DOCUMENT RESUME ED 096 169 SE 016 469 AUTHOR Reeve, W. D., Fd. TITLE The Teaching of Mathematics in the Secondary School. National Council of Teachers of Mathematics, Yearbook 8 [1933]. INSTITUTION National Council of Teachers of Mathematics, Inc., Washington, D.C. NIB DATE 33 NOTE 271p. AVAILABLE FROU National Council of Teachers of Mathematics, Inc., 1906 Association Drive, Reston, Virginia 22091 ITRS PRICE MF-$0.75 HC Not Available from EDRS. PLUS POSTAGE DESCRIPTORS Articulation (Program) ;Course Content; curriculum; Effective Teaching; Geometry; *Instruction; Junto: High Schools; *Mathematics Education; Reference Books; *Research Reviews (Publications); *Secondary School Mathematics; *Yearbooks ABSTRACT The first of six chapters in this yearbook discusses articulation between junior and senior high school in terms of several specific content and topic areas. The following chapter is a selected review of research in mathematics education for the years 1915-1931. Investigations are categorized into one of nine areas and a 132-entry bibliography is included. The third chapter is devoted to a wide-ranging discussion of intuitive geometry. Chapter 4 suggests curriculum considerations for grades 7-12 with differentiation for varying ability levels. The next chapter presents the mathematics studied in German schools along with the methods, apparatus, and models used. Organization of a unit of instructioa is the topic of the last chapter, and a detailed example is given using direct linear variation as the subject. (LS) I ON %Cs D THE NATIONAL COUNCIL OF cl TEACHERS OF MATHEMATICS THE EIGHTH YEARBOOK THE TEACHING OF MATHEMATICS IN THE SECONDARY SCHOOL U S OE PANTME NT OF HEALTH VI NV `l) 4F PROOL/CttHIS EDUCATION WELFARE (.1 BY MICRO NATIONAL INSTITUTE OF 10. ILL 1 N tillANTFO Sy EDUCATION ri 1-4 KCAL (A.? . .01 N .4.% 111 I Nwl 144e, I : IIle.. et Cw1T, rYt lel II ,1 t 14ew w .1 404 ,, AN() 01411114./A1 (945 org. NA? e. N . N1 1 N N NO114 Att14 PO% 14 NA tI' ;NA, N%! c), 4. '1 Is :1. N,' NI I /I I. 01/C AI ION 0.414't 14 l'14i I 1 W "111441 1 c nu T,.nt At N I. II 'f ...I A' s sq 14, - 'Of V 14i . RYA . ', 1 1 (slV 11.10 (IA NI If HURL:\ L OF PUBLICATIONS eacbcro College, Columbia Itnitersitp N IiW YORK CITY 19 2 Copyright, 19111 111k SiA1'1oN11. CIIVM:11. TKWIIISKy6 or ht %Iv emnica Cur re.pondence relating to and order% for a 'bikini% alcollie', of the Eigh.h Yearbook and earlier Yearbook. %hookl heddreeti to liven ..tu or Plt111.1CATIoNs, 7'11.1CliFit4 Col 1111i1.1I'N11111,4111% 525 11'ettraoth Street. New York City l'rinted 111 the United Stater A rno-6.a J. J. L1111.11, ANL RkaiLtihleANY, N 11 EDITOR'S PREFACE This is the eighth ofa series of Yearbooks which the National Council of Teachers of Mathematicsbegan to publish in1926. The topics covered in thepreceding volumes areas follows: i. A Survey of Progress in the Past Twenty-FiveYears. a. Curriculum Problems in TeachingMathematics, 3. Selected Topics in the Teaching of Mathematics. 4. Significant Changes and Trends in theTeaching of Mathe- matics Throughout the World Sincefofo. 5, The Teaching of Geometry. 6. Mathematics in Modern Life. 7. The Teaching of Algebra. Bound copies of all except the firsttwo Yearbooks can bese- cured from the Bureau of Publications,Teachers College, Columbia University, New York City, for $1.75each. The first is out of print and the second can be obtained boundin paper for $1,25. The purpose of the EighthYearbook is to presentsome of the important phases of the teaching ofmathematics in the secondary school, particularly those that havenot been treated in current magazines as fully as theyare discussed here.Space does not per- mit us to treat as many differenttopics as we should liketo present, but it is hoped that what is includedwill be of assistanceto many persons interested in the secondary school. I wish to expressmy personal appreciationas well as that of the National Council to all contributorswho have helped to make this yearbook possible. W. D. REEVE THE NATIONAL COUNCIL01,"I'EACHERS NIATHENIATICS °mum President---WILLIAM BET? Rochester, N. Y. First riee-President--MAutimHtLORDRANDT, Maywood, Second Pier- !'resident .- -MARYPoTTER. Racine, 1VI:4. Necretary-Treasurer KoWIN W. Si' 111E111E11,Western Illinois State Teachers College, NIacomb, EDIToRIAL Co M M ITTEE Editor-in-Chief and Business Managerof The Mathemaths Teacher and the rearbook: W. D. RumTeachers College, Columbia University. Associate Editors: VEKA SANFORD,School of Education, 1Vestern Re- serve University,Cleveland, Ohio; HERBERT E. Si AUGHT,Uni- versity of Chicago. ADDITIoNAL MEMBERS ON VIEBARD OF DIRECToRS C. \L Avstni, Oak Park,111 1933 1933 One Year H. C. BARBER, 22 Garden St.,Boston, Mass. MARY KELLY, Wichita, Kilns 1933 flIARTE: GcoLE, Columbus, Ohio 1934 Two Years - MARIE S. SABIs ,Denver, Colo 1934 C. Louis TMELE, Detroit,Nlich 1934 ['JOHN P. EVERETT, Kalamazoo,NIich 1935 Three YearsELstt; P. JosiNsost, Oak Park,Ill 1935 RALEIGH SelloRLING, AnnArbor. Nlih. 1935 The National Council of Teachersof Mathematics is a national organization of mathematics teacherswhose purpose is to i. Create andmaintain interest in the teachingof mathematics. 2. Keep thevalues of mathematics beforethe educational world. 3. Help theinexperienced teacher to become agood teacher. 4. Improveteachers in service by makingthem better teachers. 5. Raise thegeneral level of instruction inmathematics. Anyone interested inmathematics is eligible to membership upon paymentof the annual dues of $2.00.This entitles one to receive the official journal ofthe National Council (TheMathema- ti.s Teacher).All correspondence relating toeditorial business matters should headdressed to The MathematicsTeacher, 525 West taoth Street, New York City. V CONTENTS 11A111.11 tAI4E ARTICULATION (W JUNIOR ANL) SENIORHIOliSCI1001. lIATHEMATICS E. R. Branch 11, .\ SUMMARY OF SOME SCIENTIFIC INVESTIGATIONS OP THE TEACHING OF HIGH SCHOOL. NIATIIRMATICS BCHZ 14 111.THE TEACHING OF IN GEOMETRY 55 IV.COHERENCE AND I )IVERSIT V IN SECONDARY MIATIIEMA- TICS Ralph Beath.).165 V.Tim.NIAT/I EN! ATICAL COLLECTION Grin11.1)/jI 216 VI,UNITS OF INSTRUCTION IN SECONDARY MATHEMATICS J. S. Georges244 V THE TEACHING OF MATHEMATICS IN nu; SECONDARY SCHOOL. VI ARTICULATION OF JUNIOR AND SENIOR HIGH SCHOOL MATHEMATICS By E. R. BRESLICH Mr Schoolof Etinca lion, Csiversily of Chicago, Chicago, Illinois The need of reorganizing traditional mathematics.Algebra, geometry, and trigonometry as taught in our high schools were originally organized for students in colleges.Later they were taken over by the college preparatory schools and high schools, being offered at first in the senior and junior years.Gradually they were moved downward to the early years of the secondary schools. They were preseited to sigh school students almost as they had been taught in the colleges. When it was found that high school pupils encountered serious difficulties in the study of alp bra and geometry, efforts were made to reorganize or to reconstruc, these courses. Because cur school system was organized on the 8-4 plan, it seemed to be impossible to find a solution of the problem.For, on account ofthe gap existing between the elementary and high schools. the teaching of algebra and geometry had to be deferred to the ninth and tenth school years.This made it necessary to crowd a large amount of algebra into a year's time and to force the pupils to advance at a rate too rapid for understanding and assimilation. Since all the time of the second year was needed to cover the extensive content of demonstrative geometry, algebra had to be completely dropped during that period. Simplification of the problem of reorganization by the junior high school.Attempts have been made by individual schools to solve the problem by offering some algebra in the lastyear of the elementary school.However, such efforts usually failed for two reasons : h;gh school algebra was not easily adapted to the interests and abilities of elementary school pupils; and high school teachers were unvilling to accept algebra taught in the eighth grade as an equivalent to high school algebra.Offen it was completely dis- regarded and the work done in the eighth gradewas repeated in the ninth grade. a THE EIGHTH YEARBOOK The development of the junior high school offered a real oppor- tunity for the reorganization of secondary school mathematics, making it possible to extend downward the period of secondary 2(111Cati(111, to give instruction in algebra and geometry at an early period, and to distribute the content of these courses over a period of several years. This involved a reconstruction of the mathemati- cal curriculum of the secondary school, which would offer introduce tory work in algebra and geometry in Grades 7 and 8 and the more advanced work in the later grades. The gap between junior and senior high school mathematics. The reorganization necessitated the training of teach. r. qualified to teach the new courses; elementary school teachecs were un- familiar with the mathematics of the secondary school and high school teachers were not accustomed to pupils of elementary school age.To satisfy this need, courses in junior high school mathe- matics were offered by the universities.A new type of mathe- matics was being developed for the junior high school, while the senior high school continued their program of traditional courses in plane geometry, advanced algebra, solid geometry, and trig- onometry. The administration and supervision of the mathematics in the junior and senior high schools is usually not carried on by the same supervisor, and the teaching is done by two distinct faculties. Neither division knows much about the other. The development of two types of secondary school mathematics, the separation of the junior high school from the senior high school, and the creation of two distinct faculties teaching the courses tend to cause a gap in secondary school mathematics fully as serious as that which formerly existed between the mathematics of the ele- mentary and high schools.Steps should be taken to bring about a closer coiiperation between these faculties.