Arithmetic in General Education. National Council of ME-$0.75 HC Not Available from EDRS ...

345 Pages·2011·7.16 MB·English

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)
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The National Council of Teachers of Mathematics
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SIXTEENTH YEARBOOK
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ARITHMETIC
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GENERAL EDUCATION
THE FINAL REPORT
OF THE NATIONAL COUNCIL.
COMMITTEE
ON ARITHMETIC
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,,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