ARITHMETIC.1

Next to the development of reading, the changes in the study of arithmetic are most significant in indicating the tendency of the time.

Arithmetic has long been considered the ideal, if not the principal, disciplinary study. Its place in the old course was second to none. Its exercises were designed less to directly assist the pupil in the avocations of life than to call out his reasoning faculties, to cultivate habits of accurate thought, and to train his powers of analysis. These conditions are gradually changing. The belief is gaining ground that problems having more or less adaptability to the business of life, furnish as much insight into arithmetical logic as the elementary pupil has time to gain; that the discipline and information furnished by other subjects are more valuable than the discipline of those portions of arithmetic which convey no information likely to be profitable in the daily affairs of the average man.

Less time proportionally is given to arithmetic in Chicago than in any other city in the country, only 9.3 per cent. being there devoted to that study; while in Boston, notwithstanding the wide attention attracted to the "simplification” of the subject and the reduction of the time devoted to it, it still apparently occupies one-sixth of the whole time. The school committee of Boston did not take as advanced a position in 1887 when they struck from the required course "the mensuration of the trapezoid and of the trapezium, of the prism, pyramid, cone, and sphere; compound interest, cube root and its applications; equation of payments, exchanges, similar surfaces, metric system, compound proportion, and compound partnership," as did Superintendent Howland in 1886, when he made the following a part of his annual report:

In the higher grades, too, many subjects have been introduced that are no part of arithmetic, in any true sense, as gold investments, United States bonds, insurance, banking, etc., which no child or man but the specialist will ever need. What business man ever resorts to the least common multiple or the greatest common divisor, topics upon which our pupils spend so much time which should be given to the use and the logic of numbers?

"We are surely but slowly getting away from the so-called arithmetical analysis, which consists of a mere riddle of words to the young pupils, giving no knowledge, no intelligence, no reasoning power.

"Much of this old aralysis aud definition had no other result than that of confusing and confounding the pupil, and deadening his interest in the study and practical application of numbers."

Mr. Howland is not yet satisfied that arithmetic has found its proper place in the Chicago course, and he would evidently be content to see the time even further reduced, for in his report for 1887-'88 he says:

"It has long seemed to me that in the city the eager heart must grow hungry over the dry fruits of 3 or 4 years in geography, a year and a half in United States history, and 8 years in arithmetic, with so little that interests or concerns them in their daily life or contributes to success or real intelligence.

"Why could not a course be provided in addition to the usual branches of the grammar grades to vitalize their work and awaken their observing and thinking powers! For instance, in the fifth grade once or twice a week place physics-matter, gravitation, weight, friction, force, power, inertia; in the sixth, light, heat, sound; in the seventh, electricity and magnetism, with chemistry and geology in the eighth.

"Perhaps better than twice a week would be to omit arithmetic or geography for a term."

Taking into consideration the small proportion of time already allotted to arithmetic in Chicago, Mr. Howland goes much further than the great majority of the profession generally-certainly no other superintendent has expressed such radical views as those quoted. But, nevertheless, changes appear everywhere in the general direction of emphasizing the "little that interests or concerns the pupils in their daily life," and of eliminating all those parts which "no child or man but the specialist will ever need."

GRAMMAR.

Grammar also shows the effects of the demand for a closer application of school studies to the duties of life. Many whose school attendance has not yet ended began the formal study of the structure of language in the earliest years of their school life. Parsing, analysis, declension, conjugation, etc., or what is frequently alluded to in late reports as "technical grammar," but a few years ago were encountered by the pupil after 2 or 3 years of study at most. Statements recently received by this office show that at the present time, out of 69 of the principal cities, in bnt 2 (Mobile,

Ala., and Utica, N. Y.) is the study of grammar begun as early as the third year, and in 1 of them, Mobile, the entire elementary course covers but 5 years. In only 2 cities (San Francisco, Cal., and Baltimore, Md.) is it begun as early as the fourth year. In 14 cities it is begun in the fifth year, in 27 in the sixth year, in 20 in the seventh, in 6 in the eighth, and in 1 city, Burlington, Vt., not until the ninth

year.

Table 8 shows these facts so far as 29 of the most important cities are concerned, it having been found impracticable to include all the cities in the more detailed table. This postponement of the study of grammar as a science does not imply the abandonment for that time of all study of language, but rather a change which brings the art of grammar into greater prominence, for, as parsing, declension, conjugation, analysis, etc,, are pushed further up in the course, their place is taken by "conversation exercises" and "language lessons." In making such changes the reasons assigned never refer to the general value of "technical" grammar as a disciplinary study, and rarely to the inability of young children to study it with mental profit. It is conceded that the science of grammar as a means of culture has a value peculiarly its own, since it is the only study of the elementary school that deals not with the subject-matter, but with the form of thought, and hence the only subject that takes the pupil into the sphere of abstract thought. But in the admitted fact that the formation of habits of correct speech is not dependent upon a knowledge of rules and definitions relative to the constructions of language and their mutual dependence is found the justification for the lessened weight attached to such study. As Fitch expresses it:

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"The practical art of using the language in speech or writing with good taste and correctness is probably best to be attained by talking to the pupil, by taking care he hears little but good English, by correcting him when he is wrong, by making him read the best authors, by practicing him much in writing, and when he makes a mistake by requiring him to write the sentence again without one. It will certainly not be attained by setting him to learn Murray's, or, indeed, any other grammar."

The art is the thing directly useful; the science has no obvious relation to practical affairs. The ability to speak and write correctly is not only desirable but essential in every walk of life; the technical rules of etymology and syntax are almost valuless per se. Therefore, in accordance with the movement whose progress is here recorded, the art, i. e., the practical, increases in importance in the course of study, while the science, i. e., the disciplinary, decreases in the same proportion.

GEOGRAPHY AND HISTORY.?

In relation to geography and history it may be said that while in their treatment they have undergone important changes, those changes have resulted from the adoption of more intelligent methods of teaching rather than from any change in the general purposes of instructions.

Essentially "information subjects," they have always been taught with that end principally in view. That they were encumbered with useless details that drew the mind of the pupil from important general facts and ruling principles was due, not to a belief that such teaching was the more effective discipline of the mind, but to a less intelligent comprehension of what information best serves the pupil. Such changes being the result of greater efficiency on the part of the teachers are naturally followed by a clearer understanding and a more rational knowledge of the subjects on the part of the pupils. They further save the time previously frittered away for the acquirement of more advanced knowledge and, consequently, if no diminution of time accompanies the adoption of better methods, a wider acquaintance with the subject taught may be expected. In the case of geography and history no tendency is appar ent to materially alter the time apportioned and there seems to be nothing to justify a belief that the time now devoted to these subjects is either considerably more or considerably less than at any recent period.

The inference, therefore, is that at the end of the elementary course the pupil of to-day knows more that is worth knowing of geography and history than did the pupil of any past period. But whether the increased efficiency of the instruction in these branches changes the direction of the resultant of all the forces brought to bear upon the pupil's mind is a question which depends upon whether the improvement in the teaching of the other subjects has progressed in the same ratio. Speaking generally, it is safe to say that the ability to distinguish between the essentials and the non-essentials in the accomplishment of a definite aim is displayed in no one particular branch more than in another and that in this respect the improvement in teaching has been uniform in all subjects.

Fitch's Lectures on Teaching.

See Table 1, 2, 9, and 10.

Hence the conclusion follows that the effects of the instruction in geography and history are relatively not greater in the course of to-day than in the old course, and that the general bent of the mind is not influenced by either of these subjects any more in the new education than it was in the old.

The same applies equally to spelling and to writing, which are purely instrumentary branches, and in nearly as great a degree to drawing and music, the representatives of æsthetics in elementary schools. The ends in view in the teaching of all these branches remain what they have been since they were brought into the curriculum. More time, however, is given to drawing than formerly and somewhat more to music, but there has been no material change in this respect in the other subjects.'

SUBJECTS COMPARATIVELY NEW TO THE COURSE.

Having described the effects of changed conditions and beliefs upon the older brauches of instruction it is now in order to consider the new subjects which these conditions have caused to be brought into the elementary course. Of these the natural sciences and civil government are now most generally taught. General history, algebra, geometry, and the several branches of manual training have not yet been extensively introduced, although each of them finds favor in the eyes of many of the foremost American educators, and it is probable that neither subject has attained its full degree of popularity.

German, French, and Spanish appear in some of the elementary courses, but they do not belong to the same category with the studies just named, for it can not be said that the object of such instruction is to give roundness and completeness to the character of the training. This teaching is given only in those cities in which there is a considerable foreign element who demand instruction in their own language, and is based on local and administrative rather than on general and pedagogical grounds, for reasons of the latter class apply to immigrants only, and not to the great body of the pupils.

Manual training represents the extreme application of the principle which demands that each course shall be complete in itself as far as it goes and shall impart knowledge capable of being applied in everyday life. While instruction in natural science, civil government, etc., seeks to add symmetry to the attainments and to make the pupil a more complete man by anticipating the high school and the college, manual training goes further, and by anticipating the apprenticeship or the technical school would contribute to the acquirements necessary to the complete workman. This subject, however, was fully discussed in the Report of 1887-88, and further reference to it here is unnecessary.

NATURAL SCIENCE.

The time shown by Tables 1, 2, and 13 to be devoted to natural science does not convey a correct idea of the importance of that branch of instruction in the course of study. The figures represent in the main only the time occupied by those oral lessons given with the sole object of imparting such information, but equally as important as these are the reading lessons and the conversation exercises in which the subjects read or discussed are taken from the sciences. These exercises have not the study of science for their direct object, and the acquisition of scientific facts is an incidental aim only. In classifying them, therefore, they are considered as belonging to the instruction in those subjects that furnish the primary reason for their existence.

A pupil can not be taught to read understandingly unless something is provided which is worthy of being understood; nor can a profitable language lesson be conducted without a subject of conversation worthy of the dress of language with which it is clothed.

In reading the subjects are largely scientific through design, as already explained, but in the conversation exercises or language lessons by a sort of natural selection, the matters which are most likely to suggest themselves are those which are incidentally valuable in conveying information in the domain of the sciences. What better means, e. g., could a teacher adopt to draw her pupils into an unrestrained conversation in which she may have a favorable opportunity for criticising their forms of expression, than an informal talk upon some familiar animal, bird, or flower?

No satisfactory estimate can be made of the extent of the instruction given in elementary science in this indirect way, but it undoubtedly plays an important part in the sum total of knowledge which the pupil receives during the course. We may, however, more accurately judge the amount of instruction which is given by means of the regular "oral lessons" for which nearly all the courses provide.

In Washington, D. C., science-teaching occupies a larger proportion of time than in any other of the twenty-nine cities selected, nearly one-tenth the time being so filled.

See Tables 1, 2, 4, 5, 6, and 7.

In the two lowest grades the time for science is equally divided between the observation of plants, the observation of animals, and physiology. The last named branch is studied continuously throughout the course, especial attention being paid to the conditions of health. The phenomena of vapor in its different forms and effects" are studied in connection with geography in the third year, and in the fourth the same subject includes a study of "the phenomena of contour, its causes and effects, or elementary physical geography and geology." Physics is taken up more formally in the seventh year, its study embracing the following:

"1. Matter and its properties: (a) Divisibility of matter-molecule. (b) Porosity. (c) Density. (d) Phenomena of attraction-gravitation, cohesion, adhesion; Constitution of matter; three states of matter-solid, liquid, and gaseous.

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2. Heat: (a) Ways of producing heat-by mechanical force, by chemical force. (b) Effects of heat in matter-expansion, solids, liquids, and gases; change of stateliquefaction, evaporation. (c) Communication of heat-conduction, solids; convection-liquids and gases; radiation. (d) Effects of heat in nature- dew, fogs and mists, clouds, rains, and winds.

"3. Sounds: (a) Nature of sound-vibration; a vibrating body always the origin of sound; sound waves. (b) Transmission of sound-through solids, liquids, and gases; velocity of transmission. (c) Pitch of sounds. (d) Intensity of sounds."

The San Francisco course also devotes considerable time to elementary science, physiology and hygiene receiving particular attention. In the schools of California practical entomology, a branch of science having a peculiar bearing upon the industries of that State, is taught in accordance with the provisions of a State law. Especial reference is had to insects injurious to crops and fruits.

In Boston, too, natural science receives its due share of attention. In the first three years of the course simple conversational exercises are provided for, in which lessons are given on the human body, familiar plants, animals, and the phenomena of nature. In the grammar schools, these exercises are continued with a wider scope for the first two years; in the next or sixth year of school, hygiene and the common metals, minerals, and rocks receive attention; in the seventh and eighth the work is confined to physiology and hygiene; in the ninth, the common facts of physics are taught by observation and experiment.

In Cincinnati in the first four years of school the oral lessons relate principally to the human body and to the color, size, form, action, and uses of familiar objects, including plants, animals, flowers, fruits, grains, etc. In the fifth and sixth years the lessons are more descriptive in their character, and are based upon such well known objects as dew, rain, snow, hail, frost, ice, fog, clouds, the sun, the moon, rivers, mountains, countries, etc. In the sixth year one lesson a week is given in elementary physics. The instruction covers "(a) matter, its properties, three states; (b) air, its composition, properties, weight, and pressure; (c) effects of heat on air, winds, land, and sea breezes, cyclones, etc.; (d) air rendered impure by breathing, ventilation: (e) water, its composition, properties, specific gravity, floating bodies, pressure; (f) three states of water (solid, liquid, vapor), effects of heat on water, steam, specific gravity of ice; (g) formation of vapor in the atmosphere-fog, clouds, rain, hail, snow, dew, and frost." Physiology is studied more minutely in the seventh year than in the previous grades, especial reference being had as usual to the conditions of health.

In Indianapolis the work outlined for the first three years in plants, animals, and physiology is more than usually comprehensive. In the fourth year the work in composition is closely related to the study of entomology, butterflies and moths being particularly the subjects of investigation. Ornithology is the only branch of natural science studied in the fifth and sixth years, and, like entomology in the fourth grade, it is studied in connection with language. Physiology is taken up the eighth and studied from a text-book.

In St. Paul, also, the work in science occupies a large place in the course of study, receiving nearly 8 per cent. of the whole time. All instruction in this line given in the first two years is in connection with language. In the third year herbivorous animals are studied in the first quarter, carnivorous animals are in the second, and other orders of animals in the third; in the last quarter zoology is dropped and botany is taken up, especial attention being given to trees. In the fourth year the study of plants is continued in the first quarter, giving way to ornithology in the second; birds and fishes receive attention in the third quarter, and in the fourth botany is again studied, this time more particularly in relation to flowers. Invertebrates, the habits and uses of animals, the distribution of herbivora, rodents, birds, reptiles, and fishes by families, and plants useful to man for food, clothing, or shelter, are respectively studies of the several quarters of the fifth year. In the sixth year rocks and minerals, atmospheric phenomena, water, and ethnology are the subjects investigated. The earth, forms and properties of matter, heat, and the mechanical powers are studied in the seventh.

The "spiral course" arranged for the St. Louis schools by Dr. W. T. Harris during his superintendency should be mentioned. Its plan is thus described: 1

"The course should be sketched in such a way as to make several complete circuits during the eight years of the district school course. The lowest one should seize certain striking features in each department, making a strong impression and silently determining the mind to reflection and observation in the domain of natural science. The second course must travel round in the same path, but more systematically and in detail. The third one, still deepening and generalizing the ideas of the pupil, would make the effects permanent. Three courses were fixed upon for this reason. The 8 years of the district school course thus allowed 3 years each to be given to the first and second course and 2 years for the third. Inasmuch as the subjects were taken up with a considerable degree of scientific strictness in the high school, the course of study in natural sciences would now extend from the commencement in the primary schools to the last year of the high school. A pupil coming into any grade in the schools and remaining 3 years would known something of each of the great departments of nature."2

From "How to Teach Natural Science in the Public Schools," by William T. Harris, LL. D. 2 The details of the course were as follows:

FIRST YEAR OR GRADE.

PLANTS, OR OUTLINES OF BOTANY.

First quarter.-Flowers, their structure, color, perfume, habit, and shapes. Inasmuch as the pupils of this grade enter school in the early fall or spring, their first quarter's work can be illustrated directly from the garden.

Second quarter.-Leaves, fruit, seeds; shape, uses, sap, decay.

Third quarter.-Buds, roots, their purpose; stalks and trunks, bark of plants, wood.

Fourth quarter.-Circulation of sap; what is made from sap; sleep of plants, etc.; review of topics of the year.

SECOND GRADE OR YEAR.

ANIMALS, OR OUTLINES OF ZOOLOGY AND PHYSIOLOGY.

First quarter.-Blood, what it makes; how it is made; the ground, what comes from it as food for animals; stomach and teeth; circulation of the blood.

Second quarter-Breathing; brain and nerves; use of the senses; seeing; protection of the eyes; hearing; smell; taste; touch; the bones; muscles.

Third quarter-Brains and nerves in animals compared with those in man; limbs of animals and their uses; the hand in man, and its substitutes in animals; what instruments and tools animals pos sess for attack and defense.

Fourth quarter-Wings and fins; clothing of man and animals; wherein man is superior to animals; intelligence of animals; sleep, its uses; death, what it is; review of topics for the year.

THIRD GRADE OR YEAR.

ELEMENTS OF PHYSICAL NATURE.

First quarter.-Air; wind; flying and swimming compared; pressure of the air; pumps; barometer; air pumps; pop-guns; gases distinguished from liquids; gunpowder.

Second quarter-Balloons; bubbles; heated air; chimneys; draft and ventilation; uses of water; water level; attraction in solids and liquids.

Third quarter.-Water in the air, clouds, snow, frost, and ice; heat and cold; communication or conduction of heat; effects of heat; steam; light; color; electricity; magnetism. Fourth quarter.-Gravitation; motion of the earth; friction; review of the year's work.

FOURTH YEAR OR GRADE.

BOTANY MORE SYSTEMATICALLY STUDIED.

First quarter.-Modes of studying parts of plants; leaf, stem, inflorescence, flower, root, seed, woody plants, fruit, illustrated by familiar examples."

Second quarter.-The difference in species of trees, their habits, place of growth, and use to man; pine, cedar, willow, oak, beech, maple, walnut, hickory, sycamore, ash, poplar, birch (what "deciduous" and evergreen" signify), magnolia, live-oak, honey-locust, banyan, laurel, mosses.

Third quarter.-Food plants: (1) Wheat, barley, oats, rye, Indian corn, rice; (2) potatoes, yams, beets, turnips, onions, beans, peas; (3) apples, peaches, pears, plums, cherries, oranges, bananas, lemons, bread. fruit, dates, pine apples, figs, grapes; (4) sago, tapioca, sugar-cane, cocoanut palm (its various uses); (5) pepper, cinnamon, cloves, nutmeg, vanilla; (6) tea, coffee, cocoa, maté; (7) Irish moss.

Fourth quarter.-Plants useful in the arts: (1) Indigo, logwood; (2) olive (oil), flaxseed (oil), pine, turpentine, rosin, tar; (3) caoutchouc, gutta pereka. Medicinal plants and stimulants: Sarsaparilla, cinchona (quinine), aloe, tobacco, opium, rhubarb. Plants valuable for clothing: Cotton, flax, hemp.

FIFTH YEAR OR GRADE.

ZOOLOGY, PHYSIOLOGY, AND HYGIENE,

First quarter.-Classification of animals, their differences and resemblances.

I. Vertebrates: (A) Mammals-(a) orang-outang, monkey; (b) bear, cat, dog, lion, panther, tiger, cougar, wolf, leopard; (c) kangaroo, opossum; (d) beaver, squirrel, t se; (e) sloth, ant-eater;