Table Of ContentCONTRIBUTIONS OP MATHEMATICS TO A PROPOSAL FOR
REORGANIZING GENERAL EDUCATION IN SECONDARY
SCHOOLS ON THE BASIS OF A CORE PROGRAM
DISSERTATION
Presented in Partial Fulfillment of the Requirements
for the Degree Doctor of Philosophy in the
Graduate School of The Ohio State University
By
ELSIE JUNE STALZER, 3.S., M.A.
THE OHIO STATE UNIVERSITY
1952
Approved by:
Adviser
ACKNOWLEDGMENTS
I am deeply indebted t.o Dr. Harold Alberty, my advisor, for
his guidance in conducting this study. His advice and counsel and
his unceasing interest in the study have been a source of constant
encouragement. I should also like to acknowledge the help given by
Dr. Harold Fawcett and Dr» Earl Anderson who served as members
n.
of my advisory and reading committees*
h. J. S .
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L0&676
TABLE OF CONTENTS
CHAPTER Page
ACKNOi/LEDGMENTS.............................. i
I THE PROBLEM AND ITS SETTING................... 1
Introduction ............................. 1
A Program for Reorganization............... 5
Previous Studies........... 7
Purpose of the Study............. 9
Basic Assumptions........................ 9
Hypothesis................................ 9
Plan of the Study....................... 10
Limitations of the Study............... 11
II PROCEDURES USED IN DETERMININGT HE POSSIBLE
CONTRIBUTIONS OF MATHEMATICS TO THE CORE
PROGRAM........................................12
Introduction ............................. 12
The Cooperative Nature of Certain Aspects of
the Study.............................13
Problem Areas Appropriate for a Core Program. 15
Criteria for Constructing Core Activities . . 24
Development of the Core Activities........ 26
Development of the Contributions of Mathe
matics to the Core Activities.......... 27
III POSSIBLE CONTRIBUTIONS OF MATHEMATICS TC THE
CORE PROGRAM................................29
Introduction.......... 29
Mathematical Concepts Essential to Carrying
out the Core Activities. ......... . 29
Possible Contributions of Mathematics to the
Core Activities ................. 39
1. Problems of Orientation to School
Living........................ 42
2. Problems of Self-Understanding . . . . 57
3. Problems of Developing Values and
Beliefs........................ 85
4. Problems of Social Relationships in a
Democracy..................... 105
5. Problems of Employment and Vocation. . 134
6. Problems of Conserving Natural
Resources..................... 155
7. Problems of Education in American
Democracy..................... 186
- ii -
TABLE OF CONTENTS (cont.)
CHAPTER Page
III (cont.)
8. Problem* of Constructive Use of
Leisure......................202
9. Problems of Family Living...........219
10. Problems of Communication...........235
11. Problemso f Democratic Government. • 250
12. Problems of Personal and Community
Health.......................272
13. Problems of Economic Relationships in
a Democracy.................. 305
14. Problems of Critical Thinking . . . . 333
15. Problems of Achieving Peace in the
Atomic Age .................... 357
16. Problems of Intercultural Relations . 380
IV ANALYSIS OF POSSIBLE CONTRIBUTIONS OF MATHE
MATICS TO THE CORE ACTIVITIES.............. 408
V MATHEMATICS ESSENTIAL FOR GENERAL EDUCATION . . 417
Introduction ............................ 417
Some Formulations of the Mathematics Needed
by All.............................. 418
The Adequacy of the Fifty-Three Concepts. . . 422
Can Mathematics Be Learned in the Core7 . . . 434
VI SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS. . . . 440
Summary of Study....................... 440
Suntaary of Findings....................442
Conclusions ............................. 444
Recommendations........................ 445
BIBLIOGRAPHY.............................. 449
APPENDIX..................................451
AUTOBIOGRAPHY ............................. 468
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LIST OF TABLES
TABLE Pace
I NUMBER OF ACTIVITIES IK EACH PROBLEM AREA IN
"WHICH MATHEMATICAL CONCEPTS ARE ESSENTIAL......... 408
II MATHEMATICAL CONCEPTS ESSENTIAL TO CARRYING OUT
THE CORE ACTIVITIES............................. 409
III NUMBER CONCEPTS ESSENTIAL TO CARRYING OUT' THE
CORE ACTIVITIES. ........................ 410
IV CONCEPTS OF MEASUREMENT ESSENTIAL TO CARRYING OUT
THE CORE ACTIVITIES............................. 411
V CONCEPTS OF RELATIONSHIP ESSENTIAL TO CARRYING OUT
THE CORE ACTIVITIES............................. 413
VI CONCEPTS OF PROOF ESSENTIAL TO CARRYING OUT’ THE
CORE ACTIVITIES.................................414
VII CONCEPTS OF OPERATION ESSENTIAL TO CARRYING OUT
THE CORE ACTIVITIES............................. 416
VIII FREQUENCY OF CONCEPTS ESSENTIAL TO CARRYING OUT
ACTIVITIES IN THE PROBLEM AREA ONE, ORIENTATION
TO SCHOOL LIVING.............................. 452
IX FREQUENCY OF CONCEPTS ESSENTIAL TO CARRYING OUT
ACTIVITIES IN THE PROBLEM AREA TWO, SELF-
UNDERSTANDING...................................453
X FREQUENCY OF CONCEPTS ESSENTIAL TO CARRYING OUT
ACTIVITIES IN THE PROBLEM AREA THREE, DEVELOPING
VALUES AND BELIEFS.............................. 454
XI FREQUENCY OF CONCEPTS ESSENTIAL TO CARRYING OUT
ACTIVITIES IN THE PROBLEM AREA FOUR, SOCIAL
RELATIONSHIPS IN A DEMOCRACY..................... 455
XII FREQUENCY OF CONCEPTS ESSENTIAL TO CARRYING OUT
ACTIVITIES IN THE PROBLEM AREA FIVE, EMPLOYMENT
AND VO CAT ION....................................456
XIII FREQUENCY OF CONCEPTS ESSENTIAL TO CARRYING OUT
ACTIVITIES IN THE PROBIEI.i AREA SIX, CONSERVING
NATURAL RESOURCES............................... 457
- iv -
LIST OF TABLES (cont.)
Page
FREQUENCY OF CONCEPTS ESSENTIAL TO CARRYING OUT
ACTIVITIES IN THE PROBLEM AREA SEVEN, EDUCATION
IN AMERICAN DEMOCRACY......................... 458
FREQUENCY OF CONCEPTS ESSENTIAL TO CARRYING OUT
ACTIVITIES IN THE PROBLEM AREA EIGHT, CON
STRUCTIVE USE OF LEISURE....................... 459
FREQUENCY OF CONCEPTS ESSENTIAL TO CARRYING OUT
ACTIVITIES IN PR03LEM AREA MINE, FAMILY LIVING. . 460
FREQUENCY OF CONCEPTS ESSENTIAL TO CARRYING OUT
ACTIVITIES IN PROBLEM AREA TEN, COMMUNICATION. . . 461
FREQUENCY OF CONCEPTS ESSENTIAL TO CARRYING OUT
ACTIVITIES IN PRO3LEM AREA ELEVEN, DEMOCRATIC
GOVERNMENT................................... 462
FREQUENCY OF CONCEPTS ESSENTIAL TO CARRYING OUT
ACTIVITIES IN PROBLEM AREA TWELVE, PERSONAL AND
COMMUNITY HEALTH.............................. 463
FREQUENCY OF CONCEPTS ESSENTIAL TO CARRYING OUT
ACTIVITIES IN PROBLEM AREA THIRTEEN, ECONOMIC
RELATIONSHIPS IN A DEMOCRACY................... 464
FREQUENCY OF CONCEPTS ESSENTIAL TO CARRYING OUT
ACTIVITIES IN PROBLEM AREA FOURTEEN, CRITICAL
THINKING..................................... 465
FREQUENCY OF CONCEPTS ESSENTIAL TO CARRYING OUT
ACTIVITIES IN PROBLEM AREA FIFTEEN, ACHIEVING
WORLD PEACE IN THE ATOMIC AGS.................. 466
FREQUENCY OF CONCEPTS ESSENTIAL TO CARRYING OUT
ACTIVITIES IN PROBLEM AREA SIXTEEN, INTERCUL'L’URAL
RELATIONS.................................... 467
- v
LIST OF CHARTS
CHART Page
I MATHEMATICS ESSENTIAL FOR GENERAL EDUCATION
(BASIC STRUCTURE)............................... 423
II MATHEMATICS ESSENTIAL FOR GENERAL EDUCATION. . . . 424
- vi -
CONTRIBUTIONS OF MATHEJIATICS TO A PROPOSAL FOR
REORGANIZING GENERAL EDUCATION IN SECONDARY
SCHOOLS ON THE BASIS OF A CORE PROGRAM
CHAPTER I
THE PROBLEM AND ITS SETTING
Introduction.
One of the most significant problems facing the American seoondary
school is that of reorganising general education to meet the needs of
youth* In a culture characterised by rapid and fundamental change#
it is no longer possible to assume that the conditions under which one
generation lives oan be passed on substantially unchanged to the next
generation. Change is a major aspect of our age. Youth of today
are confronted by problems not even oonteraplated by their parents.
To provide a program of general education which will meet the needs of
youth and help them live successfully in an ever-changing society is
the challenge of the Amerioan high sohool. Faunoe and Bossing des
cribe the situation in this statementi
...life has beoome vastly more oomplioated. The insights#
the skills# and the knowledge that might have enabled
oitisens to live successfully in 1900 are quite inadequate
today. Our world has beoome a oomplex# technological
maelstrom of rapid mobility# constant ohange# and inter
dependence# in which the citizen must acquire certain
oritioal abilities in order to survive. ...Thus the high
sohool of today.•.confronts a radically new ohallenge
stemming from the needs of youth who live in a world like
ours.l
^Roland Faunoe and Nelson Bossing# Developing the Core Curriculum#
p. 40.
2
There ia little evidence* however* that the secondary school Is
meeting the challenge* It oontlnuea to be an Institution dominated
by a traditional concept of general education* In most schools* the
program required of all on the grounds that it provides for the
common needs* problems* and Interests of youth* consists largely of
logically organised subjects* such as the social studies* English*
mathematics* and solenoe* These courses frequently are the first in a
series of highly specialized courses* One group of educators analyses
the situation as follows*
The impaot of specialism has been felt not only in those
phases of education whioh are neoessarily and rightly
speoialistlo; it has affected the whole structure of higher
and even secondary education* Teachers* themselves pro-*
ducts of highly teohnical discipline* tend to reproduce
their knowledge in olass. The result is that each subject
being taught by an expert* tends to be so presented as to
attract potential experts* This complaint is perhaps more
keenly felt in colleges and universities * *. .Even an ele-
mentary course is devised as an introduction to a specialism
within a department) it is significant only as the begin
ning of a series of courses of advancing complexity* In
short* such introductory courses are planned for the special
ist* not for the student seeking a general eduoation*^
Suoh courses frequently defeat the very purposes they are striving
to achieve* They are not designed to deal with the common needs* prob
lems* and interests of youth* Each subject area is organized in terms
of its own inner logio* Beal problems are treated but incidentally as
they serve to enrioh the subject-matter field*
In suoh a framework* youth arc likely to gain few insights into the
problems they face as they go about the normal processes of living* For
5-----------
General Education in_a Free Society* Report of the Harvard
Comoittee* pp* 56-57*
s
life is not oomposed of problems which can be ohanneled into subject-
matter oompartments, Generally speaking, life oonfronta the individual
with problems whose solutions are not the exolusive property of a
given subjeot-matter area, but which must oome from the integration of
knowledge from many fields. Solutions require the use of a wide
variety of resources in men, materials, and techniques.
If the major problems of youth in our culture are to be dealt
with realistically, the traditional subjeot-matter approaoh must give
way to an approaoh based on broad units of w>rk which know no subject
boundaries. This oalls for a drastio reorganisation of the general
education program.
To be effective, a program of general eduoation must be based on
the needs, problems, and interests of youth in our oulture. Thus, any
reorganisation of general eduoation oalls for refleotion on the ideals
and values of demooraoy and analysis of the needs, problems, and
interests of youth as they arise from the matrix of democracy.
Here, it is assumed that the basic ideals of democratic living
*
discussed by the Committee on Seienoe in General Eduoation are com
monly aooepted. Briefly, these are* the optimal development of the
individual; the use of cooperative means in developing significant
personalities; and faith in the method of intelligence in opposition
to reliance on external authority, as the better method for solving
problems of living. Such a set of ideals and values implies some
g
Committee on the Function of Soienoe in General Eduoation, Science
in General Eduoation, pp. 35-52,
