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that the protest against the excessive and unnecessary time given to mathematical instruction in all our schools which has begun, will continue, none can doubt. As is well known, no primary or secondary school programme of this country can be scratched without revealing an omnipresent Tartar known as arithmetic. This mathematical Cossack is ever found firmly settled in his saddle, and foraging for subsistence hither and yon, upon friend and foe alike. The result is, that in the classical preparatory school the boy is hampered and handicapped by serious mathematical studies which absorb time that he could more profitably devote to his mother-tongue, to modern languages, and to 'science studies. On the other hand, in the scientific or English courses, the pupil fitting for the scientific school, or for business, is forced to take unwelcome draughts of Latin. These last are somewhat diluted, it is true, and are given perhaps on the general principle entering into the administration of certain family medicines, viz., that if not of any direct service to the patient, they can do him no possible harm. But in point of fact, while as a rule the Latin given in these brief courses can be of little or no value to a pupil fitting for the scientific school, time is taken from subjects having a direct personal bearing on his future career. It is interesting to note how, in France, this feature of instruction is managed.
A French boy having passed through the grades of the lycée classique, as exhibited in the preceding table, and intending to devote himself to a literary profession, proceeds without further ado to his examination for the baccalauréat és lettres wherein mathematics plays but a subordinate part, as is indicated by the small percentage of time given it in the lycée course. But, for the benefit of graduates designed for the national schools, or for those who prefer to present themselves for examination for the baccalauréat ès science instead of ès lettres post-graduate lycée mathematical courses are instituted. The classe de mathématiques élémentaires, for instance, has for its object the study of matters comprised in the programmes of the baccalauréat és sciences, as well as those of the military (Saint-Cyr), the naval, and forestry schools and the central school. The curriculum of this class devotes seven and a half hours per week to mathematics, four and a half hours to science studies, two each to the mothertongue, Latin and modern languages, three hours to history and geography, one hour to philosophy, and four hours to drawing. This course is of but one year. It is usually taken by pupils from the classe de rhétorique, but may be taken by pupils from the classe de philosophie who wish to review and increase their mathematical attainments. A much stiffer and more comprehensive drill in mathematics is afforded by the classe de mathématiques spéciales. This course is also of but one year. The instruction given in this class has for its object the preparation of pupils who have completed the lycée course, and who purpose entering the polytechnic, the superior, or the central schools. None are admitted to this course who have not previously manifested an apti. tude for it. The hours of recitation per week are, mathematics eleven hours, descriptive geometry three hours, physics and chemistry five hours, natural history three hours, French language two hours, modern languages two hours, history and geography three hours, and drawing two hours ; total, thirty-one hours.
The instruction to-day given in France under the name of l'enseignement secondaire spécial has found a secure footing only after many years of violent discussion and constant opposition. Its career, however, has been steadily advancing and gaining in public consideration ever since its organization in 1865. Its programme was extended and revised in 1881, and in 1886 it was organized on its present basis. The courses of study have been framed with especial reference to the requirements of a large class of pupils of good social position, who have neither the desire, the tastes, nor perhaps the leisure for long years' study of dead languages. It is a response to the needs of a large class for a preparation for actual life in various careers, which the classical courses are incapable of giving. The school is in a sense the Realschule of the French, differing from its German congener, however, by the entire elimination of Latin from its programme. The course comprises six years of study, crowned, at its successful termination, by the diploma of bachelier de l'enseignement secondaire spécial, the possession of which entitles the holder to admission to the examinations for the baccalauréat ès sciences, for the military school of Saint-Cyr, and, with the exception of the Polytechnic School, which still holds to its classical requirements, to other national schools with requirements of a general similar character.
However interesting, as an illustration of French school meth. ods, the curriculum of the secondary special schools may be, the severity of the course, as a whole, renders it unlikely that it will ever be very closely imitated in this country. The recitations here range from twenty-five to twenty-nine hours per week, giving, for the whole course, 6,360 hours, against 4,3604 hours in the American representative of the same type of school.* The official programme shows that the instruction of these 6,360 recitation hours are distributed as follows: Mother-tongue, 1,000; modern languages, 1,160; history, 360; geography, 280; mathematics, 1,080; science studies, 960; drawing, 960 ; penmanship, 160; bookkeeping, 80; morals, 40; legislation, 80; political economy, 40; philosophy, 160. The ages of the pupils average eleven years in the first and sixteen in the last class. The recitation hours of a pupil passing through the last two grades of the grammar school, and the four years' course of the English High School in Boston are, barring certain changes on account of options, as follow: Mother-tongue, 1,1114; modern languages, 494 ; history, 570; geography, 152; mathematics, 722; drawing, 760; book-keeping, 95.
* As the secondary special schools of France occupy about the same place in the French system as the upper classes of grammar schools and the English high schools occupy in ours, the French programmes of these schools have been brought by the writer into comparison with a typical American school the courses of the two upper classes of the grammar schools and those of the English High School of Boston being employed as a fair American representative.
Here, again, as in the case of the French classical lycée course, the instruction in the mother-tongue is found to be less than in the American representative school. The hours devoted to mod. ern languages (1,160) are, in fact, somewhat in excess of those given to French (1,000), and, it may be added, are in most marked contrast to the time allotted to the same study in the Boston High-School programme (494), even after the latter has received a credit under this head for a certain number of hours that in point of fact are used by many pupils for Latin.
Mathematics, which, as has been seen, plays but a subsidiary rôle in the classical lycée course, in the secondary special course assumes more prominence comparatively, the average being 41 hours against 37 hours' recitation per week in the typical American programme. Yet even here it is not up to what may be termed the United States standard. A tabulated exhibit of the hours of the classical courses of the two countries shows that an average of only one hour and fifty minutes per week is given to mathematics in the classical lycée course, compared with an average of three hours and forty minutes in the Boston classical school course. A comparison of that course with the French secondary special programme develops also the fact that a typical American classical school not only devotes more hours to mathematics than the French consider essential for a preparatory scientific course, but also exhibits the further surprising fact that the Boston English High-School course, with two years of grammar-grade school prefixed to it, actually gives less time to mathematics than is devoted to that study in the six years' course proper of the Latin School. And this is not by any means peculiar to the Boston school courses. The programmes of other schools exhibit a treatment of the mathematical subjects quite similar. At Phillips Exeter precisely the same number of hours is given to mathematics in the classical and scientific courses. At Williston, even after adding the course in surveying to the mathematics, the percentage of the latter to the whole course is less than on the classical side.
From the data here given it seems clear that if we are to hope to put our schools on anything like an equality with those of France, to say nothing of those of other civilized countries of the world, certain modifications of our school programmes have certainly to be made. First and foremost among those changes there would seem to be indicated a need for a certain specialization of our school courses with reference to the different demands made upon the schools by different classes of pupils. That our schools of primary and secondary grade, as they stand to-day, do not respond to the varied requirements of American society, seems quite obvious. The complaint of President Eliot sufficiently indicates their shortcomings, so far as a preparation for college is concerned. For many years professors and teachers at scientific and technical schools have mourned the dearth of preparatory schools that should give them pupils not handicapped by great deficiencies in training of the powers of observation. Business men are quite unanimous in their belief that the schools do not afford a satisfactory training for commercial pursuits, while he who runs may read their many deficiencies for the constantly increasing class of pupils whose period of school life terminates in the grammar grade.
The main cause of the present stage of development of the school system is not so deeply hidden that one has to search long for it. The average American school programme at the present time is simply a living illustration of a development, on American lines-influenced and modified by national characteristics
-of the old educational theory that literature and language are the basis of all mental culture and training. The educational structure reared on this theory, beset and more or less damaged by modern assaults, has been repaired here and patched there, but the old framework and the old foundations have ever remained to cramp intelligent reconstruction and practical reform. The result is in the main a hotchpotch with which no one is thoroughly satisfied. It would seem to be a clear case of the old house repaired and refurnished, until it is satisfactory to no one. It is passing strange that the school system of the United States, in respect to its want of specialization, should stand almost unique among the many examples of the national aptitude in adopting means to ends. In business life, in professional life, in industrial pursuits, our nation has shown itself peculiarly clever in its concentration of labor in systematic, well-defined channels having special reference to the results to be attained. Yet, when we come to compare our school programmes with those of other nations, we not only find that we do not do as much school work, nor as satisfactory work, but that what we do is done in an antiquated and unscientific manner. In France, for example, we find a school system that in its superior primary course gives to the child of the humblest artisan not only a solid foundation in all essentials of mother-tongue instruction, but, by means of its complementary courses, in manual training and modern languages as well. We likewise find a clean-cut, well-defined course in the special secondary schools for the child who seeks preparation for commercial or professional life by modern methods; while, by the systematic arrangement of its classical lycée course, results are achieved which excite the admiration and envy of the president of one of our most honored universities. Turning to our own programmes, we find what can only be characterized as a more or less futile effort to build on one foundation several distinct structures, each one of which is diverse in the special ends sought to be accomplished. In our effort to do everything, we have failed to do anything sufficiently well to entitle it to favorable comparison with the results attained by a more skillful apportionment of labor.
We can also learn from the French programmes that if American schools are to accomplish results comparable with those attained in France, American children have not only to work on more specialized lines, but have also to work more. There can be no doubt that the outcry against “long school hours” and “home study," which for many years past has been so resonant in this country, has seriously affected the efficiency of our schools. As the exhibit of school programmes here given shows, the average hours of recitation in American fitting schools are very considerably less than in those of France. And those of France are to about an equal degree less than the hours of the German gymnasia and Realschulen. It is full time that a halt be called on the further progress of this absurd clamor. The idea that a healthy American boy, between the age of eight and fifteen years, let out of school, as he generally is in these days, at from one to two o'clock, should not do a certain amount of systematic study at home, certainly can but be characterized as absurd. It is probable that but few persons, who have not made special inquiry in regard to it, appreciate the extent to which this sentiment against out-ofschool study now prevails in this country. If it has had the effect of crippling the public schools, it may be said that it has really paralyzed many private ones where this feeling is pandered to. The advanced age of pupils entering the private fitting schools, as well as the advanced age of college matriculates, is to a great extent due to this disinclination of parents to submit their children to regular systematic study in their earlier school life. In collecting the data for this paper the writer has been pleased to