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Curricula in Mathematics

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Curricula in Mathematics UNITEDSTATESBUREAU OFEDUCATION 619 BULLETIN, 1914,NO. 45 - - WIIOLE NUMBER t$4 CURRICULAIN MATHEMATICS ACOMPARISON OFCOURSES IN THECOUNTRIES REPRESENTED IN THEINTERNATIONALCOMMISSION ON THE TEACHING OFMATHEMATICS By J. C. BROWN HORACE MANNSCHOOL TEACHERSCOLLEtE NEW YORK CITY With the EditorialCooperation of DAVID EUGENESMITH, WILLIAM F.OSGOOD, J. W. A. YOUNG MEMBERS OF THE COMMISSION FROMCIE UNITED STATES . WASHINGTON GOVERNMENTPRINTING OFFICE 1915 1 I ADDITIONAL COPIES 11. OP THIS PURIJCATION MAT DR PROCURED PROM ,T/MR/SUPERINTENDENT Or DOCUMENTS %Z. GOVERNMENT PRINTING OPPICK WARRINGTON, D. C. AT 10 CENTS PER COPY A CONTENTS.' Page. Introduction a 5 I. General arrangement of the courses in typical schoolp of the various countries . 7. Austria I.. .7 Belgium \.. 8 Denmark 10 Finland , 11. France .,. 12 Germany 13 Holland 16 Hungary 17 Italy 19 Japan 20 Roumania 21 Russia.., 22 Sweden 23 Switzerland 24 Table 1 25 II, The work in mathematics in the first school yeadr 26 III. The work in mathematics in the second school year 28 IV. The work in mathematics in the third school year 30' V. The lork in mathematics in the fourth school year..., 33 VI. The work in mathematics in the fifth school y 36 VII. The work in mathematics in tho sixth school yr 40 VIII. Tho work in mathematics in the seventh school ear , 45 IX. The work in mathematics in the eighth school year 51 X. The work in mathematics in the ninth school year 58 '. X1. The work in mathematics in the tenth school year 64 XII. Tho work in mathematics in.theeIeventh school year 70 XIII. Tho work in mathematics in the twelfth school year 76 XIV. The work in mathematics in the thirteenth school year 80 XV. Graphic representation of work in mathematics 81 XVI. Certain important points of Aifforenco between the work_in mithe- . matics abroad and in the United States...o.f 87 XVII. Bibliography V 88 ' 3* 1xTRODUCTION. 'file International Commission ().11the Teaching of Mathematics, created hy:te International Congess of Mathematicians at Rome, l'IMS,.suisinitted a large body of reports to the congress at . Cambriliv,ngland, in lq12.Those for the United States have been publisheciits bulletins of the Bureau of Education (Bulletin, 1911, _ Numbers; S, 9,1 '2 13,16; 1112, Numbers 2, 4, 13, 14).The congies4Alite.e.ted the commission do continue its activities and to submit ftirthry reports to the congress to be held., at Stockholm, Sweden, hi 1916. The following bulletin has been prepared as, a part of the report.,'this country for the second period of the commission's labors. k of this period will naturally consist, to a consid- erable ex a ieparation by each nation of a digest of the results . of the earl ork of tik commission, as seen from the point of view of that nation. NO one believes in the bodily transplantation of a.course of study or oft metlitids of work from one nation to another; yet the very existence of the commission, and the phenomenal success of its work, are evidence of the widespread conviction that every nation can profit from a careful comparative study. of the work of other nations. The material that folloivs shows that ,thetYpes of school organiza- tion and the curricula in mathematics of the leading nations of Europe hare much more in common with each other than with those of the United States.European nations will therefore sometimes' find in the practice of their sister nations encouraging confirmation of their own customs, whereas the United States will be confronted by the question as to whether she alone has found the path that is best, at least for herself.Some line of divergence between the general practice in EuropeSand that of the United States are mentioned in the concluding remarks of this report (p. 87).Historical and other reasons for the existence of the divergencies and easily found.Rea- sons, sometimes of a theoretical; sometimes of a- practical, nature, `may doubtless also he found sufficient to warrant the present continu- ance of some or all of these .divergencies.At the same time the possession of authoritative statements of the practice of the world's loading nations, as contained in the reports from which the material that follows is taken, caii put prove helpful and stimulating to the educators of the United States.The efficient supervisor or the alert teacher will surelyiprofit by a. serious study of the curricula in Other 6 countries as set forth in this bulletin.H6 may find little or notithig 6 k INTBODUCTI", that is directly usable in his own environment, but ho can not' help .being aided in his effort to improve his ow= work, according to local needs and conditions, by a witler knowledge of what is done in corre- sponding ctiseer the world at larger. All of the statement .of fact in the bullethA are based upon reports of the iuteniational commission to the congress at Cambridge. A complete bibliography of .tie reports used is given ern page SS.The data for the various nations .1kave perforce been given with varying . degrees of completeness, depending upon the information available in the reports.As the age at which pupils enter school varies some- what in different countri'ef3,..;:the_ age of the pupil, rather than the scho& year, was chosen as' lly basis of comparison) Unless otherwise stated, i&l; to Tee tinder:good that the European schools arekr boys only.nelittivelNlittle is as yet done in most of the EuropeatAountries for the Matheniktical education of girls beyond the fundamentals of arithmetic. The scitnty information thatavail- able is given in appropriate connections."=, The public schools of the United States comprise, lit mast caeca, an eight-yew elementary course, fol- lowed by a fouridar course in the secondary school.In some mil the course in the elementary school is seven years and in the secondary school five years in length.. In titre instances boar the elementary and the secondary school courses are six years In length. The age of compulsory school attendance varies somewhat in the fitfTerent States, but it Is usually from the age of 6 or 7 to 14.Most pupils enter the elementary school at t he-4g° of 6 or 7.Both the elementary and the secondary tchools are free to all pupils of the school district. The courses in the elementary schools of the country are more nearly uniform than Blase °lithe secondary schools.In the elementary schools the attempt Is made to lay the founiLarl?n for a good gerlral education. limiting, writing, arithmetic, history, geography, elementary science, and spelling are the Important sub- jects of thercurriculum.There is but little opportunity for choice of coursei_in these schools.In the sec- ondary Khali a pupil is sometimes permitted to select those subjects that lie especially wishes.Certain subjects are often required, and the pupil is permitted to select a prescribed Amber of additional subjects. In many of the larger cities there are secondary schools of s arloas types, such as commercial, manual tralo ing, and Industrial. A pupil who has completed the course in a good elementary school may enter a secondary school without examination.' Many of the colleges and universities admit notes of secondary schools upon the pres- entation of a diploma or a certificate, but some colleges and Mei admit only by examination. In this report the Now York State spume of *Ludy is rather cl followedin outlining the subject matter of the elementary school.This, course is fairly ti !cal of the best courses °Lille country. "4" Arrangement of school year the United States. 'ElementarySecondary Age of pupil. Schoolear.... school. school. 6- 7 s. First 1 7- 8 ,, Second 2 8-9 Third . t 3 44, 9-10 Fourth 4 10-11 Fifth 6 11-12 Sixth 6 12-13 Seventh 7- Eighth a L3-' 1 Ninth 16-1 Tenth Eleventh 16-14 7 f 17-18 Tweith CURRICULA IN MATHEMATICS. 1. GENERAL ARIIANGEMENTCTI THECOURSES IN TYPICAL SCHOOLS OF THE VARIOUS COUNTRIES. -AUSTRIA. Arranoement of 8:^hoolyrara. 4-- School , Volk- ttymnn- Real- Age of pupil. Real- gymna- year. schule. schule. , slum, whole. sium. 6-7 First. 1 7-8 Second.. 2 8-0 Third 3 9-10 Fourths. 4 10-11 1 Fifth. 5 1 1 1 11-12 Sixth I 1 2 2 2 12-13 Seventh.! 2 4 , 3 3 13-14 Eighth.. 3 4 4 4 14-15 N,,intb_. a , ' 15-16 Tenth 6 1 6; 6 16-17 Eleventh 7 7 7 17-18 Twelfth. 8 8 . I The minister of education has general supervision of-education in all of the 14 Provinces into which Austria is divided.In each Province there is a superintendefit of education, who stands midway between the minister and lower-school authorities. Each Province is divided into districts and each district ha i3 its school council. The members of this school council are nominated by the teachers of this district and appended by the higher-school council. Each district is divided into smaller sub-' divisions and each of these has its local boa Compulsory education extends from the sixth to the fourteenth year.Coeducation he rule in the rurardistricts and the exception in the cities. The administration o( secondary education is vested in the minister of instruction. Each Province ans an inspector and a local board.Albschools, whether public or private,tare subject to the same regulationsas the State schools.Most of the secondary schools are maintained b5 the State. Thew; are two kinds of elementary schools: (a) Thecommon primary, usually called tho Voildix-hule, and (b) the superior elementary school, called the Bilrgerschule.
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