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Ostwald on Education

by Warwick Sawyer


Editors' note: This article forms part of our series on the education of the mathematically gifted. The issues raised although not all specifically to do with mathematics are clearly of great general educational relevance.



Friedrich Wilhelm Ostwald was one of the most colourful characters of his time. He was born in Riga in 1853 and died in Leipzig in 1932. A brilliant scientist and an inspiring teacher, he was a man of wide sympathies and varied interests. He campaigned vigorously and courageously for a number of causes; for example, one of his books, published in 1912 in the militarist and nationalistic Germany of Wilhelm II, called for "
internationalism, pacifism and a systematic plan for the preservation of natural energy resources". [1] He was intensely and outspokenly critical of the school system as it existed in that time and place, and made extensive studies relating to education. These investigations began, for reasons that will appear, with the experiences in school of men who were later to make great original contributions to science. His verdict, in his book Grosse Manner (Great Men), published in 1909, was that the schools had done everything possible to hinder the development of these men. He made it clear he did not regard great men as a race apart; they had the qualities of ordinary humanity in a more intense degree; their conflict with educational institutions simply showed more dramatically and visibly the damage that was being done to the average pupil.


Education


In his autobiography,
Lebenslinien, Ostwald describes how the initial impulse to this investigation happened. "One of my Japanese students brought to me a question from his government, asking how I had managed to train so many particularly gifted and successful students. Japan had set aside considerable sums in order to develop the scientific potential of their country as quickly as possible. Naturally the administrators of these funds wanted to make sure they were properly used and begged for my assistance in this respect".


"
I had first of all to answer that it was not due to any conscious effort on my part that things had worked out the way they had. I was only aware of having kept the way open for my students, so that my young colleagues could forge ahead by their own efforts, and not have their course indicated or even forced on them from outside. The general direction of work in our laboratory of course was determined by the general leading ideas of our science - osmotic pressure and electrolytic dissociation in the first part of my teaching life, catalysis in the second half. As each new colleague chose, from this unlimited field of investigation, that aspect which he felt particularly suited to his ability and taste, the results came almost automatically".

"
Yet the question stimulated me to meditate more thoroughly on these things. . . . That an astonishing number of exceptionally gifted workers had developed under my supervision could be seen from the fact that many of my students had quickly obtained university teaching posts, and most of them had soon become professors. I compared this situation with that of another chemical laboratory, with twice as many students as mine, where the director was held in unbounded respect -almost adoration - by his students so that he had tremendous influence on them. In spite of this, mediocrities were produced, of which only rarely did one attain to junior rank in a university, so that I was compelled to recognise the existence of some factor that influenced my students favourably and was lacking at the other place".

"At that time I was only able to solve the positive side of the problem. I did not become enlightened as to the negative aspect of the other laboratory until after the death of its director when accounts of its operations were published by former students. These accounts were all the more reliable as they invariably expressed gratitude and favourable feelings".


"
According to them, the decisive part of their training, the choice and completion of the doctoral thesis, happened as follows. The director collected problems, which he had found by reading or thinking, and wrote these on a slip of paper. Mostly these consisted in proving the correctness of the director's ideas or the falsity of an opposing view; almost always a particular result was expected. Accordingly a student, who had received such a note, strove to get this result and regarded his work as a failure if it led to some other conclusion".


"
The organisation of work in my institution was entirely different. First of all the tastes and abilities of the candidate were investigated and taken into account: free choice of problem was not only permitted but insisted on. In the seminars I emphasised again and again that conclusive proof of an expected result was seen as a fulfilment of requirements, but that its value was of the lowest order. Unexpected things are often much more valuable, for, like the irregularity in the bark of a tree, they mark the place where soon a bud will break out that may grow into a novel branch of science. For I had a lively apprehension of the danger, which arose from the extraordinary fruitfulness of our guiding principles, that the frequent correctness of deductions based on these might make beginners blind to those things that could not be accounted for by these principles....".-

"This view was the result of my historical studies, which had again and again shown me the harmful effect of preconceived ideas."[2]

Already as a student Ostwald had acquired an interest in thc history of discovery. He had been stimulated by the lectures ol Karl Schmidt in the history of chemistry. These involved masses of dates, which Ostwald found very boring, but he continued to attend the lectures because they contained "lively and clear pictures of great scientists, whose names ceased to be abstract labels. It was made clear that discoveries were not the effortless achievements of supermen hut were often made with the greatest difficulty after many false starts." Thus from a very early age Ostwald had been interested not only in the discoveries of science but also in the means by which they had been made and the personalities of the scientists who made them.

In the introduction to Grosse Manner Ostwald expresses the opinion that many more people are born with the potential for great achievements than ever come to fulfilment. It is not enough to be born with natural ability: there must he favourable circumstances if this ability is to develop.

There were thus three questions to be answered - what an the qualities that make for outstanding achievements in science how can these qualities be recognised in the young? What kind of treatment is required to foster their development?


A Science of Education?

Is it possible to find an objective answer to these questions - particularly the last? Can a teacher say more than, "This is how I like to teach and it seems to work fairly well?" It is clear that Ostwald hoped to apply his habits of scientific thought to human development; in the introduction to Grosse Manner he says, "If we know more accurately the natural history of this species" (i.e. the gifted) "we shall learn to avoid those harmful influences by which so many potential geniuses are destroyed." At first glance, the idea of a science of human development seems repulsive; it suggests a dehumanising, deterministic, mechanical theory with rigid norms. This clearly is not what Ostwald had in mind; one need only read two or three pages of Ostwald to realise he believed a scientific investigation would show that an educational system is effective in proportion as it proves itself adaptable to the infinite variety of human nature.

In fact Ostwald's attitude even to the science of chemistry was not quite what one might guess. It was not until 1909 that he accepted the existence of atoms and molecules, since he thought atomic theory gave too mechanical an explanation of the universe.[3] Indeed he thought scientists themselves did not appreciate what was meant by a scientific law. They naively accepted a deterministic picture suggested by a superficial acquaintance with mechanics, in which the motion is completely determined by the initial conditions. But mechanics deals with an idealised, not a real, situation. The statement that a body falls with constant acceleration under gravity is true only with a uniform field in a vacuum; it does not take account of the wind that may be blowing, of the rotation of the earth and the earth's motion around the sun, of magnetic forces that may be acting, and so on. A scientific law is an approximate statement of what happens in selected situations; it never describes completely the complexity of nature. Such statements can be made about human nature, but they are rarely very surprising; for instance, one can assert that there is a vanishingly small probability that a professor, on his way to a university lecture, will kill a man.[4]

A scientific study of education therefore need not be dehumanising: it is simply a matter of reviewing our experience and drawing reasonable conclusions from it. Stimulated by the Japanese question, Ostwald looked hack on his years as a teacher and considered the question - had it been hard to pick out from the mass of incoming students those who would make outstanding achievements? The answer was - no, not at all; once or twice he had been mistaken, but not more than that. In the main, there had been no surprises. Those he expected to do well had done well.[5]


"
One who has devoted his whole life to the discovery of natural laws cannot become aware of such an observed regularity without immediately becoming convinced that here is a situation promising successful research.''[6] His correct forecasts must have been based on some common feature of very different personalities, which he had been aware of, hut not in a fully conscious way. He went for long solitary walks to think the matter over and eventually felt able to give an answer to the Japanese student; "I emphasised that we can recognise particularly gifted students by the fact that they are dissatisfied with the regular course of instruction. For the regular syllabus, both in depth and breadth, is based on what experience shows the average student can cope with; if a student is unusually gifted, what is meted out to him will be too little quantitatively and above all qualitatively and he will ask for more." [7]


The Case Studies


To supplement his own experience, Ostwald drew on his wide reading in the history of science. In
Grosse Manner he presents six case studies - Davy, Mayer, Faraday, Liehig, Gerhardt and Helmholtz - and seeks to draw general conclusions about the nature, recognition and treatment of the gifted.

In reading about great men one naturally wonders about the experiences of great women. Ostwald himself comments on this. His studies had been concentrated around chemistry, physics and some parts of mathematics. In the nineteenth
century no woman made an independent contribution of the first rank to these. In a footnote he mentions that it is too early to assess the work of Marie Curie.
[8] (Her isolation of polonium and radium in fact came two or three years after the book was written.) Emmy Noether was 26 years old at the time and was still not widely known as a leading mathematician of our century. Myself I have no doubt that a study today of gifted women and their conflicts with over-rigid institutions would lead to essentially the same conclusions as Ostwald found for men.

One difficulty in former times was that science was not even regarded as part of education. Darwin's extraordinary youthful interest and ability in nature study were ignored; he was pronounced a failure on the basis of his work in Latin. In the past many schools, in Germany and elsewhere, showed complete authoritarian rigidity. I remember vividly the picture of a school given in a textbook from which I learnt the German language. The first exercise for translation ran as follows; "The teacher speaks, the pupils listen. The teacher commands, the pupils obey." This voice from the past gives a fair picture of many schools in Ostwald's time. And as, in the Gymnasium, what the teachers commanded was that pupils should spend nine years in secondary school learning Latin and Greek, it is not surprising that denunciation of this system runs as a thread through Ostwald's writings. The Humanists, as he saw it, were anything but humane. He approved, of course, of the study of the classics by those whose interests led them in that direction.

Freedom in education is not always easy to achieve. The idea itself is often misunderstood as "simply letting children do what they like". It is clear that Ostwald, who had helped to train professors of chemistry in universities throughout the world, did not attach this meaning to freedom in education. It was rather a matter of encouraging students to pursue, vigorously and persistently, a course of study suited to their abilities and tastes.

Early Maturity and Specialised Interest

Ostwald, after describing the experiences of his selected men, discusses the generalisations that can be drawn.

"We can state without hesitation as a very general rule that most great men in their youth showed early maturity . . . this early maturity shows itself in the fact that such children very soon discover some field which interests them particularly and that they attain in this field knowledge and skills which go far beyond those of other children of the same age, in whom similar interests are lacking."[9]

This driving interest must arise from a fascination with the subject itself, not from some external consideration. "The industrious hut not gifted pupil, who from love for his parents tries to do well at school is an example of this external motivation; so also is the ambitious young man who has chosen a particular field because he hopes to 'make a career' in it, that is, to win money and influence. Such foundations are not those on which exceptional achievements are built." [10]

Ostwald refers to the mistaken folklore that early maturity is unhealthy. He points out that a mother is delighted if her child learns to walk or talk earlier than is usual: the instinct of the mother to recognise this as a healthy and favourable sign is entirely correct. The myth that precocious children are destined for an early grave is entirely false.

"History gives us examples in all fields of child prodigies who later produced achievements of the first rank. I think on the one hand of Mozart, who at 8 years old had mastered the whole of musical technique up to the most difficult aspects of counterpoint, and on the other hand of William Thomson, who went to university at the age of 10 years. And if people want to point out that Mozart died very young, it can equally be said that William Thomson reached the age of 80 and right up to the end of his life enriched science through his works."


"
We may conclude that early maturity is always an indicator of the possibility that we are dealing with a future genius he problem then arises how to deal with such children. In the old legends, young heroes went to their doom through their own actions. Today the future heroes of thought are not infrequently destroyed because people make every effort to prevent them doing the things for which their hearts yearn. Under the delusion that precocious achievements are unhealthy, people try to stop the unfortunate gifted children developing in accordance with their gifts, and hold them hack artificially, to their great harm, instead of giving them the one thing they need, freedom to develop."[11]

Ostwald gives examples of how geniuses reacted to school. Mozart and Thomson were fortunate, as their interests were those already existing in their families. Faraday went to work at the age of 12 with the three Rs only. Darwin hated his school. Davy was thankful that his teacher left him alone. Mayer did well at mathematics but in a school devoted to classics was always at the bottom of the class. Helmholtz was bored and used to work problems in optics under the desk during Latin lessons. Liebig was forced to leave school "after being too long a disgrace to the school".[12]

There were two reasons why geniuses tended to come into conflict with the schools. One was the lockstep, the expectation that all the pupils would work through each subject at the same pace. The other reason was that geniuses early decide on their goal in life, and concentrate on achieving it, with deliberate neglect of anything that distracts them from it. This view of how a pupil should divide his time and energy is liable not to coincide with that of the school.

On the conflict caused by the lockstep, Ostwald writes, "It is easy to see the inevitability of this effect, as clearly the average syllabus can only be designed for average talents, so long as one makes the gross educational mistake of linking together pupils of the same age by division into classes, in such a way that differences in speed and depth of understanding are methodically suppressed. The institution of school classes rests on the unstated assumption that all pupils are equal in talent, interest and industry, or at least can be made so. Obviously, there is no fact less open to doubt than the wide variation of human personality. Our schools thus run into an incurable contradiction to reality. . . . To avoid it schools must be organised in such a way that gifted students are led through the subjects more quickly than the less able. This is perfectly possible to organise and in fact has been done."[13]

Ostwald rejected the idea of separate schools for the gifted. Rather he wished to see schools organised in such a way that not only geniuses but all pupils, quick, average or slow, could advance at the rate most natural to them.

If you wanted an estimate of the ability of a pupil, the obvious course would seem to be to approach a teacher, hut in view of the blindness of schools just noted, any information volunteered by a teacher ''should he treated with the utmost caution. there are splendid teachers (who often remain unrecognised) who represent the ideal both in the way they view their profession and in the way they carry it out; such teachers will usually give an accurate judgement of the pupil. But of necessity, for obvious reasons, most teachers judge a pupil by how little trouble he causes them. The gifted student does not experience any difficulty in learning the regular material; however, from time to time he makes such high demands by questions and objections that the teacher is embarrassed and becomes impatient or angry. Also, giftedness is always a particular talent: the devotion of the pupil is one-sidedly directed and what is not in that direction is neglected. All these circumstances work together to influence the judgement of the teacher unfavourably. Usually he will say, 'this boy seemed very promising when he was young. As he grew older he caused the school more and more difficulties, and now we are doubtful whether anything at all can he made of him.' For the ideal of the average teacher is not the pupil of genius, but the 'good boy' who makes the least trouble for the teacher."[14]


After cataloguing the conflicts of great men with their schools, Ostwald comments, "
One could say that these were exceptions . . . and conclude simply that, because the classical school was unbearable to great men, it must have been just right for the average. . . . But we have seen that great men are not separated from ordinary people by an impassable mental chasm, but rather show a particularly strong development of certain characteristics, which are also present, in a lower degree, in other people. We must conclude that the conflict of future great men with the classical school is so strong precisely because the school clashes so flagrantly with these characteristics. . . . Accordingly its effect on average pupils will be to destroy completely these valuable characteristics . . . for in the average pupil these qualities are not protected by their exceptional strength and so lie defenceless against the influence of the school".

"What are these characteristics? We have seen that they are concerned in the first instance with independence of thought; secondly, there is the ability to observe facts and to draw correct conclusions from them".

"These are characteristics which are in no way confined to the exceptional man; anybody who wants to do anything well in everyday life must have them in some measure. What is the attitude of the school to these qualities?"

"The answer is regrettably not in doubt; it suppresses them on principle."[15]

Our schools today clearly differ from those of Prussia a century ago, but there are still points about the treatment of bright children - and indeed of all children - that we can learn from Ostwald. I will return to this matter at the end of this article.

On What Resources do the Gifted Draw?


Ostwald continues, "
In view of the poor offerings of the schools, the question arises - how have the great men in their early years obtained the knowledge which they require in order to carry out their work? The question is all the more pressing since, as we can easily satisfy ourselves, their achievements occur at a very early stage of youth or manhood, in accordance with their early maturity in childhood".

"The answer is - through books. This happens in every case. Davy amazed everybody by his ability to master the contents of books. Faraday became a bookbinder, as he saw no other way to satisfy his thirst for books: his first efforts at experimental work consisted in carrying out the experiments described in his books, so far as his means permitted. Similarly Liebig explicitly stated that he had devoured all the books in the Court Library, and we find Helmholtz as an assistant to the librarian of Pepinière; he too reported that he had gained his mathematical knowledge by private study of books. For his long lonely voyage Mayer provided himself with plenty of books. Gerhardt's whole activity centred around literary work, that is, knowledge of books".

"This is a very noteworthy result. It shows that oral instruction by a teacher is of little importance for men of the first rank, even though it may be of decisive importance for those of the second rank. None of the great men named above was brought into the direction his life took by another great man.... It is in the nature of things that a person of originality will not in the least wish to accept the leadership of another. And the stimulation, which an exceptional lecturer gives out so abundantly, is not needed by a future genius simply because the genius usually has already more plans than he is able to carry out."


"
On the other hand, self-tuition through books is precisely the form of education that suits him. Books permit the free choice of direction, since we read only those in which we hope to find what we are looking for. Again, a book does not compel that passivity which the oral instruction of a lecture requires A reader can decide how long to spend on each individual question, while a lecturer keeps to his own tempo, not that of the student. How often a beginner comes up against a difficulty which for the moment he cannot overcome in any way! The lecturer knows nothing of this and goes placidly on: then it all is lost on the hearer since he is already out of his depth. The book on the other hand is patient and waits until the reader has achieved understanding, and perhaps has meanwhile obtained help from other books, and so forth."[16]


The Needs of the Majority


At this point, Ostwald points out how relevant these thoughts are for the education of the public in general. "
We ought, far more than is usually done in school, to foster in every pupil the conviction that practically the whole of human knowledge is contained in books and that all that has to he done is to find suitable ones, which as a rule is not hard. In recent times so much has been done to help the access to good books of people of limited means. I have gained the impression, in occasional lectures to working people on self-education through books, that in broad layers of society this art is almost unknown. For example, when I mentioned that, in trying to learn any difficult material, it is advisable not to do this from just one book, but to get hold of two or three on the same topic, this was regarded as something nobody had ever thought of."[17]

Informal Help


Ostwald then returns to the question of resources for the gifted. "
Besides books we often find in the youth of great men an intelligent friend or uncle, who takes a personal interest in the young enthusiast. . . . The effect of such adult help is not to determine the thoughts and work plans of the young genius, but rather to help him to find himself, which is often a difficult thing for these young fermenting minds. Their own thoughts and plans crystallise in the course of explaining them to a sympathetic and experienced person, and this has an extremely clarifying influence."[18]

It was mentioned above that geniuses often did not fit neatly into educational schemes, so that teachers were liable to give a biased estimate of them. A reliable judgement could usually be obtained from a friend of the type just described."
[19]


Relevance to Today


Heaven be thanked, our schools are very different from those Ostwald attacked, yet there are a number of things we can learn from him even today. His writings can help to modify some views which are held even by people of good will, who are aware of the problems of the gifted and are anxious to help.

For instance there is the idea that we should provide "enrichment, not acceleration" - we must not let the gifted hear in advance about something they are due to meet at the appointed time in a standard syllabus. This shows a total lack of understanding of the situation. It appears most clearly if we consider extreme examples. When Emmy Noether was four years old, she pointed to a chair and said, "This chair has four rows of brass nails with 12 in each row, so there are 48 nails altogether." The example of Gauss is even more striking. He learnt to read when he was two years old. Nobody told him anything about arithmetic but apparently he somehow found out for himself the meaning of numerals, and before his third birthday pointed out that his father had made a mistake while doing his accounts. Now, what kind of "enrichment" should be given to Emmy Noether to make sure she does not learn any more arithmetic until she is in a class that knows the 12-times table, or to Gauss until he joins a class doing money sums? What musical experiences would be permitted to the eight-year-old Mozart?

Now of course great mathematicians are rare, hut there is a continuous spectrum of abilities; it ranges from geniuses to bright committed students who are only a year or two ahead of average development, and beyond these to average students, and rather slow students and very slow students. At all levels problems arise in meeting this variety among pupils. The problem is easiest when we are dealing with geniuses and the gifted. It is a fundamental error to suppose that they will fit into any fixed syllabus. They have to take their education into their own hands, through reading, supplemented by group discussion and whatever occasional consultation or advice it is feasible to provide. But will this not harm them socially, by making them stand out as a group apart? Ostwald has already provided the answer. The whole population needs to know how to find things out, how to make correct use of libraries and books. The gifted should be one group among many learning how to do this, though they would require much less help than the others.


I do not mean to imply that schools should be organised exclusively on the basis of individual work; class and group discussion should be an ingredient of education, and it is excellent if co-operative activities can be found to which different types of pupil contribute different kinds of knowledge and strength. Then we might reach a unified society in which human variety is accepted and foolish and unnecessary embarrassment is not caused by the presence of someone much above, or much below, average intelligence.


I suppose a lot must depend on one's own past experience. If you had mathematics doled out to you in an unimaginative and largely incomprehensible manner, you will find it hard to imagine mathematics as a subject of fascination, to be searched out, and read, and pondered. You will tend to regard it as something done to children, rather than as something done by them.


My own recollection, in both schools that I went to after the age of eight, was of being expected to learn from books, sometimes in classes where two or more different subjects were being studied. In 1961 I visited a number of schools in England to study how mathematics was organised. One of these schools was Marlborough, where for two weeks I relieved Douglas Quadling of all his teaching duties. The older boys I hardly saw at all. They would be working away and occasionally come for help and advice. This was, in the past, the whole idea of sixth-form work, that students should read independently under the general direction of a teacher as a preparation for university, where they would be completely on their own. My impression is that this is less common than it used to be; if so, we have gone backwards rather than forwards.

The examples just quoted were from the private sector. I would be interested to hear details of independent mathematical or scientific work in comprehensive schools and sixth-form colleges.

The most wonderful school I ever knew was a Lancashire elementary school which I used to visit between the years 1937 and 1944. It was in Prestolee, a mill village between Manchester and Bolton - a district not noted for its amenities. Immediately on entering the school you were aware of an unusually peaceful and harmonious atmosphere. The school was organised like a public library. Children were moving around, quietly pursuing various tasks. This state of affairs had been reached in accordance with one of Ostwald's principles, by beginning with the actual interests of each child. You might ask a child of six, "What are you doing?" and receive the answer, "I am researching on ducks." This meant a teacher had discovered the child was interested in ducks and had said, "See if you can find a book about them." I still have some books, written by these children, on the basis of what they had found out for themselves. Needless to say, not all the children were gifted. They were a living justification of Ostwald's belief that nearly everyone can learn how to use books intelligently.

Sometime ago, at a conference on the education of the gifted, I expressed the view that the only solution was to let the gifted read ahead on their own. Several teachers immediately rejected this as entirely impractical; pupils, they said, were not willing to read independently. It is interesting that these teachers did not feel it was possible to achieve with the gifted what two outstanding teachers had been able to achieve with a whole school in an industrial district during the world slump, and what many teachers managed to do in the past in one-room rural schools. I can only repeat that it is possible, and we must search for the way to do it.

References

Only the following three sources were used in writing this article.

S:
Scribner's Dictionary of Scientific Biography, volume XV (Supplement
I), Note that the biography given under Ostwald in the main part is the son of the man we are dealing with.

GM: Grosse Manner, by F. W. Ostwald.

1.3: The third volume of the autobiography,
Lebenslinien by F. W. Ostwald.

I. S.
2. 1.3, pp. 121-124.
3. S.

4, 1.3, p. 9 and following.
5. GM, pp. 1-2.
7. GM, p. 3.
6. GM, p. 2.
8. GM, p. 417.
9. GM, p. 338.
10. GM, p. 339.
11. GM, pp. 340-341.

12. GM, pp. 341-344.

13. L.3, pp. 128.129.

14. L3, pp. 129-130.

I5. GM, pp. 344-345.

16. GM, p. 346.

17. GM, p. 347.

18. GM, p. 348.

19. 1.3, p. 129.

Copyright © W. W. Sawyer & Mark Alder 2001

This version 20th February 2001

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