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ations, when it was not known that there was such a thing as the Science of Education. But that day is surely past. Education is a science and art that requires as special training as any subject. It is surely time now that we should complete the circle of the professions in our universities by doing tardy justice to this one. Their wants in other subjects are being gradually and honorably supplied by the foundation of new chairs, representing new ideas of the age. Education still remains an open want.

A Chair of Education, fully established, should include

1. A Professor of Education, who would give a full course of lectures on the science and art of teaching.

2. A Training College, of which the professor would be principal, and in which a staff of lecturers would give instruction in subjects that are not included in the university classes, but are necessary for the complete education of the teacher, similar to the extra-mural lecturers in medicine.

3. A Practicing School, with the very best appointments in classrooms, furniture, and apparatus, under a competent head master, with a full staff of assistants, in which the best practice of the art of teaching would be carried on, and in which would be afforded every opportunity for the efficient practical training of the future teacher, a school holding the same relation to education that the infirmary and its clinical lectures do to medicine.

4. An Educational Library and Museum, with a full collection of all works on education, and of all educational apparatus and appliances, similar to the educational department in Kensington Museum, -a complement to the other professional museums already in the universities.

The subject is too extensive to be entered into in detail in this place, but the above may be sufficient to indicate what should be done to supply a claimant want in our universities and in one of our most important professions. In determining on the best means of using the large funds that may be at the disposal of the Commission, few should more commend themselves than the establishment of such a chair in some one of our universities, with its complementary educational machinery. These endowments are left mainly for educational purposes; and here is an opportunity of supplying a great educational want, and of raising the educational status and efficiency of the country, such an opportunity as seldom offers itself to a Commission appointed to consider the best means of disposing of certain sums for certain important purposes.-Letter to the Scotch Commissioners of Education.

ISAAC TODHUNTER.-CONFLICT OF STUDIES

AND OTHER EDUCATIONAL ESSAYS.*

PROGRESS IN DEVELOPMENT OF HIGHER STUDIES.

If we cast our eyes back for a period of fifty years we shall arrive at an epoch when the higher education of England remained still, as it had been for many generations, solely and exclusively classical. An illustrious man trained at this time stated in later life, with well-feigned regret, that he belonged to the prescientific period. Suddenly a strong current arose in favor of useful knowledge; the machinery of lectures, mechanics' institutions, and cheap literature was employed for the diffusion of this useful knowledge among the humbler classes. Whatever might have been the result of these agencies within the sphere of their immediate operation, it cannot be said that any decisive influence was produced on the schools and colleges which supply the most elaborate education.

At a later period, when the machinery set in action for the benefit of the humbler classes had decayed in power, when mechanics' institutions had fallen into debt and difficulty, when lectures had given place to musical and other entertainments, when popular literature had ceased to affect to teach and aspired only to please, the exclusively classical education of the upper classes in England first encountered serious criticism. Perhaps not more than ten or twelve years have elapsed since these time-honored studies began to experience any vigorous rivalry; though for a considerably longer period the elements of mathematics had gained a partial and temporary toleration.

ARTIFICIAL VALUE ATTACHED TO CERTAIN STUDIES.

In balancing the claims of various modes of education and systems of studies, we must remember that our decision must depend very much on the precise benefit which we hope to secure. We may propose to educate an individual mainly for his own benefit, or for that of others, as for instance, the state. If we take the benefit of the state as the principal end, we shall probably be led to the conclusion that the indications of any special excellence should be carefully watched and encouraged, even at the expense of the general development of the powers. If a youth shows any of the tastes and habits which have been in past time the presages of military distinction, we may hold that the law of the safety of the country justifies the cultivation of this promise even to the neglect of

* Prof. Todhunter is a Senior Wrangler at Cambridge, 1848, Fellow and Mathematical Lecturer of St. John's College, is the author of a valuable series of Mathematical Textbooks for Colleges and Schools. The Essays in the volume from which these extracts are taken are:-I. The Conflict of Studies. II. Competitive Examinations. III. Private Study of Mathematics. IV. Academical Reform. V. Elementary Geometry. VI. The Mathematical Tripos. London: Macmillan & Co. 242 pp.

higher intellectual qualities, or to the peril of moral excellence itself. This may be an extreme case; but let us take a more moderate example. Suppose a youth to exhibit a fondness for imaginative exercises and literature, which may be the dawn of poetical genius. Moreover let us suppose that, in spite of the authority of an ancient sage, we find a function and a value for poets in our commonwealth; then we may conclude that we ought to stimulate the imagination : though perhaps it might be for the true happiness of the individual if the memory and the reason were trained rather than a faculty which is already unduly developed.

UNDUE INFLUENCE OF SPECIAL PRIZES AND EXAMINATION.

Although we have no such despotic power as to compel an individual to cultivate just that faculty which seems strongest, yet by our system of competitive examinations and prizes we tend to the same result. We take a boy at school who seems to exhibit an aptitude, say for mathematics, and foster that taste in every way we can. The boy comes to the University; he is already saturated with mathematics, and so must have almost exhausted the special benefit which that study is held to confer; at the same time, in other departments of knowledge, such as languages, history, natural science, he may be very deficient. Nevertheless he is kept for three or more years still at the old pursuits, exercising only those energies which have been abundantly developed, and leaving others dormant which have been too long neglected. If our object is to train mathematical teachers and professors this may be defended, though perhaps with only partial success; but if, as we commonly maintain, our object is to cultivate the mind so as to render it well fitted for future exertion in any direction which has to be followed, our arrangements are open to serious doubts.

The excessive cultivation for examination purposes of one department of knowledge to the exclusion of others seems to me one of the great evils of our modern system of bribing students by great prizes and rewards to go through our competitive struggles. We are in danger of giving up all pretence of a general course of training for youth, and of allowing and even encouraging boys to select some special subject which they fancy they prefer, or rather perhaps which they least dislike. I should desire quite a contrary system; a scheme of study and examination should be drawn up after due deliberation, and all candidates be required to pass through this before the avenues to special distinction were opened. In theory, perhaps this is still attempted; but in practice we seem to deviate from such a course more and more every year at Cambridge. For instance, students of classics are no longer compelled, as they formerly were, to pass a mathematical examination for their degree; and for the most part undergraduates in the colleges are excused from attendance at lectures on the subjects which they do not profess to cultivate. Even where an attempt is made to prescribe some general course the standard in each department is fixed so low as not to ensure more than the simplest rudiments of knowledge.

EXAMINATION VALUE OF SUBJECTS VALUED.

As we must employ some mode of testing the diligence of teachers and the attention of pupils, it seems inevitable that there must be processes of the nature of examinations; hence it is important to pay some attention to the adaptability of subjects to the exigencies of examinations. It seems to me that the older subjects, classics and mathematics, are strongly to be recommended on the

ground of the accuracy with which we can compare the relative performance of the students. In fact the definiteness of these subjects is obvious, and is commonly admitted. There is, however, another advantage, which I think belongs in general to these subjects, namely, that the examinations can be brought to bear upon what is really most valuable in the subjects. It is of course easy to say that the art of examination by long practice on these subjects has arrived at a degree of excellence far beyond what ought reasonably to be expected in the case of studies of quite recent popularity; but this does not seem to me to explain the matter completely. Take, for instance, mathematics, and observe how real and fresh the examination papers can be made; they in fact abound in new results which are quite commensurate in importance and interest with the theorems previously established and studied. Now, for a contrast, take the subject of history: this may be readily admitted to be important and instructive especially for the original inquirer who has to seek for evidence, to estimate its value, and to combine it in a consistent whole. But it may be seriously doubted whether the valuable parts of the subject can be developed in our usual systems of examination. From the cases, not, I admit, very numerous, which have fallen under my own notice, I have formed an unfavorable judgment on this matter; it appears to me that we find in examination papers chiefly dates and striking, obvious events, which form rather the skeleton of history than history itself; that the mere receptivity of the students is all that can be tested, to the exclusion of the faculties of comparison and of judgment; though these may be well developed by original researches in the subject. Thus, briefly, it seems to me that much of what constitutes the real value of mathematics can be tested by examinations, but in history there is little of this merit.

[Experimental and Natural Sciences are considered by this author as not satisfactory for examination purposes.]

SPECIAL ADVANTAGES OF MATHEMATICS.

Leaving aside such points as are well known and obvious, I should like to draw attention to the inexhaustible variety of the problems and exercises which it furnishes; these may be graduated to precisely the amount of attainment which may be possessed, while yet retaining an interest and value. It seems to me that no other branch of study at all compares with mathematics in this. When we propose a deduction to a beginner we give him an exercise in many cases that would have been admired in the vigorous days of the Greek geometry. Although grammatical exercises are well suited to ensure the great benefits connected with the study of languages, yet these exercises seem to me stiff and artificial in comparison with the problems of mathematics. It is not absurd to maintain that Euclid and Apollonius would have regarded with interest many of the elegant deductions which are invented for the use of our students in geometry; but it seems scarcely conceivable that the great masters in any other line of study could condescend to give a moment's attention to the elementary books of the beginner. The possibility of the early employment of the constructive and imaginative faculties is an important gain for many students who become weary of the prolonged and unvaried exercise of mere receptive attention. In the pursuit of a new language we may secure advantages of a similar kind but probably of inferior value; but in the early stages of most studies

there seems nothing to correspond: it is scarcely conceivable that examination papers in history or the natural sciences can offer any tolerable equivalent in merit and importance to the problems of mathematics.

Another great and special excellence of mathematics is that it demands earnest voluntary exertion. It is simply impossible for a person to become a good mathematician by the happy accident of having been sent to a good school; this may give him a preparation and a start, but by his own continued efforts alone can he reach an eminent position. The rough processes by which prizes are awarded to the possessors of knowledge regard only the results offered for inspection, and overlook the finer gradations of merit which depend on the mode of acquisition. Suppose, for example, that rewards are bestowed for the cultivation of modern languages; a person who obtains the reward may have earned his distinction by his own persevering application, mainly or exclusively, but on the other hand he may owe it to the fortunate incident of residence in a foreign country, or of habitual intercourse with those who spoke the language as their vernacular. The resulting amount of knowledge is no just index of the labor and perseverance which have been expended in gaining it; the credit to be properly assigned for the accomplishment may indeed belong to the successful candidate, but it may, and perhaps more justly, be attributed entirely to his friends and relatives.

A similar consideration applies, though with diminished force, to the study of the classical languages; the foundation of knowledge in these subjects can be laid in years so early that the pupil exerts but slightly his own will; his success is a combination depending indeed partly on his own ability and application, but still more on the judgment or kind fortune which deposited him in a good school.

We repeatedly see youths enter the universities whose position in the final classical examination is already practically assured; but distinguished success in the mathematical competition cannot be confidently expected, whatever be the ability of the candidate, unless he is willing to subject himself to steady and continued discipline. In whatever line of study distinction is sought the advantage of good teaching is great; but probably among all the pursuits of the University mathematics preeminently demand self-denial, patience, and perseverence from youth, precisely at that period when they have liberty to act for themselves, and when, on account of obvious temptations, habits of restraint and application are peculiarly valuable.

Nor do I know any study which can compete with mathematics in general in furnishing matter for severe and continued thought. Metaphysical problems may be even more difficult; but then they are far less definite, and, as they rarely lead to any precise conclusion, we miss the power of checking our own operations, and of discovering whether we are thinking and reasoning or merely fancying and dreaming. I speak now, as on former occasions, of studies as they present themselves to minds of average power and of ordinary conditions. For persons of exceptional ability any intellectual pursuit may prove stimulating and strengthening. In other words, discoverers and original geniuses form a class apart; we may admire them, but we should not inadvertently assume that their pursuits when adopted by inferior disciples will be as vivifying as to the great masters themselves.

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