. However, it is through magnetic tapes and the services of qualified readers (doing voluntary work in pupils' free time) that we try to keep the most interested boys as up to date as possible in this ever progressing subject.

The same limitations as mentioned in the previous article still apply to this school, so that we are able to teach Biology and Chemistry only, in general, to junior forms, but extra tuition is given by staff in out-of-school time whose pupils wish to study further in these two branches of Science. Two boys have studied more Chemistry and one obtained a good grade at “O” level in this subject. Another boy is hoping to emulate him in 1973 and another boy is studying Science more generally, especially Biology. (It should be noted that our examination Board does not require a practical examination at “O” level).

To this standard I have found that I have been able to add considerably to the pupils' interest by performing many small scale "test-tube" Chemistry experiments and that only a moderate stock of basic chemical apparatus is needed. One also needs a carefully chosen stock of chemicals. Comprehension of chemical reactions can be aided by smell, noise such as fizzes and pops, standard gas tests, sometimes by taste and often by the use of the light probe. The electronic thermometer for the blind also helps in a number of cases. The light probe can indicate colour changes (e.g. illustrate the difference between hydrated and anhydrous copper sulphate) by reflection, and can show the formation of precipitates by the blocking of the light transmitted through glass apparatus by such a reaction. It is possible to give some idea of titration colour changes with the usual indicator dyes and the light probe, but we have found that an audible pH meter can be produced, to special order, for the blind.

We have added to our collection of models and bones for Biology teaching and we find that by rearing small animals and studying them and by using the growing vegetation in the College grounds, we can add to interest. We perform simple growing experiments with plants and carry out elementary soil analysis and do a few other simple experiments in this subject. Experiments are going on elsewhere in Biology teaching to the blind.

From the apparatus point of view we have benefited very much from the fact that the R.N.I.B. has been successful in obtaining commercial production of (1) chaindial (electronic) balances which are brailled, (2) digital timers (stop watches working to 0.1 seconds with brailled read-out in digital form), (3) electronic brailled thermometers, (4) light probes, and (5) metre rulers brailled in centimetres and half centimetres. Consequently, we have advanced from having just a few of the above to having enough for full class use. This has enabled us to extend our class experiments very considerably. We also have an R.N.I .B. brailled micrometer gauge reading to 0.01 millimetres for senior pupils to use.

We purchased a commercial digital balance (Torbal) to try it out. This does not require weights; it has brailled numbers in the read-out windows and has superior electronic indication to that used in the chaindial balances. With its aid a junior pupil can weigh to 0.001 gramme accuracy in a minute or so. However, the snags are:- (1) high cost - over £200, (2) too great a sensitivity and, (3) it needs mounting on an extremely rigid (stone) support because it is so sensitive. I find that one must teach a technique of use and one must slightly modify the system or inexperienced juniors may be a little confused by its sensitivity.

The next few paragraphs refer to “O” level Physics apparatus. The heat syllabus has been modernised to a type of Nuffield Physics by making use of the 12 volt 50 watt immersion heaters. This greatly helps with the teaching of. S. I. units which are now used in examination questions. At the same time it makes the subject a little more interesting to pupils, we find, and it certainly reduces the tedium of some of the calorimetric calculations.

Other "Nuffield" materials have become available and thus we have been able to extend the junior experiments in heat e.g. use of styrocell beads to show expansion, use of silica to contrast with glass in expansion, use of various rods to show variations in heat conductivity. We have, also a joule meter but, at present, this is only of use to the teacher using electrical methods in latent heat and specific heat demonstrations. At present, the joule meter cannot be brailled but if this could be done it would be most useful for pupils. The problem is a commercial one. I use an audible electronic infra red detector and thermocouples with light spot galvanometers (light probes show meter currents), also, in heat experiments. (It was necessary for us to carry out a small electronics job to render the infra red detector audible).

We have extended the range of class electrical experiments by purchase of a number of sturdy coils and rheostats. It is surprising how many experiments this had added to the repertoire. The College is fortunate in possessing a specially designed electronic voltmeter/ ammeter in braille read-out form. This is an audible instrument and can be used like an electronic thermometer for quick voltage or current measurements but, as yet, this is more or less a patent device in prototype form; but we can give details if more information is desired. We still use the ordinary voltmeters and ammeters (preferably large scale devices) for most class work since these instruments must be studied for examination purposes and because they are easy to use with a light probe.

The following are some of the other devices we have introduced:-

1. A linear air track and centisecond timer, which, with photocell control, enables various mechanics experiments to be performed more accurately and more interestingly. The timer (working to 0.01 seconds) can be fitted with a home made braille scale.

2. The water ripple tank and stroboscope to study wave phenomena. We have found it useful to give a better idea of the more complex phenomena but one must rig up special light detection devices to show the effects and carry out measurements.

3. An audio oscillator and accessories is very useful, we find, both for sound experiments and as an indicator device in other branches of Physics. Some idea in sound interference and diffraction can be roughly demonstrated, but we use the most useful 3cm. wavelength radio transmitter/receiver to back up all wave phenomena work.

4. Alpha, beta and gamma sources of radioactivity with means of audible detection and particle counting. We have adapted a spark counter and pulse electrometer for use in this field. Approximate measurements can be made with these set-ups.

5. The Van de Graaf generator and a few modified electrostatic devices are useful to illustrate items in this branch of Physics. The electroscope can be made to influence a light probe and so can be used for demonstration work.

6. We use the Barkausen effect and especially low voltage A.C. to illustrate more clearly what magnetic fields are and what they can do.

7. We find that a number of devices, like the cathode ray tube, the demonstration diode etc. can be used fairly successfully to demonstrate facts about electron behaviour.

8. We are trying to improve the method we use at present for oscilloscope trace detection.

The above all refer to "O” level work. In the sixth form we find we can adapt a very wide range of experiments indeed and obtain very commendable results. Our range of sixth form experiments is quite wide - we adequately cover the syllabus for the “A" level examination. So far we have had four entrants; all have passed with grades “D” or above, one (completely blind) obtained a “B” grade, and, above all, every candidate carried out an excellent practical examination (aided by a sighted amanuensis who mainly acted as a recorder).

Recently, we are using a sighted piece of apparatus called the "F i-Monitor" which determines liquid levels etc. by electrical capacitative detection outside the tube containing the liquid. The monitor operates an audible device (home made or purchased) or operates a relay which will switch 250v. mains 10amps (or 20amps if desired). By use of the relay, the monitor detecting the mercury thread, the device acts as an efficient thermostat by controlling an electrical heater. This monitor avoids troubles experienced with light probes caused by variations in illumination due to persons moving about.

Appendix 7: Computer Education for the Blind.

The electronic digital computer has played a major part in the rapid growth of commerce and technology during the past twenty years. Most large industrial and commercial organisations now operate at least one computer, and many Government departments have very large systems. Scientific research establishments are large computer users too, as are most universities and polytechnics. It is therefore easy to see why, in the past five years, many local education authorities have felt the need to give pupils in secondary schools some knowledge of computers and the ways in which they can be used.

As a rule computer courses in schools have been run as an extension of the Mathematics syllabus, partly because of the feeling that the computer is a mathematical tool, and partly because modern trends in the teaching of Mathematics have introduced the logical concepts which are essential to a proper understanding of the way in which a computer works. There was inevitably at the start a lack of collaboration between schools, and staff who had not the necessary acquaintance with the subject have been called upon to teach with only a few sources of reference. The result of this has been that Computer Programming is often the only aspect of the subject to be covered, and the teachers may lack practical experience of Computers. However, those who become closely involved with computers when they leave school do have some previous knowledge which may be of use to them, while others probably regard the course as another chore of going to school.

But more recently some universities and technical colleges have started Computer Science teaching projects in schools. These projects are usually backed by local authorities, and are providing an opportunity for experimentation in teaching many subjects which might broadly be described as Computer Understanding, rather than Computer Science, which is off-putting to the non-Science pupils.

It is not surprising that there has been a desire to extend these new developments in Education into schools for the Blind. It was even thought at one time that Computer Programming would be an occupation well suited to blind people, but though there are a number of blind people employed as computer programmers, they tend to be those with a particularly strong bent in that direction. One of the major problems has been the difficulty of producing computer output in a form which is suitable for use by a blind programmer, particularly when the final result must be in a form which can be read by a sighted person. A sighted assistant may be useful to a blind person working as a programmer in a research establishment, but this is unlikely to be an economic proposition in a commercial organisation. For these reasons we must consider the teaching of Computer Understanding to the Blind, not as a vocational training, but rather as a part of their general education.

A knowledge of computers and the way in which they work must nowadays form a valuable part of the general education of any student, whether blind or seeing. The chief reason for this is that the computer is now so widely used that it is almost certain that even those who do not work with computers will find themselves confronted with computer output at some time in their life, even if it is only on a payslip or a bank statement. But in the case of blind students there is a further point to be considered, particularly in respect of those who intend to continue their studies after leaving school, by going to a university or some similar establishment.

Our universities probably form the largest single group of computer users in the whole Country. It is thus clear that students following courses in the technical subjects, such as Mathematics, Science and Engineering, will be expected to make use of computer facilities as a normal part of their studies. However, it should be realised that many other subjects find uses for computers, for example in information retrieval and cataloguing and indexing. Whilst in this latter case the student may not have to write the program which is to be used, he may be concerned in specifying what is required, and to do this he needs an understanding of what is possible.

To aid the blind student, a limited number of specialist computer publications have been put into Braille. Usually these are programming manuals relating to the use of one programming language on only one type of computer, and are of little use to the person who is only concerned with the general principle. By teaching the subject in broad terms in schools these problems are largely overcome, and the student who needs to delve deeply may safely do so.

Now we must consider in outline the methods which may be used in the teaching of Computer Understanding to the Blind. Most subjects are taught in a manner very similar to that used for sighted students, but in this subject which is relatively new even in sighted schools, no definite pattern has yet arisen by which we can set our standards. However, the one aspect which most methods have in common is that the pupils are usually allowed to have access to a computer as early as possible in the course. This is done by means of computer terminals, which are simply electric typewriters connected to a computer so that information typed in by the operator will be printed and will also go to the computer, and the computer may send information back to the operator by causing it to be printed by the typewriter. By this means the student is able to hold a conversation with the computer and thus learn the language.

The conversational technique of programming is extensively used both by computer programmers and in education. Its particular advantage for the student is that it helps to maintain his attention since the computer gives him an almost immediate response. However, it has a serious disadvantage in that an instruction which is in error will be reported back to the operator as soon as it has been typed in. This tends to make the student operator less careful than he might otherwise be since he is not aware of the amount of computer processing which is required to analyse his illegal instruction. This could be a lengthy operation which would delay other work being run on the computer at the same time.

In the case of a blind person the standard computer terminal is of no value since its printing is not in a form which he can read. Obviously some type of upward brailler similar to the Perkins is needed, with the facility for being operated either manually or by electrical signals from the computer. Such a piece of equipment probably exists in the United States, but as far as is known it has not yet been successfully produced in this country. Experiments have been carried out by Hatfield Polytechnic in conjunction with Chorleywood College, but because of technical problems a satisfactory design for such a device has not yet been achieved.

Because of the specialised nature of the equipment, a braille computer terminal is likely to be a very expensive machine, and would probably require special servicing and maintenance. Furthermore, since a terminal can only be used by one student at a time, it would be necessary to have several for class work, and the cost would then become prohibitive. Even if the finance were available it would be necessary to provide a special program within the computer to convert the Braille codes into the internal codes for use by standard programs. It would also be necessary to modify a number of messages output by the computer as many of these would be longer than the maximum acceptable length of a Braille line. There would be a similar problem on input where standard programs expected lines of data longer than a Braille line. It would be possible to overcome both these problems in the code conversion program, but this method would not be suitable for tabulated output. There is too a tendency for computers to produce a vast amount of printed paper, even by sighted standards, and if one were to convert all of this into Braille it would be almost impossible to handle. Thus modification of the usual sighted methods would seem to be unacceptable, and we must therefore look for an entirely new approach.

As an alternative to a course in Computer Programming, a much broader approach might be considered. This has the advantage that it is more likely to be of interest to pupils who are not studying Mathematics or Science. At the same time the subject can be taught in general terms without the use of any special equipment, and it is therefore easier to accommodate the course within the normal school budget. It may be desirable, within the framework of a general Computer Understanding course, to spend some time in writing programs, but this should only be attempted if facilities are available to run such programs on a computer and produce output from the computer in a form which is acceptable to the Blind. But this practical part should only form a small portion of the course although some students may wish to take it further in their own time and they should be encouraged in this.

By teaching the subject in a non-technical way it is possible to avoid the jargon and special features of individual computer systems. Instead the pupils should learn the fundamental principles of operation of a computer and study in outline the history and development of computers. They should learn about the various pieces of hardware which comprise a computer installation, and they should understand the properties of different data storage media. Logical processes should be explained, and pupils should learn to write a sequence of logical instructions as a prelude to writing a computer program in some high level programming language. The importance of accuracy in data and program preparation should be emphasised, by means of examples if possible. The applications for which general purpose computers are used should be discussed, and one typical application; such as a payroll system, might be described in detail. Some specialised computer applications might also be looked at particularly if they are topical, but it will not be possible to go into any great detail. The effect which computers have had on Society may provide a field for some lively class discussions, especially as this aspect is likely to be of more interest to the less technical students.

There is a great lack of standard text books covering the subject of computer education, and barely any suitable material in Braille. It will therefore be necessary to produce such material locally. As mentioned above, pupils should have to write logical sequences of instructions, this method being used in preference to flow diagrams. Diagrams may be useful to describe a process in outline, but Braille diagrams become much too complex to be used to describe a process in fine detail. It would also be valuable to provide samples of paper tape and punched cards for students to examine: these are readily available from any computer installation. A visit to a computer installation may be useful, but more for the purpose of meeting and talking to the people who work there than for examining the equipment. There is little enough to see, let alone feel, in a computer room, and anyhow most computer managers guard their machines most jealously. However, a few sample pieces of computer hardware may be exhibited in a school museum.

It is not yet clear when is the best time to introduce blind students to computer studies of any sort. At Chorleywood the subject is taught from the fourth year upwards, and this has proved very acceptable. But Chorleywood is fortunate in having Miss A. M. Sims, who is keenly interested in Computer Science, and has taken special training in the subject. There has also been a great deal of assistance from the staff of Hatfield Polytechnic, whose schools’ Computer Science course is followed by the girls at Chorleywood. This course is of a very practical nature, the pupils having access to a computer on which they can run programs, and it is unfortunate that the girls are unable to get results from the computer in a form which they can read for themselves. They do use a computer terminal, but with the assistance of a sighted girl who reads back to them what has been printed.

At Worcester an experimental Computer Understanding course is being run as part of the Sixth Form General Studies syllabus. The subject is being taught in very broad terms, and as yet no programs have been run on a computer, purely because printed computer output is of no use to the Blind. Computer time is available with a local firm, should it be needed, and a means of converting output into Braille is being sought. However, it is unlikely that an on-line terminal will be used since this could become just a means of wasting computer time rather than a valid teaching aid. It is not our intention at Worcester to train competent computer programmers, and so little, if any, of the value of the course will be lost if no programs are written. But we are looking into the problem of computer output with some urgency.

From the above it will be seen that there are certain areas in which a great deal more work has still to be done. It is not clear which aspects of the subject should be taught, or in what detail, although some guidance on this matter may come from the British Computer Society or from the National Computer Centre. Also information on the way in which the subject is taught in other countries would be most valuable.

If a satisfactory means can be found by which a blind person can communicate with a computer then it is certainly worth investigating the use of computer terminals in a conversational mode for teaching purposes. By careful selection it would be possible to greatly reduce the amount of paper produced by the computer whilst still retaining the required information. It is possible that the greatest scope for further research lies in this field, and it does offer some most challenging work in developing new processing techniques which could well be of use to sighted computer users as well as to the Blind. Sighted people tend to be unperturbed by large quantities of computer output, yet to the blind person redundancy can be so confusing as to hide the most significant material. This applies equally to programs and to data and results.

As a computer professional I have found it a most interesting and rewarding experience to teach on a part time basis at Worcester. I have had a great deal of help and encouragement from many members of staff at Worcester, and for this I am most grateful. I have also had a considerable amount of support from my employers, the Metal Box Co. Ltd., and in particular from Mr. H. W. Gearing, who is manager of the Computer Services Department at Metal Box. Miss Sims at Chorleywood made me most welcome and provided a lot of useful information when I visited her last year.

Without the support of all these people, and many more besides, it would not have been possible to present this paper. I have not tried to lay down any definite rules, but rather have surveyed what is being done. The rules will come when we have a great deal more experience. In the meantime it is to be hoped that those who are engaged in this work will continue their efforts, and that by some suitable means these efforts will be co-ordinated.
B. N. R. Magill
1st February, 1973.

Content author: library@rnib.org.uk

Last updated: 20/11/2008 11:13

Print

More info

In your area

Quiz

Smokers are twice as likely to develop eye diseases such as cataracts and age-related macular degeneration, which can lead to blindness.




Your stories

June's story - June Croft was told she had glaucoma after having an eye test. She was given drops to prevent further deterioration and later had an operation. 'Having an eye test is the most important thing you can do. It stopped me from going blind. People don't realise how quickly something can go wrong with their eyes. It doesn't hurt, everyone should do it.' June's full story.