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programme which it recommended for gradual adoption. These changes are five in number.

The first is the introduction of elementary natural history into the earlier years of the programme, to be taught by demonstrations and practical exercises rather than from books. The term natural history was doubtless intended to include botany, zoölogy, geology, and physical geography. Some room for these subjects is already made in most grammar-school programmes, and the recommendation of the association refers as much to methods of teaching as to time allotted to the subject. The association recommends that the teaching be demonstrative, and that adequate apparatus be provided for teaching these subjects. There is a lamentable lack of the proper apparatus for teaching geography in the public schools. Indeed, in many schools there is no proper apparatus for teaching geography or any other natural-history subject to young children. Natural-science apparatus has been provided in some exceptional high schools, but as a rule grammar schools are still destitute in this important respect.

The second recommendation is the introduction of elementary physics into the later years of the programme, to be taught by the laboratory method and to include exact weighing and measuring by the pupils themselves.

The third and fourth recommendations cover the introduction of algebra and geometry at the age of 12 or 13.

The fifth is the offering of opportunity to study French or German or Latin or any two of these languages from and after the age of 10.

III. Such are, in brief, the proposals for shortening and enriching the grammar-school course. I want to use the rest of the time allotted to me in discussing the objections to these various changes.

The first objection I take up is the objection to a reduction in the time devoted to arithmetic. Many teachers are shocked at the bare idea of reducing the time given to arithmetic, because they believe that arithmetic affords a reculiarly valuable training, first, in reasoning, and secondly, in precision of thought and accuracy of work. They perceive that the greater part of the school progamme calls only for memorizing power and they think that arithmetic develops reasoning power. The fact is, however, that mathematical reasoning is a peculiar form of logic which has very little application to commen life and no application at all in those great fields of human activity where perfect demonstration is not to be obtained. As a rule, neither the biological nor the moral sciences can make use of mathematical reasoning. Moreover, so far as mathematical reasoning is itself concerned, variety of subject is very useful to the pupils. The substitution of algebra and geometry for part of the arithmetic is a clear gain to the pupil so far as acquaintance with the logic of mathematics goes. Again, practice in thinking with accuracy and working with demonstrable precision can be obtained in algebra, geometry, and physics just as well as in arithmetic. It is quite unnecessary to adhere to the lowest and least interesting of these exact subjects in order to secure adequate practice in precision of thought and work.

The second objection is that there are children in the grammar schools who are incapable of pursuing these new subjects. Assuming that this allegation is true of some children, I have to remark, first, that we shall not know till we have tried what proportion of children are incapable of pursuing algebra, geometry, physics, and some foreign language by the time they are 14 years of age. It is a curious fact that we Americans habitually underestimate the capacity of pupils at almost every stage of education, from the primary school through the university. The expectation of attainment for the American child or for the American college student is much lower than the expectation of attainment for the European. This error has been very grave in its effects on American education all along the line, from the primary school through the university, and till within twenty years the effects were nowhere worse than at the college grade. It seems to me probable that the proportion of grammar-school children incapable of pursuing geometry, algebra, and a foreign language would turn out to be much smaller than we now imagine, but though this proportion should be large it would not justify the exclusion of all the capable children from opportunities which they could profit by. At the worst this objection can only go to show that it will be necessary to adopt in the grammar schools a flexible instead of a rigid system-some selection or choice of studies instead of a uniform requirement. Those children who are competent to study a foreign language should certainly have the opportunity of doing so at the proper age, that is, not later than 10 or 11 years; and those who are competent to begin geometry at 12 and algebra at 13 should have the chance. If experience shall prove that

a considerable proportion of grammar-school children are incapable of pursuing the higher studies that fact will only show that the selection of appropriate studies for children by their teachers should be adopted as a policy by the public grammar school. To discriminate between pupils of different capacity, to select the competent for suitable instruction, and to advance each pupil with appropriate rapidity will ultimately become, I believe, the most important functions of the public-school administrator-those functions in which he or she will be most serviceable to families and to the state.

Another objection to the changes proposed often takes this form-they are said to be aristocratic in tendency. The democratic theory, it is said, implies equality among the children, uniformity of programme, uniform tests for promotion, and no divisions in the same schoolroom according to capacity or merit. I need not say to this audience that these conceptions of true democracy in schools are fallacious and ruinous. Democratic society does not undertake to fly in the face of nature by asserting that all children are equal in capacity or that all children are alike and should be treated alike. Everybody knows that children are infinitely diverse; that children in the same family even are apt to be very different in disposition, temperament, and mental power. Every child is a unique personality. It follows, of course, that uniform programmes and uniform methods of instruction, applied simultaneously to large numbers of children, must be unwise and injurious-an evil always to be struggled against and reformed, so far as the material resources of democratic society will permit. It is for the interest of society, as well as of the individual, that every individual child's peculiar gifts and powers should be developed and trained to the highest degree. Hence in the public schools of a democracy the aim should be to give the utmost possible amount of individual instruction, to grade according to capacity just as far as the number of teachers and their strength and skill will permit, and to promote pupils not by battalions, but in the most irregular and individual way possible. A few days ago I heard an assistant superintendent in an important city declare that many grammar-school teachers in his city objected to any division among the fifty or more pupils in each room; any division, that is, according to the attainments and powers of the individual pupils. They wanted all the pupils in a given room to be in one grade, to move together like soldiers on parade, and to arrive at examination day having all performed precisely the same tasks and made the same progress in the same subjects. If that were a true portrait of the city graded school it would be safe to predict that the urban public school would before long become nothing but a charity school for the children of the dependent classes. Intelligent Americans will not subject their children to such discipline when they once understand what it means. The country district school, in which among forty or fifty pupils there are always ten or a dozen distinct classes at different stages and advancing at different rates of progress, would remain as the only promising type of the free school. Not only is it no serious objection to the new proposals that they must diminish uniformity in schools-it is their strongest recommendation. So far from the changes proposed being of aristocratic tendency, they are really essential to a truly democratic school system; for they must be adopted and carried into effect before the children of the poor can obtain equal access with the children of the rich to the best education they are capable of, whatever the grade of that education may be. Accessibility of appropriate opportunity is the essence of democratic society; not equality of gifts, attainments, or powers, for that equality is unnatural and impossible; not abundance of inappropriate opportunities, for such abundance is of no avail; but accessibility of such appropriate opportunities as the individual can utilize for his own benefit and that of society. The American grammar-school programme now actually prevents an intelligent child from beginning the study of a foreign tongue at the right age. We all know that that age is very early, long before the high-school period. It prevents him from beginning the study of algebra and geometry at the right age. It makes it impossible for him to get a chance at the right kind of study of natural science. If a boy is not to go to the high school, he loses that chance forever under our present system. If he is going to the high school he does not get the chance till much too late. The poor boy in the United States should have as good a chance as the child of a rich man to obtain the best school training which his character and powers fit him to receive.

Is not that a fair statement of what democratic society may reasonably aim at and seek to effect through its own grammar schools? Yet the existing grammar-school programme actually prevents the poor boy from getting that chance. The rich man can obtain for his children a suitably varied course of instruction,

with much individual teaching, in a private or endowed school; but the immense majority of American children are confined to the limited, uniform, machine programme of the graded grammar school. A democratic society was never more misled as to its own interest than in supposing such a programme to be for the interest of the masses. The grades for pupils from 6 to 15 years of of age are an obstruction to the rise through democratic society of the children who ought to rise. Uniformity is the curse of American schools. That any school or college has a uniform product should be regarded as a demonstration of inferiority-of incapacity to meet the legitimate demands of a social order whose fundamental principle is that every career should be open to talent. Selection of studies for the individual, instruction addressed to the individual, irregular promotion, grading by natural capacity and rapidity of attainment, and diversity of product as regards age and acquisitions must come to characterize the American public school if it is to answer the purposes of a democratic society.

Fourth. It is further alleged that the changes proposed are chiefly for the advantage of the well-to-do children whose education is to be carried beyond the grammar school to the high school, and possibly to the college above the high school. They are indeed for the interest of this class of children; but they are more for the interest of the children who are not going to the high school, and for whom therefore the grammar school is to provide all the systematic education they will ever receive. The Association of Colleges in New England distinctly says that it makes its recommendations in the interest of the publicschool system as a whole; "but most of them are offered more particularly in the interest of those children whose education is not to be continued beyond the grammar school." Take, for example, the subject of geometry. It has many and very important applications in the arts and trades. Every mechanic needs some knowledge of it. Its applications are as important as those of arithmetic, if we except the very simplest and commonest arithmetical operations. That the great mass of American children should leave school without ever having touched this subject, except perhaps in arithmetic under the head of mensuration, is a grave misfortune. To introduce variety into the grammar-school programme is in itself likely to profit the children who are never to go to school after they are 14 years of age even more than the children who are. A child who is dull in one subject may be bright in a different subject. Thus a child who has no gift in language may be keen and quick in natural-history studies. A child who has no taste for arithmetic may prove unusually strong in geometry. One whose mind is not easily moved through purely mental exercises may be intellectually developed through drawing and manual training. In college we are extremely familiar with these diversities, and the elective system is now giving in most American colleges free play for the profitable exhibition and cultivation of these diverse gifts. In a similar manner the grammar school will be better for even the dull and slow children if its studies are made more various and its whole system more flexible.

A fifth objection to the introduction of new subjects is that children are already overworked in school. In an address which I gave rather more than a year ago I pointed out that there are two effective mechanical precautions against the ill effects attributed to overwork at school, precautions which it is delightful to see are more and more adopted. They are good ventilation and the systematic use of light gymnastics at regular intervals during school hours. School time ought to be the best managed of all the day from a sanitary point of view, excepting these hours which the children pass out of doors. If the schoolroom were invariably healthier in every respect than the average home we should hear less about overwork at school. There is, however, a third precaution against overwork which is quite as important as either of those already mentioned; it is making the school work interesting to the children. Four years ago I asked the attention of this department of the National Educational Association to the depressing effect which lack of interest and conscious progress in school work has upon children. To introduce new and higher subjects into the school programme is not necessarily to increase the strain upon the child. If this measure increases the interest and attractiveness of the work and the sense of achievement it will diminish weariness and the risk of hurtful strain.

Lastly, there is an apprehension lest the introduction of the new subjects recommended should increase existing difficulties with regard to promotion. Parents are sensitive about the promotion of their children. They want the dull ones and the bright to be promoted at the same rate. Their sympathies are quite as apt to be with the slow children as with the quick. I believe that this practical

difficulty should be met in part by the abandonment of uniform attainment or of a standard of required knowledge as ground of promotion. In Harvard College, where there is no such thing as a uniform programme of study for all students, and where, indeed, there is small chance that any 2 students out of 1,450 will pursue the same course of studies during their four years of residence, we have long since abandoned uniform attainment as ground of promotion from one class to another. The sole ground of promotion is reasonable fidelity. I venture to believe that this is the true ground of promotion in grammar schools as well, and that by the sole use of this principle in promoting the difficulty now under consideration would be much alleviated, if not done away with. The right time for advancing a child to the study of a new subject is the first moment he is capable of comprehending it. All our divisions of the total school period into years, and into primary, grammar, and high schools, are artificial and in most cases hurtful or hindering to the individual. The whole school life should be one unbroken flow from one fresh interest and one new delight to another, and the rate of that flow ought to be different for each different child. Economical schcol administration inevitably interferes somewhat with the desirable continuity and variety of motion, but the most skilful and wisest administration is that which interferes least.

On reviewing the progress of this reform since I had the honor of discussing the question," Can school programmes be shortened and enriched?" before this ⚫ department of superintendence four years ago, I see many evidences that a great and beneficent change in public-school programmes is rapidly advancing. The best evidence is to be found in the keen interest which superintendents and teachers take in the discussion of the subject. Through them the proposed improvements will be wrought out in detail, their influence will be successfully exerted on parents, committees, and the public press; and their reward will be, first, the daily sight of happier and better-trained children, and secondly, the elevation of their own profession.

Algebra and geometry in grammar schools-President Eliot criticised.-Edward Brooks, LL. D., superintendent of schools, Philadelphia': The programme for "eight grades," as recommended by President Eliot, is almost universally adopted in our graded schools. In Philadelphia pupils enter the primary schools at 6 years of age, and have an eight years' course to complete the grammar schools. Very bright pupils are allowed to do it in less time. The same thing is generally true of the cities of the country; very few have a nine years' course; almost none a ten years' course. His suggestion of combining studies has also been adopted in many of our public schools. With primary grades it is a very common practice to unite geography and history, and with more advanced grades political and physical geography have usually been taught together for many years.

I doubt very much whether there is any advantage to be derived from the introduction of algebra into the grammar-school course. To the ordinary citizen in practical life a knowledge of algebra will be found of little value. No one buys or sells by algebra; and a knowledge of polynomials or the quadratic equation would be of little use to the housewife in the discharge of her duties. Indeed, no one of the mathematical branches would be of so little value in the ordinary practical affairs of life as algebra. Besides, we can not advocate the study of algebra on account of its disciplinary value, for no mathematical branch gives so little mental discipline that the ordinary business or professional man would find of use. As a disciplinary study the elements of algebra will be found to be far inferior to either arithmetic or geometry. Much of algebra is a mere calculus, and the aim of the student is to become expert with the manipulation of symbols, a form of mental operation entirely removed from that of ordinary life. In place of algebra I would urge a more general introduction of arithmetical analysis, usually known as mental arithmetic. This form of reasoning, originating with Warren Colburn, is better adapted to sharpen and strengthen the analytical powers of young students than any other branch of the grammar-school curriculum. It is far superior to algebra in developing the thought power of the student. It is also generally simpler and shorter in its methods of reasoning and operation than algebra. Take the problem that President Eliot gives, “The sum of 2 numbers is 24, and one is twice the other." I can obtain the results by the simple process of arithmetical analysis before the algebraist could write his equations. A problem like the following: "If A can do a piece of work in four days and B in six days, in what time can both do it?" is much more simply

1 Reported in the Journal of Education.

worked by arithmetical analysis than by algebra. And the same is true of a large number of problems. I urge, therefore, in place of algebra, that the beautiful system of arithmetical thought known as mental arithmetic be more fully introduced into our grammar schools than it is to-day.

The study of geometry as a science should not be introduced into our grammar schools. Concrete and practical geometry is already taught in most of our grammar schools under the head of drawing and mensuration. In most of these schools the pupils are made familiar with all the ordinary geometrical figures and their properties or principles. These principles include the methods of obtaining the areas of plane surfaces, the area and circumference of the circle, and the surface and volume of the parallelopiped, pyramid, cylinder, cone, and sphere. These principles are obtained, not by demonstration, but by concrete illustration, and they are applied by the children until they are familiar with them. This is all that it is practicable to do with geometry in the grammar schools. The pupils are not prepared for the logical processes of abstract geometry and can not understand them. The method of reasoning from axioms and established principles by the logical methods of geometry is too difficult for the ordinary student of the grammar schools. It is said that abstract geometry, with its demonstrations, is taught in the public schools of Germany and France; but in my examination last summer of the elementary schools of Paris corresponding to our grammar schcols I did not find a single pupil studying the science of geometry. They apply the principles reached concretely, as we do in our gram- • mar schools.

That the work of the grammar schools can be improved by shortening the course of study is a proposition that needs demonstration. That it may be enriched is a most desirable object, though it is a question whether this enrichment may not be attained by other means than the addition to or subtraction from the present course of studies. The broader question is, how shall the best results of culture and knowledge be attained in our grammar schools? The object can be attained by having a correct course of study, as rich in materials for intellectual, moral, and spiritual culture as is possible, and by having welltrained and skillful teachers to use this course of instruction to the best advantage.

Those German and French schools.-John T. Prince, agent Massachusetts board of education: President Eliot is clearly wrong in his impression of what is done in the elementary schools of France and Germany. Algebra and geometry are not in the schools that compare in any regard with our grammar grades. Algebra nowhere precedes geometry. The geometry taught is not demenst: ative, but is more like that taught in the grammar and even in the primary grades here. The colloquial speaking of the Romance languages has no such value as these later reformers would place upon it. The whole difficulty lies in the fact that the grammar schools of Europe and America are compared by men who have not studied either.

The two ideals of the course of study.-W. T. Harris, commissioner: In the schools of the United States there prevail two different ideals of the course of study; the one originating with the directors of higher education and the other a growth from the common elementary school. These two ideals clash in quite important particulars. The common-school course of study, as it appears in the elementary school and in the public high school which gives secondary instruction, does not shape itself so as to fit its pupils for entrance to the colleges. At least, if we admit that as an actual fact many high-school pupils do enter college, we must also admit that there is a constant tendency in the pub ic high school to diverge in its course of study and follow a path that does not lead to the college.

The older colleges of the States, following the traditions brought over from Europe, built their course of study on mathematics and the classical languages, Latin and Greek. They accordingly demanded of the preparatory schools a preliminary training or preparation along these lines and neglected all else.

Human learning at one period did not include much that was not conceived and expressed in Latin or Greek words. But within the past 300 years there has arisen a modern tributary stream of human learning, and it has some time since begun its demand for recognition in the course of study. This modern side of human learning includes the natural sciences and modern literature. These two contingents are almost wholly the products of the past 300 years.

The demands of the sciences and the demands of the literature of the modern languages to a share in the course of study were met in one way by the college

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