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 develop a 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 4.1 The National Council of Teachers of Mathematics c SIXTEENTH YEARBOOK s.......1 14.1 ARITHMETIC IN GENERAL EDUCATION THE FINAL REPORT OF THE NATIONAL COUNCIL. COMMITTEE ON ARITHMETIC I tt... III s.Rool.t I I Hit ,14 US OLIIMITMENT pi MIAL TM .1. I? .0..1 h MICRO N.A tOUCATION I WELFARE' t? Itv NATIONAL INtriTuf OF Y c e); EDUCATION III I N . .IV I +A tloY As It I g .1 C I \'Y ASIA 1 4 ,4 01.1 SAT r PI /A' ON 1114 I YI N", A.Itt )III NA NO! w A .teI )I. A' N, ON; N ..NA. I Ilt,t A 1 ION .1 Ail 0 Of' .4-`' !el ION t)hT"IN )1 N t %SAW I III' Id ,s )I AL NA' "NA. I k ' WI 2.. . . 'ON I (14 cN 14 1.01 WAAI't C 01.14-..111 ,,41 BUREAU OF PUBLICATIONS TEACIIERS COLLEGE, COLUMBIA UNIVERSITY NLW YORK a 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: 525 wts 120-rit CuLtiMBIA UNIVERSITY, KEET NEW YORK err% Pl1NTRI) IN THIS UNITS° STAtEA OF AMENICA r, 1. IVR11 COMPANY, NEW YORK LIT11.11 MY 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.. George Peabody College for Teachers, WREN, Nashville, Tenn. Serretaly.TreasurerEowin W. Western Illinois State Teachers SCHREIBER, 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 Years HiLD 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 Paul R. Hanna Harry E. Benz Stanford University Ohio University Stanford University, Calif. Athens, Ohio 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 Cora N. Y. tvi, Durham, N. C. C. L. Thiele Leo J. Brueckner Board of Education University of Minnesota Detroit, Mich. Minneapolis, Minn. Harry G. Wheat Guy T. Buswell West Virginia University University of Chicago Morgantown, W. Va. Chicago, Ill. CONTENTS PAGB CRAPTIA 3rIon I. 1 1 INTRODUCTION . RELATION to II. THE. FUNCTION OF SUBJECT MATTER IN Guy 7', Boswell 8 PERSONALITY III. CuRRIctmum PRoni.EsisGRADE PLAca...stENT 20 Ben A. Sue ltz POINT IV. ARITHMETIC IN THE EARLY GRADES FROM THE NUMBER SYS- OF VIEW OF INTERRELATIONSHIPS IN THE C. L. Thiele 45 TEM V. A THEORY OF INSTRUCTION FOR THE MIDDLE GRADES Harry G. Wheat 80 VI. ARITHMETIC IN THE SENIOR HIGH SCHoOl. Harry If. Benz 119 INSTRUCTION VII. THE SOCIAL PHASE OF ARITHMETIC Leo J. Brueckner 140 THE ENRICHMENT OF THE ARITHMETIC COURSE: UTIL- DEVIcE.s IZING SUPPLEMENTARY MATERIALS AND Irene Sauble 157 B. R. Buckingham 196 IX. WHAT BECOMES OF DRILL? X. THE EVALUATION OF LEARNING IN ARrnisirrit: 225 William A. Brownell XI. 2.ECENT MENDS IN LEARNING THEORY: THEIR APPLI- ARITHMETIC CATION TO THE PSYCHOLOGY OF 268 7'. R. McConnell XII. QUESTIONS FOR THE TEACHER OF ARITHMEIC F. Lynwood Wren 290 xi xii Contents CIAPTIA PAU XIII. THE INTERPRETATION OF RESEARCH William 4. Brownell and Foster E. Grossnichle 304 XIV. ONE HUNDRED SELEC1ED RESEARCH STUDIES Lorena B. Stretch 818 XV. ONE HUNDRED SELECTED REFERENCES E. A. Bond 328 ARITHMETIC IN GENERAL EDUCATION