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Buenos Ayres was separated from the confederation of the other provinces, and formed an independent commonwealth. More recently, the progress of the country has been greater and more rapid than that of most of the other South American republics.

ARISTOTLE

new minister of public instruction, Dr. Nicolas Avellaneda, in his first report to the congress (1869), earnestly advocated sweeping reforms; and the work of carrying out these reforms was begun energetically. For the year 1869, $115,000 was voted for the purpose of encouraging priAs early as 1605, the Jesuits established the mary instruction; for 1870, $95,000, and for 1871 university of Cordova, which soon became the $215,000. In 1871, a law was also passed, crealiterary center of all the territory lying in the ting a special and independent fund for the purbasin of the La Plata river. Of course, instruc- poses of primary instruction, distributing the tion during the 17th and 18th centuries was proceeds among the various provinces in proporentirely in the hands of the clergy, especially the tion to the efforts which they themselves might Jesuits; and very little was done in the way of make. This law took effect in January 1873. primary instruction. After the expulsion of the In 1872, primary instruction was given in 1088 Jesuits, in 1767, the university passed into the public and 566 private schools. The children of hands of the Franciscans and greatly declined. school age (6 to 15) numbered 468,987, while Though, after the establishment of national inde- the number of those attending schools was pendence, there were not wanting those who fully 97,549. The number of teachers was, male appreciated the importance of education, and 1558, female 1408. The expenditure for primary sought to devise plans for its future development, instruction in the same year was $1,564,350. In the progress at first was very slow. The active August 1871, the first national normal school progress of education dates from the adoption of was established at Paraná. It had, in 1872, 285 the constitution of Sept. 1860, which still rules students and 6 professors. The first principal the country. Among the first provisions, is one of the school was Dr. Geo. A. Stearns. — The for securing primary education in every province only national university, at Cordova, was re-orof the republic, making this an essential obliga-ganized, in 1870, by President Sarmiento, who tion. To the general government was given the established a number of new chairs, and called power to dictate plans of general and university from Germany professors of chemistry, physics, education; and a special ministerial department and botany, and from the United States a distinof public instruction was created. Such, how-guished professor of astronomy. In 1872, the ever, was the indifference of the people, that the government, in order to carry out its plans of secondary education, was compelled not only to offer instruction, books, and all other necessaries free, but also to pay the pupils for the trouble of attending school and studying their lessons. The National College of Buenos Ayres was founded shortly after the adoption of the present constitution. Scholarships, under the name of cecas, were established, giving to the student a monthly allowance of from ten to fifteen dollars in gold. About the same time, three other provincial institutions, the College of the Uruguay in the province of Entre Rios, and the College and the University of Cordova, were nationalized and placed upon a similar basis. Up to 1868, there were established five other similar institutions in the provinces of Tucuman, Salta, Catamarca, San Juan, and Mendoza; and, in 1868, five others were added in San Luis, La Rioja, Jujuy, Santiago, and Corrientes. In 1872, there were thirteen colleges, with 3697 students and 162 professors. The colleges are visited by an inspector of national colleges, who is himself a government employé.

In 1865, the national government took its first step in favor of primary instruction, distributing $22,000 in gold among the various provinces, for the purpose of promoting a popular movement in this direction. In 1800 and 1867, the same amount was voted by the national congress for this purpose. In August 1868, began the administration of President Sarmiento, who has done more for the promotion of education than any other statesman of South America. The progress made since then is wonderful. The

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university numbered 14 professors and 103 students. The university of Buenos Ayres is a provincial institution. It was organized in 1822 by Rivadavia, and was, at first, only a law school; but, owing to the zeal of its rector, Dr. Juan Maria Gutierrez, chairs of mathematics, experimental physics, and chemistry were soon afterwards added. Its course of instruction resembles that of French institutions; the museum has been for many years under the direction of the distinguished German naturalist, Dr. Burmeister. -See Report of the Commissioner of Education for 1872 and 1873; LE ROY, in SCHMID'S Encyclop., art. Südamerica; BURMEISTER, in PETERMANN, Die südamerikanischen Republiken Argentina, Chile, Paraguay und Uruguay in 1875 (Gotha, 1875).

ARISTOTLE, one of the most illustrious teachers and philosophers of either ancient or modern times, was born in 384 B. C. at Stagira, a Greek colony of Macedonia, near the mouth of the Strymon. From his birthplace he is often called "the Stagirite." His father, Nicomachus, was a distinguished physician and friend of the Macedonian king Amyntas II.; and from him Aristotle received the first instruction. Having lost his parents, he went at the age of seventeen to Athens, where he was for twenty years a pupil of Plato. His great teacher used to call him. on account of his restless study and his thirst for knowledge, the philosopher of truth and the intellect of his school. Subsequently, however, an estrangement arose between them, owing chiefly to the radical differences in their philosophical and educational systems. While Plato was a thorough idealist, Aristotle was just as fully a

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realist and the father of experimental science. | crippled should not be brought up at all. Until About 343 B. C., Aristotle was appointed by king Philip of Macedon teacher of his son Alexander, at that time thirteen years old. The history of Alexander, who intellectually was no less prominent among the kings of the ancient world than as a conqueror, testifies to the success of Aristotle as a practical teacher. For a long time, Alexander was anxious to show his gratitude to his preceptor; and after the conquest of Persia, he presented him with eight hundred talents, or nearly a million of dollars. Later, however, the friendly relations between Alexander and Aristotle greatly suffered from the vicious habits of the former. After completing the education of Alexander, Aristotle returned to Athens (in 335, or according to others in 331, B. C.) and taught philosophy in the Lyceum, a gymnasium near the city. In the morning, he instructed the advanced scholars in lectures acroamatic or esoteric; in the evening, he gave popular or exoteric lectures to larger circles of hearers. From the shady walks (Repinaro) around the Lyceum, in which he walked up and down while delivering his lectures, his school was called the peripatetic. After having taught in this way for thirteen years, and composed most of his immortal works on philosophy and natural science, he was accused by Demophilus, a prominent citizen of Athens, of impiety, because in a poem he had attributed divine honors to his friend Hermias. He, therefore, fled to Chalcis in Euboea, where he died, in 322, B. C., of a chronic disease of the stomach.

Aristotle's method of teaching was essentially analytic. Proceeding from the concrete, he tried to derive general ideas from a number of observed facts and phenomena; and his entire philosophy is based on the principle that all our knowledge must be founded on the observation of facts. Pedagogy, according to Aristotle, must be .founded on principles derived from the knowledge of man. The highest goal of all human activity is evdarovia, happiness, both for the individual and for the state. This ridaovia is based on virtue, which is acquired by the performance of moral actions. As man is a social being, destined to live in society, the development of virtue in general is dependent upon political life. The object of the state is to establish the complete happiness of families and communities, and the preservation of the state depends on an educational system conformable to the laws and constitution. The same education will not produce the same virtues in different persons; for the formation of character in each person is dependent on three different things, nature, habit, and instruction. It must be the aim of habit and instruction to develop the peculiar faculties which nature has implanted in each individual. In the education of a child, as it is of the greatest importance that its body be, from its birth, as perfect as possible, care should be taken that the parents be suitably matched, and that women during their pregnancy receive substantial food, and be preserved as much as possible from mental agitation. Children who at their birth are

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the fifth year of age, children should not be occupied in hard labor; on the other hand, however, they should not remain inactive, but have suitable exercises in plays adapted to their age. During this time, as well as during the two following years, education by means of habit takes place, as children observe what they subsequently have themselves to perform. Education by means of instruction begins in the 7th year of age and lasts to the 21st. This time is divided into two periods, the one extending from the 7th year to the age of puberty (about the 14th year), the other from the 14th to the 21st. Education by habit during this period continues, but the chief work is done by instruction. As a general principle, it must be observed, that a state can only exist if children are educated in accordance with the existing constitution; in democratic commonwealths. in which all in turn may rule or be ruled, it is, therefore, of importance that boys should be taught obedience, for only those who have learned how to obey will be able to rule. In regard to the subjects in which instruction should be given, three classes should be distinguished, (1) that which is necessary and useful for life, (2) that which leads to ethical virtue, and (3) that which, going beyond these, serves the highest theoretic al aims. In things pertaining to the ordinary occupations of life, the young are to be instructed only so far as such occupations are becoming to a free man. Every mechanical work, every kind of servile or menial labor, and especially every thing that might injure the body, is to be avoided. The fine arts should be practiced with a view to general culture; but no special excellence should be aimed at. In regard to ethical virtues, children must especially be taught to be considerate and temperate, in order that the exertions necessary to attain self-control may lose their original unpleasantness by means of habit. Finally, there are for ethical as well as theoretical education, certain instructional means, namely reading and writing, gymnastics, music, including rhythmics and poetry, and occasionally also drawing. The first and the last of these serve also for the necessities of life; and care should, therefore, be taken that the supreme aim of a noble education be not infringed upon. The instruction in drawing, therefore, should be given in such a way as to enable the youthful mind to understand and criticise the works of plastic art. Gymnastics educate the youth in manliness, and give to the body health and beauty. That which is properly athletic, and especially every thing that leads to rudeness and ferocity, should be avoided, a point of view which the Spartans, in their otherwise excellent educational system, somewhat lost sight of. Before the age of puberty, only easy exercises should be practiced, and all violent exertions that might impede natural growth, should be avoided. After attaining the age of puberty, boys may devote three years to other branches of instruction; then more difficult exertions and privations may be practiced; and during this time mental occupations should

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receive less attention; for the activity of the mind is impeded by the exertions of the body, and the activity of the body by the exertions of the mind. Musical education deserves special attention on account of its ethical influence. Music more than any other art, is the art of imitation, and reflects in the soul of the hearer, in a manner both attractive and instructive, the various affections and emotions of the mind. The Doric melody is specially recommended, as keeping the right mean between passionate excitement and womanish weakness. The last class of subjects to be taught in the instruction of youth, are those which serve for theoretical purposes, or for the acquisition of the so-called dianoetical virtues, which are only to be found in the more intelligent class of men. These subjects are the pure sciences, as mathematics, dialectics, and philosophy. The highest of all practical sciences, political economy, is not a fit subject for the young, as they are too inexperienced in the actions of life on which political science is based.-Like the educational theories of Plato and other Greeks, the theories of Aristotle almost exclusively refer to free-born youth. But little attention is paid to the education of the female sex and the working classes; and still less is given to the education of slaves. Aristotle recommended, however, that the moral and intellectual improvement of the slaves should be cared for.

Among the works of Aristotle still extant, the Nicomachean Ethics and the Politics contain his views on education. On the educational system of Aristotle, see SCHMIDT, Geschichte der Pädagogik, vol. 1; and ONCKEN, Die Staatslehre des Aristoteles, 2 vols., 1870-1875.- See also Aristotelis Ethica Nicomachea, edited by J. E. T. ROGERS, (Lond., 1874); and the same, translated by R. WILLIAMS, (Lond., 1874); The Politics (Greek text, with English notes), by RICHARD CONGREVE, (Lond., 1874); The Ethics, with Essays and Notes, by SIR Á. GRANT, (Lond., 1874); GROTE, Aristotle (Lond., 1872).

ARITHMETIC (Gr. αριθμητική from ἀριθμός, number), the science of numbers. This subject occupies a prominent place in the curriculum of all elementary schools, both primary and grammar, as well from its educational or disciplinary, as its practical value. On a fair estimate, not less than one-fourth of the pupil's time, for the first eight or ten years of his school life, is given to the study of this subject; but the results are too often quite inadequate to this large expenditure of time, the most that can generally be claimed being a tolerable familiarity with the processes of the fundamental rules, common fractions, and denominate numbers, with a very imperfect knowledge even of the processes of decimal fractions, proportion, evolution, and the business rules of arithmetic. Any such knowledge of the subject as enables the student to give a clear exposition of the reasons for the various processes, or as is required to render him trustworthy in ordinary business computations, is far from being the usual attainment. This arises, in part at least, from a fundamental error in the general

treatment of this branch of instruction, the dissociation, to a great extent, of mental from written arithmetic; whereas they should be so combined as to constitute only different exercises of the same subject. Quite within the memory of some of our living educators, the text-books of arithmetic generally in use were simply single books of definitions, rules, and examples. Such were Ostrander's, Pike's, Dabol's, etc. These were succeeded by two classes of text-books,―one, called Mental Arithmetics, of which Colburn's is a type; and the other, such as presented an attempt to explain the reasons of the processes involved in the different rules. Of the latter, Adams's New Arithmetic affords a fair example. Following these two lines, the science has been practically divided into two; and so diverse are these in their methods, that a pupil may be quite expert in one, and almost entirely ignorant of the other. If, in addition to this, the fact is considered that the text-books in the course have been multiplied until there are now two books in mental arithmetic, and three in written, in several of the series in general use, the reason for the length of time consumed on this subject in our public schools will be obvious. But there is still another cause which operates with considerable force; that is, the cumbering of our text-books with so many subjects that are utterly useless to the student. No branch of business requires a knowledge of greatest common divisor, least common multiple, circulating decimals, or duodecimals. It is indeed important that a pupil should know how to reduce a fraction to its lowest terms; but no ordinary case requires a knowledge of the process for finding the g. c. d., nor are we accustomed to use it. For the process itself we have no use until we reach higher algebra. and the demonstration of the process is quite too intricate for the ordinary pupil in elementary arithmetic. Again, no one. uses the processes of alligation alternate; and but few indeed of the great mass of our school chil dren can comprehend the conditions which give rise to much of our business arithmetic. It is not intimated that such problems as those which arise in stocks, arbitration of exchange, general average, etc., should not have a place in an arithmetical course, but only that they do not belong in the course for the masses. There are other topics, more elementary and more generally useful, to which the time of these should be given. And lastly, on this topic, of what conceivable use are many of the examples which occupy so much space in our books, and so much time in the course? Take the following as specimens:

of

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I bought a hat, coat, and vest, for $34; the hat cost 3 of the price of the coat, and the vest of the price of the hat: what was the cost of each? One-half of A's money of B's; and the interest of A's and of B's money, at 4 per cent for 2 yr. 3 mon. is $18: how much has each? but B, by spending $30 per annum more than A, at the end of 8 years finds himself $40 in debt; what is their income, and what does each spend per annum?

A and B have the same income; A saves of his;

But it is said by some that these things are necessary as mental gymnastics. However ap

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ARITHMETIC

plicable the principle involved in this may be,
in education there is really no need of it. If the
demands of actual life are so meager, that we
must make a large part of our discipline in
arithmetic consist in unraveling such manufact-
ured puzzles, is it not well to ask the question
whether there are not other branches of science
which will afford the needed discipline by deal-
ing with the actual and useful, instead of wasting
time and strength on the purely fictitious? The
arithmetics of to-day, however, are a great ad-
vance, in this respect, on those in use fifty years
ago; but no editor of a text-book on arithmetic
has yet felt at liberty to cut out entirely these
superfluous problems. Undoubtedly, the demands
of science and of business life furnish abundant
resources in this direction; but these more ab-
struse problems do not fall within the purview
of an elementary course, nor come within the
demands which actual life makes upon the great
majority of persons. There are a great number
and variety of intricate questions which do act-
ually arise in discounting negotiable paper, as
well as in the abstruse questions which insurance
and annuities present; but it is not the aim of
our elementary courses to train pupils for such
specialties; and when in any properly co-ordin-
ated course of study such topics are reached,
their solution will then come in the regular line
of the application of general principles, and the
student will have acquired sufficient maturity to
comprehend the business, economical, or political
relations which give rise to them.

What should constitute the course in arith-
metic. In the first place, there should be a thor-
ough unification of the processes of mental and
written arithmetic. There is but one science of
arithmetic; and every thing that tends to pro-
duce the impression in the pupil's mind that there
are two species, the one intellectual and the other
mechanical, is an obstacle to his true progress.
What is valuable in the methods now peculiar to
mental arithmetic, needs to be thoroughly in-
corporated with what is practically convenient
or necessary in written arithmetic; so that the
whole may be made perfectly homogeneous. The
basis upon which this is to be effected is, that
principles should be discussed first by the use of
small numbers which can be easily held in the
mind, and which do not render the difficulty or
labor of combination so great as to absorb the
attention, or divert it from the line of thought;
and that we should pass gradually, in applying
the reasoning, to larger numbers and more difficult
and complex combinations, in which pencil and
paper are necessary. The rationale should be al-
ways the same in the mental (properly, oral) arith-
metic and in the written, pencil and paper being
used only when the numbers become too large, or
the elements too numerous, to render it practi-
cable to hold the whole in the mind. For example,
suppose the pupil to be entering upon the sub-
ject of percentage. The first step is to teach
what is meant by per cent. In order to this,
small numbers will be used, and the process will
not require pencil and paper, nor will such num-

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Thus, the first bers be selected at first, as will cause difficulty in effecting the combinations. questions may be, "Mr. A had 300 sheep and What phrase may we use instead of '5 66 Mr. B had an orlost 5 out of each hundred; how many did he lose?" "What phrase out of each hundred?"" chard of 400 peach-trees and lost 6 per cent of them; how many did he lose?" may we use instead of 6 per cent?" To asper cent interest; sign as the first example, one like the following 'Mr. A put out $759, on would be a gross violation of this principle: what was the interest for a year?" After the principle to be taught is clearly seen, larger numbers should be introduced, and such as require that the work be written. But the same style of explanation should be preserved; and great care should be taken to have it seen that the method of reasoning is the same in all cases. To illustrate still farther; as, in practice, the computer ordinarily uses the rate as the multiplier, the form of explanation, when the whole is given orally, should be adapted to this fact. At first, If Mr. A lost 5 sheep out of such an example as the first above will naturally be solved thus: 100, out of 3 hundred he lost 3 times 5, or 15 sheep." But before leaving such simple illustralosing 1 out of 100 is losing .01 of the number, tions, the reasoning should take this form: "Since losing 5 out of 100 is losing .05 of the number. Hence, Mr. A lost .05 of 300 sheep, which is which will ordinarily be required in solving 15 sheep." Thus, in all cases, the form of thought the problem, should be that taught in the introductory analysis. A farther illustration of this "How many ounces in 5 lb.?" will naturally be is furnished by reduction. At first, the question, Since there are 16 oz. in 1 lb., in 5 answered, lb. there are 5 times 16 oz., or 80 oz." But in practice the 16 is ordinarily used as the multiplier, and it is better that the introductory (mental) analysis should conform to this fact. Hence, the pupil should be led to see, at the ounces, in any given weight there are 16 times as outset, that, as every pound is composed of 16 many ounces as pounds; and he should be reuse of what are called mental processes, there is no quired to analyze accordingly. Apart from this proper well-defined sphere for their employment. In practical applications, it is quite unphilosophical to classify the examples, by calling some mental and others written. We do not find them so labeled in actual business life. The pupil It should also be borne needs to discriminate for himself as to whether any particular example should be solved without the pencil or with it. in mind that business men rely very little upon these mental operations. They use the pen and paper for almost every computation. In the second place, in constructing our course in arithmetic, we need to give the most careful attention to the condition and wants of the youth found in our public schools. Perhaps it is no exaggeration to say, that from eighty to ninety per cent of the pupils disappear from these schools by the close of the seventh school

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year; and not more than one in one hundred takes a high school course. Since all pupils of the common schools have need of the rudiments of number, as counting, reading and writing small numbers, the simple combinations embraced in the addition, subtraction, multiplication, and division tables, the simpler forms of fractions, and the more common denominations of compound numbers, an elementary text-book is deemed to be needful for many schools. The objections often urged to having these primary lessons entirely oral are, that it makes an unnecessary draft upon the time and energy of the teacher, renders the pupils' progress very slow, does not so readily supply the means of giving them work to do in their seats, and more than all, begets in their minds a dislike for study and self-exertion, and a disposition to expect that the teacher must do all the work, and thus carry them along. But whatever disposition may be made of primary arithmetic, as usually understood, there is an imperative demand that the course in arithmetic for the masses should be so arranged that the more important practical subjects can be reached and mastered by a majority of our youth during the comparatively short time which they can spend in our schools. In order to effect this, three things will be found necessary: (1) a rigorous exclusion of all topics relatively unimportant, (2) a judicious limitation of the topics presented, and (3) care that, in the laudable desire to secure facility in fundamental processes, -adding, multiplying, etc., the teacher does not consume so much time that the great mass of the pupils will never advance beyond the merest rudiments of the subject. The range of topics to be included in the common school course, will be the fundamental rules; common and decimal fractions; denominate numbers (care being taken to reject all obsolete or unusual denominations, and to give abundant exercises calculated to insure a definite conception of the meaning of the denominations); percentage, including simple, annual, and compound interest, with partial payments, common and bank discount, and some of the more common uses of percentage. If, after this, the course may be extended, the next subjects in importance are ratio, proportion, and the square and cube roots. Much more than this cannot be embraced in a course which the masses of our youth are able to master; and in treating these, constant care will be necessary to introduce problems which occur in actual life, and as far as possible to exclude all others. Something of common mensuration should be introduced in connection with the tables of measures of extension; and the more common problems in commision, insurance, taxes, stocks, etc., will be readily introduced in percentage without occupying either much space or time.

For the few who can take a more extended course, a thoroughly scientific treatment of the subject of arithmetic is desirable; and this quite as much for its disciplinary effect, in giving breadth and scope to the conceptions, and inducing a disposition to systematize and gener

alize, and thus to view truth in its relations, as for the amount of mere arithmetical knowledge which may be added to the pupil's stock. Here we may introduce an analytical outline of the subject, presenting the topics in their philosophical relations, rather than in their mere practical and economic order and connection. Thus, in treating notation, the various forms of notation can be introduced, as of simple and compound numbers, other scales than the decimal, various forms of fractional notation, the elements of the literal notation, etc. Then, as reduction is but changing the form of notation, this topic will come next, and will embrace all the forms of reduction found in common arithmetic, as from one scale to another, of denominate numbers, of fractions common and decimal, etc., showing how all arithmetical reductions are based on the one simple principle: If the unit in reference to which the number is to be expressed is made smaller, the number must be multiplied, and if the unit of expression is made larger, the number must be divided. Passing to the combinations of number, under addition all processes thus designated in arithmetic will be treated, and the general principles out of which they all grow will be developed. In this method of treatment, the pupil will not find himself merely going over the elementary subjects through which he plodded in the days of his childhood, but new ranges of thought will be presented, at the same time that all the principles and processes of the elementary arithmetic are reviewed; the very first sections, even those on notation, reduction, and the fundamental rules, bringing into requisition most of his knowledge of arithmetic, and giving vigorous exercise to his mind in grasping new truth. But in addition to all this, which pertains to the method of presentation, there will be much of practical arithmetical knowledge to be gained. În the business rules, discount needs a much fuller treatment than it has usually received in any of our text-books. Many problems, of frequent occurrence in modern business circles, are not provided for in these books; and, in fact, some of the most common have had no solution at all which has been made public. The wonderful development of the insurance business demands that its principles and methods receive a much fuller treatment than they can have in an elementary course: this is especially true of life insurance. Foreign exchange, customs, equation of payments, etc., are other topics suitable for this advanced course, which are quite impracticable in an elementary course within the reach of the masses. Two other ends will be subserved by this method: (1) It will be a leading purpose to teach the pupil how to investigate, and to this end he should be put in possession of the great instrument for mathematical investigation, namely, the equation. Of course, only the simpler forms of the equation can be introduced; nevertheless, enough can be given to enlarge very greatly the student's power to examine new questions for himself. By means of the equation, he may be taught the solution of such problems as the fol

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