of the individual school. This is clearly stated in her book, Education on the Dalton Plan," published by G. Bell & Sons. The statement is as follows: "I have carefully guarded against the temptation to make my plan a stereotyped cast-iron thing ready to fit any school anywhere. So long as the principle that animates it is preserved it can be modified in practice in accordance with the circumstances of the school and the judgment of the staff." It would have been fatal to the movement to have insisted upon the bare "take it or leave it " principle. To refuse freedom to the school and the staff in a system based on the freedom of the child would be absurd. The initiative of the teachers in suggesting improvements in the details of the plan may be of the greatest service in securing complete success for the introduction of what should prove to be a very notable advance in educational procedure.

After carefully studying the details of the scheme, and after full discussion between the head master and his staff, unless there is a very definite desire on the part of all concerned for the introduction of the Dalton Plan the idea of attempting it should be abandoned. There are many difficulties in the way and unless there is real enthusiasm and a firm belief in the new method the experiment would be doomed to failure. Under no condition should any pressure be brought to bear upon a school to introduce the Dalton Plan; the proposal must come from the school.

WORKING OF THE PLAN.

In brief the plan is as follows: the staff draw up schemes of work for each class or form suitable for a year's course. In doing so many staff conferences should be held so that the different subjects may be properly correlated and so standardized that the claims of the various elements in the curriculum may be adequately recognized. The year's work is broken up into monthly assignments which are worked -out in some detail and helpful notes given to enable pupils to attack each subject in the best way possible, and information is given as to text-books and books of reference to be consulted. The success or otherwise of the scheme will largely depend on the care and efficiency with which the assignments are prepared. Good assignments are vital elements in the plan. From year to year the assignments will undoubtedly improve as the result of experience gained of their adequacy and the time necessary for their fulfilment.

The pupil, after a careful study of these assignments, .contracts to do the work involved, and with a full knowledge of what is before him he settles down to his month's work with a definite sense of his responsibility and a vastly increased interest in school affairs.

For more than half the school time, frequently the whole of the mornings, the pupil is free to work at his subjects in the order he prefers, always keeping in mind that within the month it is necessary for the completion of his assignment, that in each subject he must satisfy his teacher that the necessary work has been carried out. The clever child may, however, complete his assignment in less than a month and the dull backward child may take more than this time. Thus in the same class or form the backward child may complete only eight assignments whereas the super-normal child may complete as many as fifteen. Each child goes at his own natural pace and should he be absent from school for days or weeks he, on his return, goes on with his assignment from the point at which he left off and there is therefore no gap in his knowledge as is frequently involved in a similar case under the old system. Under the Dalton Plan the classroom becomes a laboratory and to emphasize this Miss Parkhurst prefers to call it the Dalton Laboratory Plan. It is a special feature of the new organization that the children doing history, for example, should carry on their work in the history laboratory; their geography in the geography laboratory, and so on. In the history laboratory will be found the text-books, books of reference, illustrations of historical interest of various kinds and, above all, the history specialist

ready to answer questions and give what Froebel called the necessary guidance," which he considered to be the true function of the teacher. The pupils can thus get solutions of difficulties they have encountered, or better still obtain indications of how they may find the solutions themselves. A child having decided that he will now give some time to geography goes quietly to the geography laboratory, where he finds the geography specialist, maps, globes, books of reference, and any material he requires for the study of this subject. This freedom of the child to pursue the studies in the way his interest suggests is a most valuable element in the Dalton Plan and is rarely abused. To waste time would be sheer folly as the requirements of the assignment in each subject are ever before him. The knowledge, moreover, that to get on with the subject in which he is most deeply interested can only be done when he has satisfied his teacher in the less favoured studies before passing on to the next assignment is a powerful incentive to give sufficient attention to his weak subjects.

It is absolutely necessary for the successful working out of the plan to secure adequate means of testing the progress made by the children. For this purpose each child has his own progress graph for each element of the assignment as estimated by the teacher. The teacher has also his own graph for showing the progress made and thus he can not only see at a glance how a particular pupil is getting on but also how he compares with others taking the same assignment. The method of testing varies from school to school and also with the stage of development reached. The younger are naturally more liable to over-estimate the progress made than the older children and the personal equation of the child is taken into consideration. The more intimate knowledge of the child acquired by the teacher under the Dalton Plan reduces considerably the necessity for frequent examinations on which time might otherwise be wasted. A high standard of efficiency in recording the progress of pupils will, however, always be required as any failure in this direction would invalidate the new method.

The number of lessons for oral discussions or definite class instruction which all members of the class or form are required to attend vary with the subject and the stage of progress. These meetings afford excellent opportunities for dealing with points in which difficulties have been frequently experienced and also in opening up new branches of a subject and emphasizing any important principles involved. The subjects of the curriculum which are not Daltonized also give occasions for the class to meet as a class or in larger groups.

THE POSITION OF THE TEACHER UNDER THE DALTON PLAN. The most important change, especially in elementary schools, is that the teacher gives practically the whole of his time to the subjects which he is specially qualified to teach. This not only is far more interesting for the teacher, but it also enables him to concentrate his reading and to study the bearing of his particular subject on other related subjects in the curriculum. The fact, moreover, that the assignments for which he is mainly responsible represent a definite whole, and that there need therefore be no overlapping or want of continuity such as that which so frequently arose under the old system, is a gain the extent of which it would be difficult to over-estimate.

The attitude of the teacher to the pupil is completely changed. His lecturing is reduced to a minimum and there is far less definite teaching. The children do the work and simply come to him for assistance and advice. The teacher no longer pursues the child; on the contrary the child now pursues the teacher. This change of relationship results in a much healthier attitude of the pupil to the teacher, to whom he goes as a friend to ask for assistance. This more intimate acquaintance on friendly terms is of great value and is fully recognized by teachers who have had experience in working under both systems.

In the early days of the introduction of the plan life certainly becomes more strenuous for the teacher. The preparation of the assignments, if they are to be really effective, make serious demands upon him. He has the satisfaction, however, of knowing that the more energy he expends in making them thoroughly efficient the less expenditure will be needed in the work of preparation of future assignments.

One of the advantages is the greatly improved sense of comradeship with his pupils so that when they become genuinely interested in their work there will be no difficulties in the matter of discipline and entries in the punishment book will be very rare occurrences.

SUB-NORMAL AND SUPER-NORMAL CHILDREN.

It has already been pointed out that the sub-normal child has great advantages under the Dalton Plan because he can work at his own pace. Though during his school course he will cover far less ground than the super-normal child he will leave school in a far better condition than under a system in which he was consistently at the bottom of each class and naturally much depressed at his constant failure to compete with children of brighter intelligence. His outlook under the new plan is completely changed, and having a job to do in his own way and in the time natural to his ability he finds pleasure in school life. In some schools where the assignments are divided into minimum, median, and maximum sections, he moves along the most suitable line suggested by his teacher. The super-normal child, who has received far too little attention in the past, can travel at a good rate under the plan and can pass from assignment to assignment at his own pace. Between these two types is the child of average ability who will follow the median course and generally complete his assignments in monthly instalments.

THE ADVANTAGES OF THE DALTON PLAN References have frequently been made to advantages under this form of school organization. The chief points may be summarized as follows:

(1) The natural cultivation of the will-to-learn.

(2) An increased interest in school life due to the children taking a more active and intelligent part in their own education.

(3) The development of a greater sense of responsibility in consequence of the children's possession of freedom to work along lines determined by themselves.

(4) The more harmonious and intimate relations between teacher and pupil and the disappearance of any necessity for the employment of disciplinary methods.

(5) The special opportunities offered to children of widely different types of mental ability.

(6) The social effect of children organizing their own work, forming sound judgments, cultivating resourcefulness, and co-operating with others as a preparation for after-school activities.

(7) The solution of the problem of the child absent from school for a period.

THE TEACHING OF ELEMENTARY GEOMETRY.

THE

By W. PARKINSON, Merchant Taylors' School. HE school-days of most people teaching mathematics to-day belonged to the times when, as a text-book of geometry, Euclid's Elements held undivided sway in this country. The magic symbol 147 means nothing now to the pupils in our secondary schools, but to their predecessors of twenty and thirty years ago it called up an immediate and vivid picture of the figure of the famous theorem ascribed to Pythagoras. The clever young mathematicians of those days knew by heart the number attached to every proposition in the first six books of the Elements, and some knew in addition even those in the eleventh. To refer back to any item of geometrical truth was both

quick and easy; everything was in its place-it had been there for some two thousand years-and progress along the path to geometrical knowledge was logical and in order.

The system had great advantages and there can be no better testimony to their reality than the fact of the system having survived the test of so many centuries. How many of the school books of to-day will last for 2,000 years? Indeed, how many will live for 20 years?

All things pass away and Euclid's Elements are no longer a source either of pleasure or of trouble. The mention of trouble reminds us that in spite of all the advantages of the old system there was trouble and a good deal of it. All those who were not clever and, to be quite honest, most of the clever ones too, had great difficulty with the early Propositions of Book I. The fifth proposition-the notorious pons asinorum-proved to be the limit beyond which many never passed. It was not so much the difficulty of what was said in the propositions; every line seemed so very obvious as to compel acceptance. The difficulty was to understand the design. They were not all asses who longed to know why they should learn to make all these obvious remarks in a certain precise order. There is a well-known story of a certain pupil of Euclid himself, who asked, when he had learned the first proposition, "What do I get by learning these things? Calling his slave, Euclid said, Give him a copper for he must make gain out of what he learns." Since his day, thousands have asked the same question, and in fairness to them a penny was not the appropriate comforter.

During the past twenty years it has been made clear that an attempt to base a logical system of geometry upon a minimum number of fundamental axioms is an exercise utterly unsuited to the stage of mental development reached by a child at the tender age of twelve. It is now generally recognized that a much sounder plan is to arrive at the earlier part of Euclid, Book I, by experiment and intuition, and to take this body of fact as a wider basis of axiom on which to build the rest of the geometrical structure.

In the transition stage there has necessarily been considerable confusion, and if the schoolboy has been troubled less, the examiner has been troubled more. Since Euclid's order was discarded there has been no accepted order to replace it, and every text-book written has differed in this respect from its predecessors. Hence the confusion.

In response to a call from teachers all over the country, the Incorporated Association of Assistant Masters in Secondary Schools, in conjunction with the Association of Assistant Mistresses, and the Educational Institute of Scotland, set up committees to consider, in the light of modern developments, what is the best method of treatment for the average teacher and the average pupil in the secondary school. The personnel of the committees was made up almost entirely of those actually facing, day by day, the difficulties of teaching elementary geometry up to the standard of the First School Examination or what is perhaps more generally known as "Matriculation standard." The whole of the report, which has been unanimously agreed upon, is definitely limited to this stage, and while it is not claimed that the treatment recommended is the only treatment or even the best possible treatment, it is confidently put forward as a very good one that will commend itself, particularly to those who have sought some guidance out of the confusion of the past few years. The first recommendation of the Report re-affirms the wisdom of Circular 711* issued by the Board of Education in 1999, and if this recommendation were accepted generally by teachers and examiners, most of the difficulties of sequence would disappear. The paragraph advises that the substance of Euc. I 13, 14, 15 (angles at a point); 27-29 (angle properties of parallels); 4, 8, 26 (congruence of triangles) should be established by intuition and experiment and that the teaching of formal geometry should be based upon the acceptance of these results. Some examin

* Reissued as Circular 851 in 1914 with slight modifications.

ing bodies have already adopted this plan, and a plea is made that it should be accepted in all the various examinations of "Matriculation Standard." It is true that systems of geometry have been developed which do not accept the parallel postulate of Euclid, but no one would contend that a rigorous discussion of the subject is suitable for a beginner.

It is suggested that the subject of areas is best approached through the measure of the rectangle. Owing, partly at any rate, to the difficulties of incommensurable quantities, Euclid does not make any use of this; he proves one area equivalent to another, but nowhere does he show that the area of a rectangle is measured by the product of the measures of two adjacent sides. Every child is trained to accept this in other branches of mathematics and physics, and to prohibit its use in geometry for reasons which are never explained to him, because he is not capable of understanding them, seems very unreasonable and likely to confuse him.

Among other things the treatment of loci, tangency, and incommensurable magnitudes is also discussed and a schedule of propositions forming a suitable beginners' course is given but, for lack of space, those interested are referred to the Report* itself for a full description.

REVIEWS.

UNIVERSAL HISTORY

World History. By Prof. H. WEBSTER.
(10s. 6d. Heath.)

The Story of Mankind. By H. VAN LOON.
(12s. 6d. net. Harrap.)

Inspired by the example, and encouraged by the success of Mr. H. G. Wells, numerous authors at the present time are essaying the task of writing a sketch of universal history. Some are better equipped in technical learning than was Mr. Wells; but few can equal him either in largeness of vision or in skill of literary presentation. Mr. Wells's book had a unity which most of its successors lack; its central theme was the evolution of a single world-polity. In the absence of some such unifying idea, world-history degenerates into a series of disjointed episodes.

The two books before us, both of which challenge comparison with Mr. Wells's 'Outline,' come from America. One is by a professor of history with a record of several excellent text-books behind him; the other is by a much travelled and versatile journalist to whom history is obviously a virgin field.

It is a

Prof. Webster, five years ago, issued in three volumes a very capable survey of European History. The present sketch of World History takes that book as its basis. The main adverse criticism of the book, indeed, would be that it is too dominantly European. Not enough is made of the civilizations of China and India. America itself, both North and South, receives strangely little attention. The second half of the volume is taken almost verbatim from the European History, with the exception of the closing sections on the Great War and the Peace Settlements. growing practice among American text-book writers to serve up the same information in book after book, with only slight changes of arrangement and title. It is a practice to which strong objections could be urged. In spite, however, of some defects, Prof. Webster's 'World History' is sound, interesting, and valuable. It treats in briefest summary the record of ancient and medieval civilization, reserving fullness of discussion for the period subsequent to the Reformation. The general idea of the book is "human progress,' social development,' upward march from the Stone Age until the present time." The volume is well furnished with maps, illustrations, and bibliographies.

man's

* The Teaching of Elementary Geometry. Oxford University Fress, 1/

Mr. van Loon's "Story of Mankind" is written for very young children. It is a collection of interesting tit-bits arranged in chronological order and expressed in colloquial phraseology. It gives a general conception, devoid of precise dates or particular details, of the main movement of mankind from prehistoric days to the present. It is illustrated by some of the most amazing drawings which it has ever been our lot to see in a historical work. On one hand they are not beautiful, but are marked by every defect which a work of art could possibly display. On the other hand they are not true, but are as remote as they could possibly be from any resemblance to the places, persons, or things which they profess to represent. Yet, strange to say, their very hideousness and unveracity gives them a certain attractiveness. The astonished beholder wonders what on earth is coming next, and why the picture labelled (say) "Rome" was not labelled "Design for a Doll's House," or Tin soldiers crossing a wooden bridge." Mr. van Loon's book has had an enormous sale in America. That is probably to the good. For though the book is quite useless to the student who desires any sort of exact knowledge, it may give to the infants for whom it was written a first idea that there were such places as Egypt, Babylonia, Greece, and Italy where events of transcendental importance were transacted thousands of years ago.

FRANCE IN THE MIDDLE Ages

The National History of France: The Middle Ages. By Fr. FUNCK-BRENTANO. Translated from the French by E. O'NEILI.. (15s. net. Heinemann.)

The work before us is the long-missing first volume of the Empire translation of M. Funck-Brentano's "National History of France." Its four successors, by MM. Batiffol, Boulenger, Stryienski, and Madelin, respectively, have already appeared and been noticed by us. Only one more now remains to be issued, viz. that on the Consulate and the Empire. The series when thus completed will cover the whole of the thousand years A.D. 814-1814, and will give a more detailed account of the course of French history than can be obtained from any other work in the English language.

The present volume, by the editor of the series, is at once learned and popular. It tells the story of France from the period of anarchy which followed the death of Charles the Great to the completion of the unity of France under Louis XI. Unlike most histories of France, it does not lay undue stress upon the biographies of the kings. While dealing adequately and appreciatively with the exploits of notable and influential monarchs, such as Philip Augustus and Philip the Fair, it passes rapidly over the insignificances of lesser royalties. The space thus saved is devoted to illuminating accounts of literature, art, and society; and to valuable sketches of the development of towns and universities. Very conspicuous are the numerous and novel quotations from medieval French literature. The translation of these into English can have been no easy task; but Mrs. O'Neill, herself an experienced historian, has achieved a distinct success in her scholarly renderings.

THE BRITISH COMMONWEALTH. A Short History of the British Commonwealth. By Prof. R. MUIR. In two volumes: Volume II. The Modern Commonwealth (1763-1919.) (15s. net. Philip.) The first thing about Prof. Ramsay Muir's new volume which strikes the reviewer is the amazingly low price that is charged for it, as prices go now. Even according to pre-war standards fifteen shillings would not have been accounted excessive for a work of more than 800 largeoctavo pages, printed in excellent type, on good paper, with a stout cloth cover. The fact that such a book can be produced even now by an enterprising publisher should cause a recrudescence of thought in the Syndicates and

Delegacies of the University Presses, by whom prices more than twice as high are charged for volumes no bigger and no better in any way than this. When the reviewer recovers from his preliminary astonishment respecting the price, the second thing that strikes him, as he turns over Prof. Muir's pages, is the vividness of the writer's style. Prof. Muir is, indeed, a master of concise and forceful expression. This narrative moves with a volume and a rapidity that carry the reader along with them in easy abandonment. The third thing that strikes the reviewer as he reads is the great ability with which vast masses of material are organized and arranged in orderly compartments, so that a highly complex story assumes system and intelligibility.

It will be remembered that Prof. Muir's first volume, published in 1920, took up the history of Britain from the earliest days, and traced it in a narrative which constantly grew in fullness down to the year 1763. The present volume resumes the story in 1763 and brings it down to 1919. It divides the subject into six main sections, as follows: (1) Disruption, A.D. 1765-89, centreing round the loss of the American Colonies; (2) Revolution, A.D. 1789-1815, in which the wars with the French occupy the first place; (3) Reconstruction, A.D. 1815-52, when social and economic problems loom largest; (4) Adolescence, A.D. 1852-1880; marked by the growth of Colonial self-consciousness; (5) Imperialism, A.D. 1880-1904, characterized by the struggle of the European powers for overseas dominion ; (6) The ordeal of the Commonwealth, A.D. 1904-19, in which the testing-time of the Great War was the most conspicuous feature.

No student of affairs who is anxious to determine the place of the British Empire in the general scheme of worldhistory should neglect to study Prof. Ramsay Muir's illuminating volume.

"

-almost every word-is weighed and examined with a meticulous and fastidious care, but the greatest achievement of the Introduction work is the masterly which, within the scope of twenty-five pages, strikes the balance between the two traditional and opposed interpretations of Aristotelian philosophy— that of an idealist whose Tò Tí v elva was not far removed from the Platonic idéa, and that of an out-and-out empirical realist-in a manner which constitutes a real contribution to philosophy. It is close reasoning, and every footnote must be pondered with care, but the whole is a work of which Oxford may be justly proud.

The Year's Work in Classical Studies, 1921-1922. Fifteenth Year of Issue. Edited for the Council of the Classical Association by W. H. S. JONES. (3s. 6d. net. Arrowsmith.) The Claim of Antiquity with an Annotated List of Books for those who know neither Latin nor Greek. Issued by the Councils of the Societies for the Promotion of Hellenic and Roman Studies and of the Classical Association. (Is. Milford : Oxford University Press.)

Proceedings of the Classical Association, January, 1922.

Volume

XIX. With Rules and Lists of Members. (4s. 6d. net.
Murray.)

Early Latin Verse. By Prof. W. M. LINDSAY. (28s. net.
Clarendon Press.)
The Making of Latin. An Introduction to Latin, Greek, and
English Etymology. By Prof. R. S. CONWAY. (5s. net.
Murray.)

.

EDUCATION. English Education from Within.

By G. A. CHRISTIAN. (10s. 6d. net. Gandy.)

The reminiscences of a man of Mr. Christian's experience, ranging from pupil-teachership to an inspectorship under the London County Council, and covering more than half a century of responsible connexion with the school system, are bound to prove interesting, especially to members of the elementary branch of the teaching profession. But when to clear recollection there is added the power of selecting the most significant incidents, and of describing them with a facile pen, the result is all the more valuable. We have found it profitable in particular to read the account of the rise and fall of payment period of our educational history. Moreover, in his several capacities as a prominent teacher, a scholastic journalist, and an inspector, Mr. Christian has naturally met a good many interesting and important people, and the personal element in his narrative adds to its piquancy. As we have said, the book will be welcomed by the writer's contemporaries, but, more than this, it is one of those documents which will always be of value to the historian of our educational progress.

CLASSICS.

The Speech against Leocrates. By LYCURGUS. Edited by Prof. A. PETRIE. (5s. 6d. Cambridge University Press.) Prof. Petrie suggests in his preface that schoolboys should be introduced to Attic oratory through Lycurgus, who is much easier than Demosthenes. Those willing to follow the suggestion -a good one, to our mind-will find this edition of the only extant speech well adapted to the purpose. The notes are very full and explain all the technicalities of which a stranger to ancient oratory is bound to be ignorant, and a brief introduction sets forth the chief facts in the life and work of the author.

A Child's Garden of Verses. By R. L. STEVENSON. Done into Latin by Dr. T. R. GLOVER. (7s. 6d. net. Heffer.) To translate the whole of a volume of any author's work into Latin verse is necessarily something of a tour de force, but we have no hesitation in saying that the reader will be delighted with Mr. Glover's achievement. Those who have either to do verses or to teach them will find this book little short of a revelation as to the possibilities of Latin verse. It is beautifully produced and makes a charming volume, marred, to some extent, by the crude egotism of the "Introduction which we think likely to disgust more than it amuses.

"

ΑΡΙΣΤΟΤΕΛΟΥΣ ΠΕΡΙ ΓΕΝΕΣΕΩΣ ΚΑΙ ΦΘΟΡΑΣ. Aristotle on Coming-to-be and Passing-Away (De Generatione et Corruptione). A Revised Text. With Introduction and Commentary by Prof. H. H. JOACHIM. (32s. net. Clarendon Press.)

No higher yet juster praise could be given to this volume than is implied in the recognition that its scholarship is worthy of the name of Ingram Bywater, to whose memory it is dedicated. Prof. Joachim began by making a translation (already noticed in these columns) for the Oxford Series of Aristotle translations, edited by Mr. W. D. Ross, and his labours led him step by step to the present monumental work. Obviously a translation was impossible without a sound text, and of the Teubner text by C. Prantl, published in 1881, Prof. Joachim's own researches upon the MSS. induce him quietly to remark: 'I regret that I have been unable to form a high opinion of Prantl's work.” (x.) The commentary is most exhaustive and scholarly; every line

"

The Charm of Teaching Children. By W. Robb.
(5s. net. Gay & Hancock.)

There are many ways of classifying books on education, and one very good way might be based upon the current philosophical distinction between the intellectual and the intuitional modes of arriving at truth. Of books of the former class, including all educational psychologies, the name is legion and the quality generally good. Of books of the latter class good examples are comparatively rare, but among them we have no hesitation in placing Mr. Robb's delightful chapters on the teacher's life and outlook. To many of our readers it will be enough to say that these chapters are well worthy to take their place by the side of D'Arcy Thompson's "Day-Dreams Mr. of a Schoolmaster," of which they strongly remind us. Robb's book makes stimulating and helpful material for the teacher's quiet hours of reflection.

Bergson and Education. By Dr. O. A. Wheeler.
(6s. 6d. net. Longmans, Green.)

"

We extend a cordial welcome to Dr. Olive Wheeler's little book on Bergson and Education." Most of the original work now being done in education is by way of experiment and measurement carried out in accordance with methods derived from physical and mathematical science. Of the value of the promise of much of this work there can be little question. But for its right direction there is as much need as ever of guiding principles derived from a survey of life as a whole, and such principles it is the business of philosophy to search for. It is because we believe that educational aims must in every age be related to the prevailing philosophy of that age that we heartily commend this book. Its exposition of Bergson's position is a model of clarity, and its applications to recent educational developments are extremely suggestive.