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Arithmetic in General Education. National Council of ME-$0.75 HC Not Available from EDRS. PLUS POSTAGE This Yearbook Is the Fina DOCUMENT RESUME 20 096 177 SE 016 477 AUTHOR Reeve, W. D., Ed. TITLE Arithmetic in General Education. National Council of Teachers of Mathematics, Yearbook 16 (1241]. INSTITUTION National Council of Teachers of Mathematics, Inc., Washington, D.C. PUB DATE 41 NOTE 345p, AVAILABLE FROM National Council of Teachers of Mathematics, Inc., 1906 Association Drive Reston, Virginia 22091 EDRS PRICE ME-$0.75 HC Not Available from EDRS. PLUS POSTAGE DESCRIPTORS Arithmetic; *Curriculum; Curriculum Problems; *Elementary School Mathematics; Enrichment Activities; Evaluation; *Learning Theories; *Mathematics Education; Reference Books; Reports; Research Reviews (Publications) ;*Yearbooks ABSTRACT This yearbook is the final report of the National Council Committee on Arithmetic. Having endorsed the ',meaning theory,' of arithmetic instruction, an attempt is made to developa position that might serve as a basis for improvement of the arithmetic program. After a chapter on the function of subject matter in relation to personality and one on curriculum problems, there follows a chapter on each of the early grades, middle grades, and high school. The next two chapters present discussions of the social phase of arithmetic instruction and enrichment activities, respectively. Chapter 9 presents a discussion of the present status of drill, followed by a chapter on evaluation. New trends in learning theory are applied to arithmetic in chapter 11. Chapter 12 poses many questions for introspective examination. The yearbook concludes with a chapter on interpretation of research followed by listings of 100 selected studies and 100 selected references. (LS) r-4 4.1The National Council of Teachers of Mathematics c SIXTEENTH YEARBOOK 14.1 s.......1 ARITHMETIC IN GENERAL EDUCATION THE FINAL REPORT OF THE NATIONAL COUNCIL. COMMITTEE ON ARITHMETIC US OLIIMITMENT pi MIAL TM I tt... ,14 III s.Rool.t II Hit tOUCATION I WELFARE' .1. I? .0..1 h N.A t? MICRO NATIONAL INtriTuf OF Y Itv EDUCATION e); c . III I N .IV I +A AsIt I I .1 C tloY g PI \'Y /A' ON 1114 1 4r ASIA,4 01.1 SAT A' N, )I. ON; N NO! w A .teII YI N", A.Itt )III NA Ail 0 Of' .4-`' t %SAW ..NA. N .1 )1 I Ilt,t A 1 ION ,s )I AL NA' "NA. I III' Id!el ION t)hT"IN . I (14 'ON cN 14 1.01 C I k ' WI 2.. WAAI't ,,41 01.14-..111 BUREAU OF PUBLICATIONS TEACIIERS COLLEGE, COLUMBIA UNIVERSITY a NLW YORK 1941 Copyright 1941 by The National Council of Teachers of Mathematics. Cot pontletive relating to and orders for additional copies of the Sixteenth Vearbook, and the earlier Yearbooks should he addressed to 11-14FALI OF PUBLICA I IONS,I FACIIER9 CULLEGI: CuLtiMBIA UNIVERSITY,525 wts 120-rit KEET NEW YORKerr% Pl1NTRI) IN THIS UNITS° STAtEA OF AMENICA MYr,1.LIT11.11 IVR11 COMPANY, NEW YORK THE NATIONAL COUNCIL OF TEACHERS OF NATHEMATICS OFFICERS PresideniNI Anv A. Porut, Supervisor of Mathematics, Racine, %Via. First l'irePreAidentE. R. DRESLICH, Department of Education, University of Chicago, Chicago, III, Second rice.PesidentF, L..WREN,George Peabody College for Teachers, Nashville, Tenn. Serretaly.TreasurerEowin W.SCHREIBER,Western Illinois State Teachers College, Macomb, Ill, Chairman of State BpresentatiVeSKENNETH E, ISROWN, 525 West 120th Street, New York City, EDITORIAL COMMITIFE EditarinChief and Business Manager of The Afathematics Tearher and the rearboohWit LIAM DAVID REEVE, Teachers College, Columbia University, New York City. Associate EditorsVERA SANFORD, State Normal School, Oneonta, N. V.; W. S. Sum.Auctt, St hool of Commerce, New York University, New York City. ADDITIONAL MEMBERS OF THE BOARD DIREcloRS I: ATE BELL, Spokane, Wash. 1940 One Year M. I,. HARTCND, Chicago, Ill. 1941 R. R. SMITH, Longmeadow, Mass. 1940 %lam. S. NIAiLoWV. Montclair, N. J. 1942 Two Years A. BROWN MILLER, Shaker Heights. Ohio 1942 Donaritv WHEELER. Hartford, Conn. 1942 C. M. Acsim, Oak Park. III. 1943 Three YearsHiLD cARDE BEM Detroit, Mich. 1943 IL W. CIIMILESWORTH, Denver, ColO., 1943 The National Council of Teachers of Mathematics is a national organization of mathematics teachers whose purpose is to: 1. Create and maintain interest in the teaching of mathematics. 2. Keep the values of mathematics betore the educational world. 3. Help the inexperienced teacher to become a good teacher. 4. Help teachers in service !o become better teachers. 5. Raise the general level of instruction in mathematics. vi The National Council Anyone interested in mathematics is ellgible to membership In the National Council upon payment of the annual dues of $2,00, The dues include sub . scription to the official journal of the Council (The Eilathratics Teacher). Correspondence should be addressed to The Mathematis Teacher, 525 West 120th Street, New Wig City, EDITOR'S PREFACE THIS is the sixteenth of a series of Yearbooks which the National Council of Teachers of Mathematics began to publish in 1926. The titles of the first fifteen Yearbooks are as follows: 1. k Survey of Progress in the Past TwentyFive Years. 2. Curriculum Problems in Teaching Mathematics. 3. Selected Topics in the Teaching of Mathematics. 4. Significant Changes and Trends in the Teaching of Mathe maties Throughout the World Slime 1910. 5. The Teaching of Geometry. 6. Mathematics in Modern Life. 7. The Teaching of Algebra. 8. The Teaching of Mathematics in the Secondary School. 9. Relational and Functional Thinking in Mathematics. 10. The Teaching of Arithmetic. 11. The Place of Mathematics in Modern Education. 12. Approximate Computation. 13. The Nature of Proof. 14. The Training of Mathematics Teachers. 15. The Place of Mathematics in Secondary Education. The present Yearbook is the final report of "The National Coun- cil Committee on Arithmetic." sponsored and financed by the Na- tional Council of Teachers of Mathematics. It should be an excel- lent companion volume for the Tenth Yearbook on "The Teaching of Arithmetic," which has had a very wide circulation. These two Yearbooks constitute valuable material for teachers of arithmetic and for those who have charge of teacher-training couses. As editor of the Yearbooks, I wish to express my personal appre- ciation to 1 he National Counzil of Teachers of Mathematics and to the members of the Committee for making this Yearbouk possible. W. D. REEVE The National Council Committee on Arithmetic Sponsored by the National Council of Teachers of Mathematics R. L. Morton, Chairman Ohio University Athens, Ohio Harry E. Benz Paul R. Hanna Ohio University Stanford University Athens, Ohio Stanford University, Calif. E. A. Bond Lorena B. Stretch Western Washington Baylor University College of Education Waco, Texas Bellingham, Wash. Ben A. Sueltz William A. Brownell State Normal School Duke University Coratvi,N. Y. Durham, N. C. Leo J. Brueckner C. L. Thiele University of Minnesota Board of Education Minneapolis, Minn. Detroit, Mich. Guy T. Buswell Harry G. Wheat University of Chicago West Virginia University Chicago, Ill. Morgantown, W. Va. CONTENTS PAGB CRAPTIA I.INTRODUCTION 1. 3rIon 1 II. THE. FUNCTION OF SUBJECT MATTER INRELATION to PERSONALITY Guy 7', Boswell 8 III. CuRRIctmum PRoni.EsisGRADE PLAca...stENT Ben A. Sue ltz 20 IV. ARITHMETIC IN THE EARLY GRADES FROM THEPOINT OF VIEW OF INTERRELATIONSHIPS IN THENUMBER SYS- TEM C. L. Thiele 45 V. A THEORY OF INSTRUCTION FOR THE MIDDLE GRADES Harry G. Wheat 80 VI. ARITHMETIC IN THE SENIOR HIGH SCHoOl. Harry If. Benz119 VII. THE SOCIAL PHASE OF ARITHMETICINSTRUCTION Leo J. Brueckner140 THE ENRICHMENT OF THE ARITHMETIC COURSE: UTIL- IZING SUPPLEMENTARY MATERIALS ANDDEVIcE.s Irene Sauble157 IX. WHAT BECOMES OF DRILL? B. R. Buckingham196 X. THE EVALUATION OF LEARNING IN ARrnisirrit: William A. Brownell225 XI.2.ECENT MENDS IN LEARNING THEORY: THEIR APPLI- CATION TO THE PSYCHOLOGY OFARITHMETIC 7'. R. McConnell268 XII. QUESTIONS FOR THE TEACHER OF ARITHMEIC F. Lynwood Wren290 xi xii Contents CIAPTIA PAU XIII. THE INTERPRETATIONOF RESEARCH William 4. Brownell and FosterE. Grossnichle304 XIV. ONE HUNDRED SELEC1EDRESEARCH STUDIES Lorena B. Stretch818 XV. ONE HUNDRED SELECTED REFERENCES E. A. Bond 328 ARITHMETIC IN GENERAL EDUCATION Chapter 1 IN'T'RODUCTION BY R. L. MORTON 01110 UNIVERSITY AN examination of materials published since the beginning of the twentieth century on arithmetic as a part of the cur- riculum of the elementary school reveals a variety of points of view but a clearly discernible trend. Many recall a period when the doctrine of faculty psychology and a correlative belief in a large measure of transfer of training found widespread acceptance among teachers. Arithmetic became a difficult and, to many, a 11 uninteresting subject.Failures among pupils were common; indeed, more pupils "failed" in arithmetic than in any other elementary school subject. Emphasis upon skill in computation. The advent of standard- ized tests, some thirty years ago, focused attention upon the elements of computational skill.Pupils and their teachers were judged by the number of examples of a prescribed kind which they could solve in a given number of minutes with a "standard" per cent of accuracy. Drill was the prevailing mode of instruc- tion. A few pupils who discovered for themselves something of the nature of the number system and who found meaning in the operations which they performed became both accurate and rapid in computation. Furthermore, some of them could use with ease the skills which they had acquired. They learned to do quantitative thinking. But the majority did not understand the number system and were unable to apply what arithmetic they had learned to the solutions of everyday problems. Failures continued to be numerous and there was evident a definite dislike for arithmetic. The flight from arithmetic. Arithmetic had become an im- portant part. of the curriculum not only because it was believed 2 Sixteenth Yearbook to have disciplinary value but also because it was universally believed1.0 be a subject of great practical worth.However, investigations of the extent to which men and women in various walks of life used the arithmetic skills which they had acquired revealed that they used far less than they were supposed to have learned.
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