DOCTORAL PROGRAMS IN MATHEMATICS AND EDUCATION AS RELATED

TO INSTRUCTIONAL NEEDS OF JUNIOR COLLEGES

AND FOUR YEAR COLLEGES

APPROVED:

Graduate Committee: L J A (TV -tu.^

Major Professor

Minor/ Professor

Committee i

Lttee Member / X

tamittee Member

/^44^9tC/

Dean of the/School of Educa

Dean of t He Graduate School

DOCTORAL PROGRAMS IN MATHEMATICS AND EDUCATION AS RELATED

TO INSTRUCTIONAL NEEDS OF JUNIOR COLLEGES

AND FOUR YEAR COLLEGES

DISSERTATION

Presented to the Graduate Council of the

North Texas State University in Partial

Fulfillment of the Requirements

For the Degree of

DOCTOR OF EDUCATION

Py

William Wingo Hamilton

Denton, Texas

June, 1967

TABLE OF CONTENTS'

Page

LIST OF TABLES iv

Chapter

I. INTRODUCTION 1 Statement of the Problem Hypotheses Background and Significance of the Study Definition of Terms Limitations of the Study Review of the Literature

II. PROCEDURES FOR COLLECTING AND TREATING DATA 30

The Samples The Questionnaires Mailing Procedures and Results of Mailings Procedures for Treating Data

III. ANALYSIS OF DATA ' 45

Analysis of Returns from College Officials

Analysis of Returns from Graduate Schools

Analysis of Returns from Panel of Experts

IV. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS . . 168

, Summary Sub^problems Hypotheses General Conclusions Recommendations

APPENDIX 196

BIBLIOGRAPHY 241

ill

LIST OF TABLES

Table

I.

II.

III.

IV.

V.

VI.

VII.

VIII.

IX.

X.

XI.

Page

Summary of Mailings to College Officials and Replies Received 40

Percentage of Colleges in Various Enrollment Categories 46

Percentage of Colleges in Various Categories as to Enrollment in Mathematics Classes 48

Percentage of Colleges Offering Various Degrees in Mathematics . . . . . . . . . . 48

Percentage of Colleges in Various Categories as to Number of Mathematics Classes 49

Percentage Distribution of Colleges as to Degree of Importance Attached to Teacher Preparation 50

Percentage Distribution of Colleges as to Degree of Cooperation between Mathematics and Education Departments 53

Percentage of Colleges in Various Categories as to the Department Conducting Special Courses for Teachers . . . . . 55

Classification of Senior College Offi-cials as to Highest Degree Held 57

Classification of Junior College Offi-cials as to Highest Degree Held 58

Classification of Junior College Offi-cials as to Academic Field 59

iv

Table Page

XII. Classification of Senior College Offi-cials as to Academic Field 59

XIII. Percentage of Colleges in Various Categories as to Size of Mathematics Faculties . . . . 61

XIV. Percentage of Mathematics Faculties Holding Various Degrees 62

XV. Percentage of Colleges in Various Categories as to Number of Staff Members in Mathematics Needed in Next Four Years . * . . . . 64

XVI. Average Number of Staff Members Needed Over Four Year Period 65

XVII. Distribution of Colleges as to Percentage of Ph. D.'s Desired 66

XVIII. Percentage Distribution of Colleges as to Degree of Difficulty in Securing New Staff Members in Mathematics . 70

XIX. Percentage Distribution of Opinions of Senior College Officials as to Future Supply of Mathematics Ph. D.'s . . . , 72

XX. Percentage Distribution of Opinions of Junior College Officials as to Future Supply of Mathematics Ph. D.'s . . . , 73

XXI. Percentage Distribution of Colleges as to Degree of Satisfaction with Current Products of Graduate Schools . . . . 75

XXII. Percentage Distribution of Opinions of Senior College Officials as to Need for Preparation in Research Methods and Teaching Methods . 78

VI

Table

XXIII.

XXIV.

Percentage Distribution of Opinions of Junior College Officials as to Need for Preparation in Research Methods and Teaching Methods . . . . . . . .

Page

Scores for Three Methods of Preparation for Teaching as Ranked by College Officials

79

81

XXV. Percentage Distribution of Opinions of College Officials as to Desira-bility of Two Types of Instruction in Education 83

XXVI. Percentage of Colleges Having Staff Mem-bers in Mathematics with Professional Doctorates 85

XXVII. Percentage Distribution of Colleges as to Number of Mathematics Staff Members with Professional Doctorates 86

XXVIII. Percentage Distribution of Opinions of Department Heads as to Desirability of Having a Staff Member Prepared in Mathematics and Education . , . , 87

XXIX.

XXX.

XXXI.

XXXII.

Percentage Distribution of Opinions of Senior College Officials as to Types of Positions for Which Professional Doctorates are Adequate Preparation

Percentage Distribution of Opinions of Junior College Officials as to Types of Positions for Which Professional Doctorates are Adequate Preparation

Scores for Six Degrees as Ranked by College Officials . .

90

91

94

Percentage Distribution of Opinions of Senior College Officials as to the Desirability of Offering Such Degrees as the Ph. D., Math. Ed., and the Ed. D., Math. Ed 99

vii

Table

XXXIII.

Page

XXXIV.

XXXV.

XXXVI.

XXXVII.

XXXVIII.

XXXIX.

XL.

Percentage Distribution of Opinions of Junior College Officials as to the Desirability of Offering Such Degrees as the Ph. D., Math. Ed., and the Ed. D., Math. Ed

Percentages of Graduate Schools Offering Various Doctoral Degrees in Mathe-matics and Mathematics Education . ,

Number of Graduates of Special Doctoral Programs in the Past Ten Years . . ,

100

104

106

Distribution of Graduate Schools as to Percentage of Graduates of Special Doctoral Programs Engaged in Teaching

Percentage of Graduate Schools Planning to Offer Special Doctorates ,

. 107

Percentage of Graduate Schools Which Would Consider Offering Special Doctorates If a Demand Should Develop

107

108

Percentage of Graduate Officials Con-sidering Professional Doctorates to Be Adequate Preparation for Staff of Ph. D. Granting School 110

Percentage Distribution of Opinions of Graduate Officials as to Types of Positions for Which Professional Doctorates Are Adequate Preparation 111

XLI.

XLII.

XLIII.

Percentage of Graduate Schools Having Staff Members with Professional Doctorates 112

Percentage Distribution of Attitudes of Graduate School Officials Toward Professional Doctorates 114

Percentage Distribution of Rank Assigned to the Ph. D., Math. Ed., by Graduate School Officials 115

viii

Table Page

XLIV. Number of Programs for Professional Doctorates in Various Categories as to Pre-requisites in Mathema-tics and Education 117

XLV. Number of Programs for Professional Doctorates in Various Categories as to Mathematic Requirements . . . . . 119

XLVI. Average Mathematics Requirements for the Degrees in Semester Hours 119

XLVII. Number of Programs for Professional Doctorates in Various Categories as to Education Requirements . . . . . . 120

XLVIII. Average Education Requirements for the Degrees in Semester Hours 121

XLIX. Number of Programs for Professional Doctorates in Various Categories as to Credit Allowed for Dissertation . 122

L. Average Credit, in Semester Hours, for Dissertation 123

LI. Number of Programs for Professional Doctorates in Various Categories as to Total Credit Required 123

LII. Average Total Requirements for the Degrees 124

LIII. Mathematics Courses Required for the Ph. D., Math. Ed., Arranged in Order of Frequency of Mention 125

LIV. Mathematics Courses Required for the Ed. D., Math. Ed., Arranged in Order of Frequency of Mention 126

LV. Education Courses Required for the Ph. D., Math. Ed,, Arranged in Order of Frequency of Mention . . . . . 127

IX

Table

LVI.

LVII.

LVIII.

LIX.

LX.

LXI.

LXII.

LXIII.

LXIV.

LXV.

LXVI.

LXVII.

Page

Education Courses Required for the Ed. D., Math. Ed., Arranged in Order of Frequency of Mention 128

Percentage of Degree Programs for Which Various Types of Dissertation Were Approved 130

Percentage of Degree Programs for Which Various Types of Examinations Were Required 131

Percentage of Degree Programs in Various Categories as to Requirement of Foreign Languages 132

Percentage of Degree Programs Requiring Special Knowledge or Skills . . . . . . 132

Percentage of Degree Programs Requiring a Practicuum or Experience 134

Percentage Distribution of Opinions of Panel as to Pre-requisites in Mathematics 135

Average Minimum Requirements in Mathe-matics for Entrance to Doctoral Programs 136

Number of Panel Members Checking Various Requirements in Mathematics and Education . . . . . . . . . 138

Average Requirements in Mathematics and Education, in Semester Hours, As Suggested by Panel 139

Mathematics Courses Suggested by the Panel for the Professional Doctorate 140

Education Courses Suggested by the Panel for the Professional Doctorates . . . . 141

Table Page

LXVIII. Percentage Distribution of Opinions of Panel as to Training in Methods of Mathematical Research . . 143

LXIX. Percentage Distribution of Opinions of Panel as to Foreign Language Re-quirements 144

LXX. Percentage Distribution of Opinions of Panel Members as to Types of Posi-tions for Which Professional Doctorates Are Adequate Preparation 149

LXXI. Percentage Distribution of Opinions of Panel Members as to the Desirability of Offering Such Degrees as the Ph. D., Math. Ed., and the Ed. D., Math. Ed 150

LXXII. Contingency Table for Computation of Chi- quare to Test Hypothesis One for Ph. D., Math. Ed 153

LXXIII. Contingency Table for Computation of Chi- quare to Test Hypothesis One for Ed. D., Math. Ed 154

LXXIV. Contingency Table for Computation of Chi- quare to Test Hypothesis Two for the Ph. D., Math. Ed 155

LXXV. Contingency Table for Computation of Chi-square to Test Hypothesis Two for the Ed. D., Math. Ed 156

LXXVI. Contingency Table for Computation of Chi-square to Test Typothesis Three for the Ph. D., Math. Ed 157

LXXVII. Contingency Table for Computation of Chi-square to Test Hypothesis Three for the Ed. D., Math. Ed. . . . . . . . 157

xi

Table Page

LXXVIII. Contingency Table for Computation of Chi-square to Test Hypothesis Four for the Ph. D., Math. Ed. . . . . . . . 158

LXXIX. Contingency Table for Computation of Chi-square to Test Hypothesis Four for the Ed. D., Math. Ed 159

LXXX. Contingency Table for Computation of Chi-square to Test Hypothesis Five for the Ph. D., Math. Ed 160

LXXXI. Contingency Table for Computation of Chi-square to Test Hypothesis Five for the Ed. D., Math. Ed 160

LXXXII. Contingency Table for Computation of Chi-square to Test Hypothesis Six for the Ph. D.} Math. Ed 161

LXXXIII. Contingency Table for Computation of Chi-square to Test Hypothesis Six for the Ed. D., Math. Ed 162

LXXXIV. Contingency Table for Computation of Chi-square to Test Hypothesis Seven for the Ph. D., Math. Ed 163

LXXXV. Contingency Table for Computation of Chi-square to Test Hypothesis Seven for the Ed. D., Math. Ed 164

LXXXVI. Contingency Table for Computation of Chi-square to Test Hypothesis Eight for the Ph. D., Math. Ed 165

LXXXVII. Contingency Table for Computation of Chi-square to Test Hypothesis Eight for the Ed. D., Math. Ed 165

LXXXVIII. National Sample of Senior Colleges Grouped According to States, and with Respondents Classified as to Position 215

Xll

Table Page

LXXXIX. National Sample of Junior Colleges, Grouped According to States, and with Respondents Classified as to Position 219

XC. Texas Sample of Senior Colleges with Respondents Classified as to Position 223

XCI. Texas Sample of Junior Colleges with Respondents Classified as to Position 225

XCII. List of Graduate Schools with Respondents Classified as to Position 227

XCIII. List of Specialists in Mathematics Education 232

XCIV. Colleges, in the National Sample of Senior Colleges, Which Stressed Teacher Education . 237

XCV. Graduate Schools Offering Professional Doctorates in Mathematics and Education 239

CHAPTER I

INTRODUCTION

In the course of the development of graduate education

in the United States, the research Ph. D. has come to be the

major degree for preparation of college teachers as well as

for preparation for research. Throughout the history of the

degree there have been those who argued that the program was

slanted toward research so much that the other chief function

of graduate education, that of preparing college teachers,

was neglected. Berelson traced the history of this question

in his study of graduate education in the United States. He

said,

If one criticism of graduate study has been made more frequently than any other, it is that the graduate school has not done right by the college teacher . . . . Several conferences of the past decade from Lake Mohonk in 1947 to the ACE of 1959, have centered on the grad-uate school and the supply of college teachers. The President's Commission of 1947 spanked the graduate schools quite hard on this issue . . . . The Committee of Fifteen was similarly critical. The Carnegie Foun-dation report was no less concerned but was more judi-cious in recognizing that "the conflict is a real one. The graduate school is uniquely the place where individ-uals may be introduced to the highest standards of scholarly investigation. It is also the primary pro-ducer of college teachers. It is inevitable that

there should be some conflict between the two objec-tives. "l

This question has been revived and placed in a new light

by certain developments in mathematics education which throw

doubt on the ability of the present system to produce a suf-

ficient number of Ph. D. graduates in mathematics to staff

all colleges with the proper ratio of teachers trained at the

doctoral level. The increasing pressure to provide a college

education for all and the greater need for more students to

have some knowledge of mathematics intensify this doubt and

raise the question of better preparation for teaching on the

part of those entering college teaching of mathematics. As

a result of these developments certain suggestions have been

made from time to time for introducing some preparation for

teaching into the traditional Ph. D. program. Also, certain

new doctoral programs have been suggested or introduced for

the express purpose of preparing those interested in the

teaching of college mathematics at the undergraduate level

rather than in university teaching or research in mathematics.

Statement of the Problem

The problem of this study was to analyze doctoral pro-

grams in mathematics and education for the preparation of

^Berelson, Bernard, Graduate Education in the United States, New York, 1960, p. 44.

teachers of undergraduate mathematics. The purpose of the

study was to determine (1) the need for such programs, (2)

the attitude of college and university officials toward them,

(3) the composition of present offerings and (4) recommenda-

tions to the future course their development should take.

To achieve this stated purpose the problem was subdivided

as follows:

1. To determine the present composition of mathematics

faculties of junior and senior colleges as to graduate train-

ing in mathematics.

2. To determine the capability of the present system

of doctoral education in mathematics to supply the needs of

junior and senior colleges.

3. To determine the degree to which these colleges are

satisfied with current products of the traditional program

for the doctorate.

4. To determine to what extent colleges are already

using people with training comparable to that proposed in

the new programs.

5. To determine the type of work for which college

officials consider the proposed degrees to be appropriate

training.

6. To determine the attitude of presidents, deans, and

heads of departments of mathematics in junior and senior

colleges toward proposed doctoral programs designed primarily

for college teachers.

7. To determine to what extent the need of colleges for

teachers and their willingness to accept those trained under

the new programs justify intensifying the offering of such

degrees.

8. To determine the extent to which doctoral degrees

designed for the specific purpose of preparing teachers of

college mathematics are now being offered by graduate schools.

9. To determine the willingness of graduate schools to

initiate such degree programs.

10. To determine whether the traditional Ph. D. is the

only terminal degree acceptable to departments of mathematics

in Ph. D. granting universities and colleges.

11. To determine the composition of current doctoral

programs designed specifically for preparing college teachers

of mathematics.

12. To determine what training in mathematics and educa-

tion should be incltided in the new program.

13. To suggest standards for doctoral programs in mathe-

matics and education designed for preparation of college

teachers of mathematics at the undergraduate level.

Hypotheses

In the final question of each of questionnaires number

one, two, and three, officials of colleges and specialists

in mathematics education were asked to select one of five

responses indicating agreement or disagreement with each of

two proposals for a new doctoral degree in mathematics and

education. The question, which was identical in each ques-

tionnaire, was as follows:

Taking into consideration the present situation in mathematics as you see it and considering the degrees as designed primarily for preparation of teachers of undergraduate mathematics in junior colleges and four year colleges, do you agree it is desirable for such degrees as the Ph. D., math. ed. and the Ed. D., math, ed. to be offered?

Ph. D., math. ed.: Agree strongly Agree No opinion Disagree Disagree strongly_

Ed. D., math. ed.: Agree strongly Agree No opinion Disagree Disagree strongly_

In every case the covering letter made plain that the degrees

to be considered were degrees such as those defined in the

description of the degrees which was enclosed with each mail-

ing. The following hypotheses, related primarily to purpose

number two, were used to test the distribution of responses

of officials and specialists, in various categories, to the

above question for each of the two degrees.

1. There is no difference in the distribution of re-

sponses of specialists in mathematics education, presidents,

deans, and heads of departments of mathematics in the national

sample of junior colleges.

2. There is no difference in the distribution of re-

sponses of specialists in mathematics education, presidents,

deans, and heads of departments of mathematics in the national

sample of senior colleges.

3. There is no difference in the distribution of re-

sponses of specialists in mathematics education, presidents,

deans, and heads of departments of mathematics in colleges

in the national sample of senior colleges which stress teacher

preparation.

4. There is no difference in the distribution of re-

sponses of specialists in mathematics education, presidents,

deans, and heads of departments of mathematics in Texas junior

colleges.

5. There is no difference in the distribution of re-

sponses of specialists in mathematics education, presidents,

deans, and heads of departments of mathematics in Texas senior

colleges.

6. There is no difference in the distribution of re-

sponses of presidents in the national samples of junior and

senior colleges and of Texas junior colleges and senior col-

leges.

7. There is no difference in the distribution of re-

sponses of deans in the national samples of junior colleges

and senior colleges and of Texas junior colleges and senior

colleges.

8. There is no difference in the distribution of re-

sponses of heads of departments of mathematics in the national

samples of junior colleges and senior colleges and of Texas

junior and senior colleges.

Background and Significance of the Study

The question of doctoral degrees designed primarily for

the preparation of teachers at the undergraduate level has

been raised frequently during the history of the development

of doctoral education in the United States. This has hap-

pened usually during periods of expansion in college enroll-

ment. Within the past two years the question has taken on

a new significance in the field of mathematics because of the

increasing need for knowledge of mathematics in a wide variety

of careers.

The importance of the problem is attested to by the fact

that the American Mathematical Society and the Mathematical

Association of America have devoted considerable attention

to it since about 1960. The efforts of these two organiza-

tions have been directed chiefly toward consideration of a

8

second doctoral degree embodying more extensive training than

the Ph. D. and permitting the dissertation to be of an his-

torical or expository nature rather than a research problem

in mathematics. The suggestion of such a degree was first

made during the summer meetings of the two societies in 1960.

A committee was appointed at this time to study the matter

and to make recommendations. A report was made in 1961 re-

commending that such a step be taken, and the name Doctor of

Arts was tentatively suggested. The governing boards of

both societies approved the suggestion in 1961. Evidently

the public endorsement of the proposed new degree stirred up

considerable controversy among mathematicians, so much so

that the committee made a final report in January, 1963, in

which it recommended that the matter be tabled until further

study could be made of the question. In the words of the

committee report,

In the light of discussions of this question which have occurred . . . it appears to us that an effective response to the problem of training and recruitment of colleges teachers is going to require an extended dis-cussion in the mathematical community, and that the task of promoting such a discussion is not an appropri-ate one for such a small ad hoc committee. We there-fore ask to be discharged.2

^Mathematical Association of America, Official Reports and Communications, American Mathematical Monthly, LXX (April, 1963), p. 473.

An interesting bit of information bearing on the problem

of supply and demand is found in "The Production of Mathema-

tics Ph. D.'s in the United States," a report of the Commit-

tee on the Undergraduate Program in Mathematics of the MAA.^

This report showed that the percentage of beginning college

teachers of mathematics holding the Ph. D. degree decreased

from 34.2 per cent in 1953-54 to 20.0 per cent in 1957-59.

At the same time, the percentage of beginning college teachers

of mathematics holding less than a master's degree rose from

8.3 per cent to 20.6 per cent. During the year 1958-59 as

opposed to the 20.0 per cent of beginning mathematics teachers

holding the Ph. D., the percentages in certain other sciences

were as follows: biological sciences, 49.0 per cent; physi-

cal sciences, 44.3 per cent; and psychology, 51.6 per cent.

The report stated,

Here again it is apparent that mathematics is lag-ging sadly behind the other scientific fields . . . . These figures appear even more discouraging when one recalls that during this same period mathematics majors at the junior and senior levels have tripled. In addi-tion, there has been considerable increase in the total number of students enrolled in colleges and in the proportion of students who take mathematics courses. It is estimated that the typical student in science and engineering takes twice the amount of mathematics taken by his counterpart fifteen years ago. Further-more, a great many students (e. g. business administra-tion, economics, psychology, and the social, biological,

^Committee on the Undergraduate Program in Mathematics, The Production of Mathematics Ph. D.T s in the United States, Berkeley, Calif., 1961.

10

medical, and agricultural sciences) now take a consid-erable amount of mathematics, whereas a few years they took almost none.4

The situation regarding the insufficient number of

teachers being produced under traditional Ph. D. programs is

further highlighted by a study by Young, chairman of the

department of mathematics at Tulane University, which was

reported in the American Mathematical Monthly for September,

1964. This was a study of the Ph. D. class of 1951. There

was a total of 217 Ph. D.'s granted in mathematics in 1951

by universities in the United States and Canada. Of these,

144 holders of the 1951 degrees were then engaged in college

teaching. But, 102 of these were on the faculty of some one

of the approximately ninety-five schools which offer the Ph.

D. in mathematics. Assuming that the distribution of this

class was typical, and applying the same distribution to the

2,500 Ph. D. degrees awarded in the period from 1949 to 1960,

Young found that the Ph. D. producing schools would have

gotten 1,200 Ph. D.fs, while the colleges which had no doc-

toral program in mathematics would have gotten only 500

teachers with the doctoral degree in mathematics. There are

roughly 900 schools in the United States which offer an

4Ibid., p. 17.

^Young, G. S., "The Ph. D. Class of 1951," American Mathematical Monthly, LXX (August-September, 1964), 787-790.

11

undergraduate major in mathematics, in addition to the Ph.

D. degree-granting schools. This meant that during this

twelve-year period there was available just slightly more

than one-half of a Ph. D. for each such school. This took

no account of the need of the junior colleges for a share

of the mathematics teachers trained at the doctoral level.

The above distribution of the twelve-year supply leaves none

available for them.

The situation of the non-Ph. D. producing schools is

intensified when the problem is examined with regard to the

research activities of the class of 1951. The argument that

the Ph. D. should be the only doctoral degree recognized as

satisfactory for preparing prospective college teachers of

mathematics comes into question when the proportion of re-

search men who go into the smaller colleges is considered.

Of the total of 217 men in the 1951 class, 133 had produced

two or more published papers since receiving their degrees.

Of these 133, only eleven were teaching in non-Ph. D.schools.

The chief argument for the Ph. D. in preparing college teach-

ers is based on the assumption that those engaged in research

are best fitted to teach collegiate mathematics. This may be

true. But, if it is, the smaller colleges and the junior

colleges have little chance of getting teachers who meet this

criterion because these men are going almost exclusively into

12

the universities which grant the Ph. D. degree. Those in-

stitutions which have developed graduate centers in mathema-

tics will continue to attract an adequate number of teachers

at the doctoral level. The senior colleges and junior col-

leges are going to have to settle, if not for less, then,

at least, for something different.

That the problem outlined above will probably become

worse instead of better is made evident when consideration

is given to the rapid growth of enrollments in mathematics

classes. According to Lindquist of the Office of Education,

U. S. Department of Health, Education and Welfare, there

was the following number of undergraduate degrees granted

in mathematics in certain years: 1951, 5,753; 1961, 11,437.

Lindquist's extrapolation of his figures yielded the follow-

ing prediction as to numbers of such degrees to be awarded

in 1970 and 1975: 1970, 40,000; 1975, 50,000. A weighing

of these figures whould indicate it to be doubtful that even

the present percentages of college teachers of mathematics

holding the Ph. D. degree can be maintained.^

Rees stressed the need for more teachers to handle the

greatly increased enrollments. She saw a rapid acceleration

^Lindquist, Clarence B., "Mathematics and Statistics Degrees during the Decade of the Fifties," American Mathema-tical Monthly, LXVIII (August-September, 1961), 661-666.

''Rees, Mina, "Support of Higher Education by the Federal Government," American Mathematical Monthly, LXVIII (April, 1961), 371-378.

13

in the need for mathematically-trained graduates of all kinds,

but said that the need for teachers was the most acute of all.

She posed an interesting question as to one of the reasons

for the small yield of mathematics doctorates as compared to

the yield in the sciences,

Why is it that so few mathematics majors go on to the Ph. D. in mathematics? Must a student be a genius to receive a Ph. D. in mathematics: Some of our stu-dents seriously think the answer to this question is "yes". In physics, a B student at college can do a very good job in his Ph. D. research; but a B student in mathematics will be rarely be accepted as a candi-date for a doctorate in mathematics. We shall cer-tainly need some of our B students as teachers, particularly in our two-year colleges if these continue to spring into being as they have been doing recently.^

Rees, in answer to the question of how the need for more

teachers of mathematics is to be met, thought serious consid-

eration should be given to the proposal for a new doctoral

degree. She noted that for some time certain schools of edu-

cation have awarded the Ph. D. degree in mathematics on the

basis of course work devoted half to mathematics and half to

education and including a thesis that may be expository or

historical. In the conclusion to his paper cited above, Young

summed up his opinion of the matter in the final statement,

Is it not time for the mathematical community to face up to the fact that for a long time most under-graduate teaching will be done by non-Ph. D.'s and to

8Ibid., p. 375.

14

begin a study of means of identifying competence among such persons?^

Definition of Terms

1. The term professional doctorate was used to mean

any doctoral degree, designed primarily for the preparation

of college teachers, which combined thorough training in the

subject matter of mathematics with preparation for teaching.

2. The terms Ph. D., mathematics education, and Ed. D.,

mathematics education were used to mean degrees similar to

those described in the Appendix. The abbreviations Ph. D.a

math, ed., and Ed. D., math. ed. were also used for these

degrees.

3. The term Ph. D. was used to mean the traditional

graduate research degree embodying a piece of original re-

search as a dissertation.

4. The term Ph. D. in mathematics was used to mean the

traditional research degree in mathematics requiring an origi-

nal contribution to mathematical knowledge as a dissertation.

5. The term Ed. D., when used in an unqualified manner,

was used to mean a research degree in education.

6. The term Ph. D. granting schools was used in this

study to apply to colleges and universities offering the re-

search Ph. D. in mathematics.

9Young, "The Ph. V'. Class of 1951," p. 790.

15

7. The term doctoral Institutions or schools offering

doctoral degrees was used to mean colleges or universities

which offered doctoral degrees of any kind.

8. The terms doctoral degree and doctorate were used

to include all doctorates of whatever type or title.

Limitations of the Study

1. Data used in determining the need for modification

of present doctoral programs and the utility of existing and

proposed new programs were limited to those data secured from

junior and senior college officials, in response to question-

naires one and two, concerning undergraduate instruction in

mathematics; to those data secured from graduate school offi-

cials in response to questionnaires four and five; and to

data secured from a panel of experts in response to ques-

tionnaire three.

2. The proposed new doctoral programs considered in

the study were limited to degrees fitting the description of

the Ph. D., math, ed., and the Ed. D., math. ed. In the study

of existing doctoral programs of this nature only those pro-

grams were considered which appeared to involve cooperation

of the department of mathematics and the school or department

of education. Thus, the degrees considered were those which

were the outgrowth of a joint, effort to develop well-rounded

programs for preparation of teachers of undergraduate mathematics.

16

3. The extent to which conclusions based on data from

returns of the survey instruments could be generalized to the

population of junior and senior college officials, to the

population of graduate school officials, and to the popula-

tion of experts in mathematics was limited by the degree to

which the opinions of officials and experts who did not re-

spond to the survey differed from the opinions of those who

responded.

1. It was assumed that

cured through the survey in

2. It was assumed that!

Basic Assumptions

the necessary data could be se-

^truments.

ments would provide an adequ

3. It was assumed that

Review of t

the return of the survey instru-

ate sample of the population,

the responses of the panel of

Education would be a representa-

of such educators relative to

specialists in mathematics

tive sample of the opinions

doctoral degrees for preparing college teachers of mathematics,

he Literature

Some reference was made to the literature in the intro-

ductory paragraphs and in the section dealing with the back-

ground and significance of the problem. Some additional

material found in the literature is also pertinent and is

summarized here.

17

The most comprehensive study of graduate education in

the United States that is available is that of Berelson titled

Graduate Education in the United States.Berelson dealt

with the broad field of graduate education, including both

doctoral degrees and master's degrees, rather than with a

particular facet of the subject as is the case in the present

study. However, certain of his findings are interesting in

connection with the problem of this study.

As mentioned earlier, Berelson traced the history of

graduate education in the United States. It is evident from

his summary of this history that the question of special doc-

torates designed for preparation of college teachers has been

present at intervals throughout the development of doctoral

education. Berelson had this to say:

The extreme version of the multitrack position is the recurrent proposal that there should be two doctoral degrees, one for college teachers and one for research-ers. The idea has been around for a long time but has never taken hold . . . . If the system had started this way, it might now seem natural to have two doctorates, separate but equal (if anything of this sort can ever be). As it is, the prestige of the Ph. D. has pre-empted the field . . . .

Another "radical" proposal is currently being dis-cussed in educational circles as a way out of the prob-lem posed by the anticipated rise in college enrollments and in view of the alleged unavailability of Ph. D.'s, the unacceptability of the Master's, and theundesirabillty

•^Berelson, Graduate Education in the United States.

18

of the second doctorate. That is to invent a new two-year degree intermediate between the present MasterTs and Ph. D. and designed especially for the college teacher. It would correspond roughly to the period of the course work for the Ph. D However, the program would be a little broader, would not be so research-oriented, and would deal more with the problems and purposes of the liberal arts college. For prestige reasons, it would have to be called a doctorate-not the Ph. D., of course, but some other version, say, the Doctor of Liberal Arts, or, by field, the Doctor of Social Science, Doctor of Humanities.^

It is evident from this quotation that Berelson felt that

special three-year doctorates would not be acceptable. It

is difficult to see why, in view of this, he proposed, as an

alternative, a special two-year doctorate. At any rate, he

bore testimony to the existence of the problem.

Berelson asked three types of respondents to express

the degree of their approval of a special three-year doctorate

and of the proposed two-year intermediate degree designed for

college teachers. For those who responded, the percentages

agreeing that a special three-year doctorate should be offered

were as follows: graduate deans, 24 per cent; graduate fac-

ulty, 25 per cent; recent recipients of the Ph. D., 35 per

cent. The corresponding percentages for the two-year degree

were respectively 47 per cent, 33 per cent, and 32 per c e n t .

^Ibid., pp. 89-90.

12Ibid., p. 292.

19

Berelson concluded that there was a real shortage of

Ph. D.'s, at least as far as the rton-Ph. D. granting schools

are concerned. The Ph. D. graduates at the time of his

study, which was made in the years from 1957 to 1959, were

going not only into the Ph. D; granting institutions but into

those colleges in this group which had the greatest prestige.

Thus, some of the graduate schools were having difficulty in

attracting the better men with Ph. D.'s. Berelson thought

that the plight of the smaller senior college would continue

to be serious in this respect. The officials to whom he

sent questionnaires concurred with him. He asked graduate

deans, graduate faculty, and college presidents whether "under

the pressures of the years ahead, the liberal arts colleges

would be able to attract, on the average, only the less able

Ph. D.'s in competition with the universities and industry."

About three-fourths of all such officials thought that this

was "already happening" or "probably will happen" with grad-

uate faculty stressing "already happening" and college presi-

dents about evenly divided between the two positions.^

Pfnister also reviewed the history of graduate education

briefly, noting the demand from some quarters for a different

emphasis in graduate education. He said,

13Ibid., p. 117.

20

The Ph. D. became the reward for advanced study at a time when the emphasis was upon original investigation, the expansion of knowledge, and the training of re-searchers. And yet there were some who were convinced that college teaching, as distinguished from university teaching, merited a different kind of preparation.

Throughout the 1920's and 1930's, conference after conference dealt with the possibility of developing two doctoral degrees, one for researchers and one for teach-ers. It was argued that the typical Ph. D. program was too specialized, and that potential college teachers needed some direct training in teaching as well as in the discipline in which they were going to teach.14

Pfnister further pointed out that certain recent developments

had made the question increasingly pertinent. The first was

the general education movement. The desire to give every stu-

dent a broad basic education during his undergraduate years,

in the face of pressure for increased emphasis on giving him

skills which are immediately marketable, increased the demand

for teachers able to provide this broad general education.

On the other hand, the factor of increased specialization of

knowledge made it increasingly difficult to secure teachers

of this type.

McGrath made certain suggestions relative to the prepa-

ration of teachers of undergraduates in "The Preparation of

College Teachers: Some Basic Considerations."^ He mentioned

14pfnister, Allan 0., "Historical Perspective and Current Issues in the Preparation of College Teachers," Journal of Teacher Education, XIII (September, 1962), 240.

•^McGrath, Earl J., "The Preparation of College Teachers: Some Basic Considerations," Journal of Teacher Education, XIII (September, 1962), 247-252.

21

the failure of the supply of teachers to keep pace with de-

mand as being a fact that was too widely recognized to require

further substantiation. This shortage and existing shortcom-

ings in the preparation of college teachers, according to

McGrath, posed a more serious national problem than was gen-

erally recognized. With reference to the particular area of

teacher preparation with which he was concerned, he said,

It is important to make clear at the outset that this discussion concerns itself with teachers of under-graduates in institutions which typically offer four-year programs leading to the bachelor's degree in the liberal arts departments. Teachers of graduate students seeking either the master's or doctor's degree require a somewhat different preparation and therefore ought to be considered separately.16

McGrath detailed four characteristics which he thought

should be present in any program for the preparation of a

teacher of undergraduate students. In brief, they were,

First, his program of studies should be broad enough within his own and related fields to acquaint him fully with the subject matter he will probably be called upon to teach to undergraduates. The typical graduate program today does not provide this breadth of intellectual preparation; the sequence of studies pursued by future college teachers becomes narrower and narrower as it proceeds, ending in a very limited field more closely related to his future research than to the needs of American youth . . . .

Second, to prepare the college teacher more speci-fically for his duties, the program of graduate studies should make possible the selection of a dissertation which involves a synthesis of existing knowledge in new

16Ibid., p. 247.

22

conceptional patterns instead of the analysis of real-ity into ever smaller units.

Third, the college teacher should know more than he does at present about the entire enterprise of higher education in the United States . . . . A considerable body of fact and theory exists relating to (1) the his-tory, philosophy, and purposes of higher education in a democracy; (2) the mechanics by which colleges and uni-versities are structured, administered, and governed; (3) the myriad variations in academic ability and in-terest among the students the teacher may encounter in different types of institutions; (4) the teaching prac-tices which have proved useful with different subjects and the varying circumstances of the classroom; (5) the means now available for appraising the results of educa-tion; and (6) the place of the teacher's own subject in the studentfs total undergraduate education.

Fourth, the future college teacher should learn the skills of his craft by performing them under an experi-enced practitioner.17

There are available in the literature two summaries of

programs for doctorates in mathematics and education which

were designed for the purpose of preparing teachers of under-

graduate students. Both of these programs have been success-

ful in that they have had a considerable body of graduates,

and in that the graduates of the programs are successfully

engaged, for the most part in the teaching of undergraduate

college classes.

The first of these programs is that for the Ed. D for

College Teachers at Teachers College, Columbia University.

This program was described by Hunt in "An Ed. D. for College

17Ibid., pp. 250-252.

23

1 ft

Teachers."-1'0 The program was designed not only to prepare

teachers of undergraduate mathematics but also teachers of

other disciplines.

Hunt said that the program for the Ed. D. for College

Teachers grew out of previous programs at Teachers College,

and that it was implemented in its present form because of

the current shortage of teachers at the undergraduate level

and because of certain shortcomings in the present traditional

doctoral programs. He summarized these shortcomings as

follows, Because the graduate schools have responsibility

for the extension of knowledge, they should, as they cogently insist, maintain specialization and research training as essentials in the Ph. D. programs, but in so doing they leave unmet two needs to which college and university administrators and other specialists in higher education have long and insistently called attention. First, effective college teaching requires breadth as well as specialization in scholarship. Sec-ond, although higher education becomes increasingly complex and college teaching requires increasing in-structional competence, college teachers and profes-sors, alone among professional groups, complete their graduate preparation in programs that ignore the prob-lems, procedures, and resources of their calling.19

The rise of the junior college, the expansion of teachers

colleges into multi-purpose colleges, and the great increase

in the proportion of youth of college age who propose to attend

•^Hunt, Erling M., nAn Ed. D. for College Teachers," Journal of Teacher Education, XIII (September, 1962), 279-283.

19Ibid., p. 280. .

24

college has resulted in an increase in the need for skilled

instructors. Hunt said, with reference to the role of these

professional degrees,

The prospective researchers and college or graduate school professors for whom the Ph. D. is appropriate will certainly continue to qualify for it . . . . The Teachers College Ed. D. in College Teaching is designed for other very able graduate students whose primary interest is teaching rather than research--a group whose primary interests graduate faculties have declined to serve and a group that graduate faculties do not ex-pect to accept in numbers sufficient to meet the coming needs of colleges.

From the point of view of the graduate schools, which are committed to intensive specialization and re-search, the doctorate in college teaching will be infe-rior. From the point of view of colleges and students, however, the doctorate in college teaching must establish itself as superior; it must identify and maintain both those professional standards that the Ph. D. program has met in part--often by chance rather than design--and oth-ers that the Ph. D. has ignored.

Such professional standards include (1) the quality of scholarship that the Ph. D. has emphasized; (2) re-search training; . . . (3) greater breadth of scholar-ship; . . . (4) specialization within an aspect of the candidatefs major field, needed for the teaching of up-per division courses for undergraduate majors and related to continued research interests; and (5) attention to the nature, structure, and problems of higher education and to instructional procedures and resources together with guided experience in teaching for candidates who have not already held instructional appointments.^

A candidate for admission to the above program must have

completed a master's degree or the equivalent in his subject

matter area, and have a high score on the Graduate Record

Examination, or the equivalent, and on other qualifying

20Ibid., p. 281.

25

examinations. The program for the degree requires a minimum

of ninety semester hours of graduate course work. Of this

total the student will do about 60 per cent in his subject

matter area or field of specialization. The minimum require-

ment in education courses is fifteen semester hours. In most

cases the candidate is required to demonstrate a reading

knowledge of at least one foreign language. In the case of

science or mathematics, competence in mathematical statistics

must be shown.

Before graduation, the candidate must have completed two

years of successful teaching in high school or college, or

have completed a two semester internship which is supervised

by a member of his major department. Each candidate must

present and defend a doctoral dissertation or project. This

may consist of research in the tradition of the Ph. D., a

scholarly treatment of an instructional problem, or a schol-

arly compilation and editing of materials of instruction.

Graduates of the program for the Ed. D. in College Teaching

are authorized to identify their field in connection with

the title of the degree, _i_. e. "Doctor of Education:

Mathematics."

The second of the two programs for professional doctor-

ates is that of the Doctor of Education in Higher Education-

Mathematics offered by Oklahoma State University at Stillwater,

26

Oklahoma. This program was described by Coon, who is a

graduate of the program, and who was at Ohio State Univer-

sity at the time of his article.21 This program requires

the equivalent of a strong undergraduate major in mathematics

for entrance, and the candidate is encouraged to complete a

Master's degree in mathematics as part of the overall program.

The general course requirements for the degree in semester

hours are as follows: mathematics, forty-five to sixty hours;

education, a minimum of ten hours; elective, ten to twenty-

five hours; dissertation, ten hours.

Certain courses in mathematics and education are speci-

fied as required courses. In mathematics, these are Complex

Variables, Real Variables, Differential Geometry, Mathematical

Statistics I, Statistical Methods II, and Experimental Design.

In education the courses required are Philosophy of Educa-

tion, Curriculum and Methods in Higher Education, and Organi-

zation and Administration in Higher Education. Coon mentioned

that the requirements in mathematics have been upgraded during

the nine years since the degree was first offered. He said,

"the first nine years of the program has seen the trend in

instruction and course content for mathematics . . . change

21coon, L. H., "The Doctor of Education in Higher Educa-tion-Mathematics at Oklahoma State University," American Mathematical Monthly, LXXVII (March, 1965), 306-310.

27

from the traditional applied problem-solving type to one

embodying a modern set-vector-topology approach to creative

thinking.

Coon said that the candidates for the Doctor of Educa-

tion are divided into three categories. Those in the first

category have as their major interest the teaching of college

mathematics with, perhaps, some interest in the preparation

of teachers. Those in the second category are primarily

interested in mathematics education with emphasis on teacher

preparation. Those in the third category have an interest

in preparing to supervise or act as consultants in mathema-

tics in large public school systems. It was, of course, the

first and second of the above categories with which this

study was concerned. With reference to the degree programs

for students in these two categories, Coon said,

The thesis for a student in the first area may take the form of an expository discussion with background and key concepts presented in a manner that exhibits origi-nality in organizing proofs and in making a contribution to mathematical thought. He may well give birth to some new concepts or theorems during the evolution of his thesis. The education phase of his program normally consists only of the prescribed ten hour block of higher education courses. Thus his preparation may.not qualify him to deal with a problem in pedagogical effects.

A candidate with a major interest in the second category will acquire a background in psychology and education sufficient to enable him to write a thesis dealing with a major area of teaching in higher educa-tion. The planning and direction of an experimental

22Ibid., p. 306.

28

teaching situation or a well organized exposition of subject matter, requiring liason between mathematicians and elementary or secondary teachers, may form the nu-cleus for his thesis. He may take more than the basic ten hour block in higher education depending on his prior background and the recommendations of his advisory committee.23

At the time of Coon's article, fourteen students had

completed the program. One was head of the mathematics de-

partment at a state college in Missouri. A second was editor

of the Kansas Association of Teachers of Mathematics "Bulle-

tin" and a teacher at a Kansas state college. A third was

teaching at what Coon characterized as a strong liberal arts

college in the midwest. Additional information as to the

graduates of this program is available in the form of an un-

published bulletin from the Department of Mathematics and

Statistics of Oklahoma State University, by Zant.^4 According

to this bulletin, as of May, 1966, twenty-six Doctor of Edu-

cation degrees in Higher Education-Mathematics had been

awarded. All twenty-six of these graduates were engaged in

college teaching of mathematics with the exception of one,

who was a mathematics supervisor in a large city school system.

Thus, there is found, in the literature, evidence of a

persistent and recurring problem. Should preparation for

23Ibid., p. 308.

2^Zant, James H., Doctoral Programs in Mathematics and Higher Education, Oklahoma State University, Stillwater, 1966.

29

college teaching include some preparation for teaching at

the doctoral level as well as preparation for research in

mathematics? If so, are professional doctoral degrees in

mathematics and education a desirable solution? Opinions

vary as to the offering of professional doctorates as part

of the answer to this problem. Two cases have been cited

where such a degree program has been put into effect with

apparent success.

CHAPTER II

PROCEDURES FOR COLLECTING AND TREATING DATA

The Samples

The nature of the problem required that data be collected

from officials of junior colleges and senior colleges, from

officials or graduate schools, and from a panel of specialists

in mathematics education. For the data from officials of col-

leges, four samples were used. One sample consisted of all

the junior colleges in the state of Texas. A second sample

was made up of all senior colleges and universities in the

state of Texas except those whose graduate catalog showed

that any type of doctoral degree was offered. From this list

of senior colleges, Arlington State College was deleted be-

cause of the fact that the candidate was a member of the

mathematics staff at this school. The third list consisted

of one hundred junior colleges outside the state of Texas,

and the fourth consisted of one hundred senior colleges out-

side the state of Texas. The national samples were drawn

from the list of junior colleges published by the American

30

31

Council on Education^" and the list of senior colleges and

universities published by the same organization.^ All junior

colleges on the list, excluding those in Texas, were numbered

consecutively. One hundred junior colleges were then selected

at random through the use of a table of random digits. From

the list of senior colleges and universities of the American

Council on Education, those which were shown to offer any

type of doctoral degree were first removed. The remaining

colleges, excluding those in Texas, were numbered consecu-

tively. One hundred senior colleges and universities were

then selected at random by use of a table of random digits.

The panel of specialists in mathematics education was

selected from three sources. The first source consisted of

present and past officers and directors of the National Coun-

cil of Teachers of Mathematics who were engaged in college

teaching of mathematics or in teacher preparation. The

second consisted of present and past members of the Committee

on the Undergraduate Program of the Mathematical Association

of America. A third list was compiled by searching the files

•American Council on Education, American Junior Colleges, 6th edition, Washington, D. C., American Council on Education, 1963, pp. 491-503.

2 American Council on Education, American Universities

and Colleges, 9th edition, Washington, D. C., American Coun-cil on Education, 1964, pp. 1283-1304.

32

°f the Mathematics Teacher and the American Mathematical

Monthly for the past ten years for names of frequent con-

tributors of articles on mathematics education. Since the

names on the third list also appeared on the first two lists,

the final list was, in effect, selected from the first two

sources. A list of forty-three specialists in mathematics

was compiled from all sources. Those who responded to the

questionnaire mailed to them were accepted as the panel of

specialists in mathematics education.

A list of graduate schools offering doctoral degrees

was compiled from the following sources: (1) the list of

colleges and universities published by the American Council

on Education,3 (2) the list of colleges and universities in

Lovejoy's College Guide,^ and (3) individual graduate cata-

logs. A total of 139 graduate schools were identified as

doctoral institutions. From this list, North Texas State

University was deleted because the candidate, was a graduate

student at this school. The remaining list of 138 schools

was used for mailings to graduate school officials. A final

list consisted of graduate schools thought to offer profes-

sional doctorates of the type under study. Of the 138 schools

3Ibid., pp. 1283-1304.

^Lovejoy, Clarence E., Love joy's College Guide, New York, Simon and Schuster, 1962.

33

in the graduate school sample, thirty-two reported the of-

fering of such doctoral degrees. A list of nine additional

schools was obtained from the list given by Lindquist5 and

from catalogs of individual schools. North Texas State Uni-

versity was included in this group of nine schools, and

information concerning the program for the Ed. D. in College

Teaching of Mathematics was obtained from official publica-

tions of the graduate school. This list of forty-one graduate

schools constituted the sample used in securing data concern-

ing the composition of current programs for the professional

doctorates. Table XCV, page 239 , lists twenty-seven graduate

schools identified as offering professional doctorates in

mathematics and education. Complete lists of all other sam-

ples, showing the number and category of respondents are

found in the Appendix, pages 215 through 231.

The Questionnaires

It was decided that questionnaires constituted the only

feasible method of securing data because of the wide geograph-

ical area covered by the samples. Five different questionnaires

were necessary in order to collect the desired data from all

sources in the samples. Certain of the questions in the

^Lindquist, Clarence B., Mathematics in Colleges and Universities, Washington, D. C., 1965, p. 69.

34

questionnaires used by Berelson were used as models for the

preliminary form of the survey instruments. Tentative forms

of all five questionnaires were first constructed. Question-

naire number one was designed to be sent to presidents and

deans of arts and sciences of all junior and senior colleges.

Questionnaire number two was designed to be sent to heads of

departments of mathematics of all junior and senior colleges.

Questionnaire number three was designed for use in securing

data from the panel of specialists in mathematics education.

Questionnaires number four and number five were designed for

mailing to graduate school officials to secure data relative

to graduate offerings.

The tentative forms of the questionnaires were revised

after consultation with the Committee Chairman and one other

member of the Committee. Following this revision the ques-

tionnaires were presented to the Committee in a meeting of

the candidate with the Committee. Certain suggestions were

made by members of the Committee, and the questionnaires were

again revised. Prior to the seminar for defense of the prob-

lem, minor revisions were made once more, after consultation

with individual members of the Committee. At the time of

the defense, further changes were suggested, and the ques-

tionnaires were again revised to conform to the suggested

changes. The committee conducting the seminar for the

35

defense of the problem further suggested that the completed

questionnaires be shown to several members of the mathematics

and education departments at Arlington State College or North

Texas State University for the purpose of determining whether

the intent of any question was ambiguous. The questionnaires

were duplicated and given to ten members of the faculty of

Arlington State College, including people from the department

of mathematics, the department of education, and, also, in-

cluding one dean. A. number of changes were necessary in the

light of the comments which were received. Following this

revision the questionnaires were printed in final form for

mailing. The final forms of the completed questionnaires,

as printed and mailed, are found in the Appendix, pages 198

through 214 . Each questionnaire is preceded in the Appendix

by the covering letter or letters mailed with it. The same

covering letters were used for questionnaires numbers one

and two. The statement of the definition of the degree titles

used, which is the first item in the Appendix, page 196 , was

included in all mailings.

Mailing Procedure and Results of Mailings

The first week in February, 1966, questionnaire number

one was mailed to presidents and deans of the schools in all

four samples. At the same time questionnaire number two was

36

mailed to heads of departments of mathematics at all of

these schools in the four samples of junior and senior col-

leges. The second week in February, questionnaire number

four was mailed to graduate deans and heads of departments

of each of the 138 graduate schools. The third week in

February, questionnaire number three was mailed to each of

forty-three specialists in mathematics education.

By early in April, 1966, it was apparent that the per-

centages of response from presidents and deans of colleges

in all four samples of junior and senior colleges were run-

ning low. It was decided to make a second mailing to these

officials. Since it was very desirable to have a high rate

of response from all categories of officials to the final

question in questionnaires number one and number two, it was

decided to make a second mailing at this time to all heads

of departments of junior and senior colleges. For this

mailing to heads of departments questionnaire number one

was mailed to all heads of departments of junior and senior

colleges who had not returned questionnaire number two.

Beginning at the first of April, questionnaire number

five was mailed to graduate deans, deans of schools of edu-

cation, and heads of departments of mathematics of those

graduate schools offering professional doctorates. These

mailings were first made to the nine schools of this type

37

identified by means other than from returns to questionnaire

number four. Mailings were made to other graduate schools

as returns from questionnaire four showed that they offered

such professional degrees. The only reason for making this

mailing to three officials of each school was to increase

the probability of getting at least one response from each

graduate school.

By May first these mailing had been completed. Between

May first and May fifteenth second mailings were made to

schools from which no response had been received. This mail-

ing was made specifically to officials who had reported that

a professional doctorate was offered by the school. Finally,

personal letters were written to those who failed to respond

to this second mailing.

In the case of questionnaire number four, which was

mailed to two officials of each of the 138 graduate schools,

replies were received from at least one official of 108

schools. Responses were received from both officials of

twenty-five graduate schools. Because no comparison of

opinions was to be made, it was decided to select, for pur-

poses of analysis, one response from each of the schools

from which two replies had been received. If only one of

the two responding officials reported the offering of a

professional doctorate, that return was selected. If both

38

officials reported such a degree or if neither reported

the offering of a professional doctorate, one return was

selected at random. Thus, 108 returns, one from each school,

were used in compiling data from questionnaire number four.

Of the forty-three copies of questionnaire number three

mailed to the list of specialists in mathematics education,

twenty-nine were returned. The twenty-nine specialists re-

sponding were used as the panel of specialists in mathematics

education and the data for questionnaire number three were

compiled from these twenty-nine returns.

Responses were received from thirty-five out of the

forty-one graduate schools to which copies of questionnaire

number five were mailed. Not all of these responses consisted

of the return of questionnaire number five. Questionnaire

number five instructed the respondents that they were free

to send departmental or college materials descriptive of the

degrees in lieu of completing the questionnaire, if this were

more convenient. A few officials replied in this manner. In

such cases, the information was translated into the terms of

the questionnaire for analysis. From this list of thirty-

five graduate schools, from which responses were received,

was selected a list of twenty-seven schools which offered

professional doctorates of the type being considered in the

study. This simply meant that, in the light of the information

39

at hand, the degrees offered by these schools were judged

to meet the requirements for inclusion in the study as a

source of data concerning the composition of current pro-

grams for such degrees. Of these twenty-seven schools,

seventeen were found to offer a Ph. D. in mathematics and

education designed for the preparation of college teachers.

Seventeen schools were found to offer a total of twenty Ed.

D. degrees, with varying designations, in mathematics and

education. A list of the twenty-seven schools together with

the professional doctorates offered by each is found in the

Appendix, page 239 .

A summary of the responses to the mailings to presidents,

deans, and heads of departments of mathematics of colleges in

the four samples of junior and senior colleges is found in

Table I. In the case of the national sample of junior col-

leges, forty-seven heads of departments responded to the

first mailing and twenty-seven to the second mailing. This

represented a total response of seventy-four, or 74 per cent.

A total of sixty-three deans and forty-six presidents of

junior colleges responded. These figures, of course, were

equivalent to 63 per cent and 46 per cent respectively.

Since the same questionnaire was used for both mailings to

presidents and deans, no record was kept of the returns on

the separate mailings.

40

w

w

p

w o w

P4

CO w M J P-*

w

Q

c

CO $ o M

pL, O

W O w J

o o

o H

co o 25 M .J M

CO (I) •H r—I a 0) p4

CO &0 e •H rH •iH cd S

cd •u o H

CO 4J C CD *0

CO CD

p4

CO a cd CD Q

CO *0 cd <D K

M-i CO

CD rH

I £ O CD

»r4 rO CO Cd CD A §

0) rH a

i CO

rH vD

CO CO rH

vO Si"

vD

CO vO

co vO

CO *

V0

CM O CNl

• vO

• vD

• CM rv

• CM

CM <t • 00 vO rH vO

cm -4" • 00 vD r-4 vO

O O

O O i—I

• CD O a s

• o H

• <D O a £

• o H

ON vO

oo

CO

CNl m

cm cm

co

co 00

in CO

vO

CM

m oo

r-l O CM Ln

QN t—1 CM

MH CO O r-4

cd

<D O o • • O • • VO ^ TH o o CM 6 CO • • CO • • rH P <4H ^ o

CM

• <D O a 5

• o H

00 vf

ON r-4

VO

o co

vo • •

in vo CM vo

O vo r-4 CM

rH

ON CO

• CD O a £

• O H

CO CO CO CO rH a) CD a> CD cd •• M W) M OJO •• U 50 U 50 rH a CD O (D O CD CD O CD O CD cd o H *H H •iH rH CO rH *H rH •H i—1 4J •rH a ^ H C« rH cd CU rH & t—l O 4J B 0 o (D O X e 0 o <D O EH cd cd ^ o CO o a> Cd ^ u CO O

CO H CO

41

In the case of the national sample of senior colleges,

the response from heads of departments of mathematics was 66

per cent on the first mailing and 18 per cent on the second

mailing or a total of 84 per cent for both mailings combined.

The total percentages of response for deans and presidents

of colleges in the national sample of senior colleges were

72 per cent and 46 per cent respectively. The overall per-

centages of response for junior and senior colleges in the

national sample were 61 per cent and 67.3 per cent respectively.

In the Texas sample of junior colleges there was a total

of forty-two schools. Twenty-one heads of departments of

mathematics responded to the first mailing and nine to the

second mailing for an overall response of 71.4 per cent. The

percentages of response for deans and presidents of this sam-

ple were 83.3 per cent and 52.3 per cent respectively. In

the Texas sample of senior colleges there was a total of

thirty-nine schools. Twenty-six heads of departments re-

sponded to the first mailing and ten to the second mailing

for an overall response of 92.3 per cent. The percentages

of response for deans and presidents of this sample were

76.7 per cent and 48.7 per cent respectively. The overall

percentages of response for junior and senior colleges in

the Texas sample were 69 per cent and 72.6 per cent

respectively.

42

Procedures for Treating Data

The data from all five questionnaires were manually

tabulated. A summary was prepared for questionnaire number

two in which responses of heads of departments of mathematics

were tabulated for each of the four samples of colleges and

for the combined samples of all junior colleges and all senior

colleges. For questionnaire number one, a summary of the re-

sponses of heads of departments, deans, and presidents to

this questionnaire was prepared for responses of heads of

departments, deans, and presidents for each of the four sam-*-

pies of colleges. A summary was prepared for responses of

heads of departments, deans, and presidents, in the combined

samples of junior colleges and senior colleges, to question-

naire number one. The responses of heads of departments to

questions one through ten of questionnaire one were then com-

bined with the responses of heads of departments to questions

17, 18, 22, 23, 24, 25, 26, 27, 31, and 32 of questionnaire

number two. These questions were identical, in the orders

given, on the two questionnaires. This meant that, in effect,

two samples of heads of departments were used, in each case,

in compiling data. For data drawn from the above ten ques-

tions, the sample consisted of the heads of departments, in

each sample of colleges, who returned questionnaire number

two plus those who returned questionnaire number one on the

43

second mailing. This augmented sample is reflected in the

following tables: Table IX, page 57 ; Table X, page 58 ;

Table XI, page 59 ; Table XII, page 59 ; Table XIX, page 72 ;

Table XX, page 73 ; Table XXII, page 78 ; Table XXIII, page

79 ; Table XXV, page 83 ; Table XXIX, page 90 ; Table XXX,

page 91 ; Table XXXI, page 94 ; Table XXXII, page 99 ; and

Table XXXIII, page 100. This augmented sample contained 84

heads of departments from the national sample of senior col-

leges and 36 from the Texas sample. It contained 74 heads

of departments from the national sample of junior colleges •

and 30 from the Texas sample. All other tables containing

data derived from responses of heads of departments reflected

the opinions of 66 heads of departments in the national sam-

ple of senior colleges, 26 in the Texas sample of senior

colleges, 47 in the national sample of junior colleges, and

21 in the Texas sample of junior colleges. Summaries were

prepared of the responses of graduate school officials to

questionnaire number four, of the responses of specialists

in mathematics education to questionnaire number three, and

of the responses to questionnaire number five giving the

current composition of programs for the professional doctorates.

From the above summaries of data tables were prepared

which broke the data down into appropriate units for considera-

tion at the proper time. From the answers to question number

44

ten of questionnaire number one, question number thirty-two

of questionnaire number two, and question number eight of

questionnaire number three, contingency tables were prepared

to be used in testing hypotheses one through eight for each

of the professional degrees, the Ph. D., math. ed., and the

Ed. D., math. ed. Because of the small number of responses

in the case of "disagree" and "disagree strongly", these two

categories were combined in the construction of the contin-

gency tables. Thus, the sixteen tables which were constructed

were four by four contingency tables. The chi-square dis-

tribution was used to test the hypotheses. The data in the

contingency tables were programmed and the computer at

Arlington State College was used to find chi-square for each

of the sixteen tables. In computing chi-square, Yates' cor-

rection was applied because of the fact that the entries in

certain cells were smaller than ten. Hypotheses were tested

at the five per cent level of significance, which required a

chi-square of 16.919 for rejection.^

g Guilford, J. B., Fundamental Statistics in Psychology

and Education, New York, D. Van Nostrand, 1951.

CHAPTER III

ANALYSIS OF DATA

In this chapter, data from the survey instruments are

presented and analyzed. The data from the various sources

are presented in the following order: (1) analysis of re-

turns from officials of the four samples of junior and senior

colleges, (2) analysis of returns from officials of graduate

schools, and (3) analysis of returns from the panel of spe-

cialists in mathematics education. Finally, the eight hypo-

theses are tested for each of the two doctoral degrees, the

Ph. D., math. ed., and the Ed. D., math. ed.

In considering the data it should be noted again that

one of the limitations of the study was that the return of

the survey instruments was, in each case, a partial return.

If some of the results seem to be too favorable to the spe-

cial doctorates, this could be because those who were most

favorably disposed toward these degrees tended to respond

more frequently than did those who were opposed to them.

Analysis of Returns from College Officials

The Samples of Colleges

A profile of the colleges in the samples is given in

Tables II through VIII.' These tables contain data derived

45

4 6

from the answers to the first nine questions of question-

naire number two, which was mailed to heads of departments

of mathematics on the first mailing to these officials. In

this group were sixty-six senior colleges from the national

sample of one hundred colleges and twenty-six from the Texas

sample of thirty-nine colleges. There were forty-five junior

colleges from the national sample of one hundred junior col-

leges and twenty-one from the Texas sample of forty-two junior

colleges.

The distribution of the colleges in all four samples as

to size is shown in Table II. Entries are given in percent-

ages of the total number of colleges reporting, as reported

TABLE II

PERCENTAGE OF COLLEGES IN VARIOUS ENROLLMENT CATEGORIES

Number of

Senior Colleges

National Sample

c/5

0 ) 6 0 Q) 0)

r-4 r—1 i—1 ex* ° § o cd C

olleges or-©

d) r - l 6 0 CX <u 6

i—I cO r—1 CO o

O r H

' ' V}"-a) 6 0 a> a>

r - 4 r - i i—! CX ° § o cd

— o r - — <u 6 0 0 )

r-i r-i O a

Undergraduate s

Senior Colleges

National Sample

CO

u O CO

• H cd

t s X 0 ) 0 )

CO H Senior

Total

cd u a o o

•i-i 'r-i

6 2 cd

525

CO

u o CO

• H cd

£ x 3 0 )

H Junior

Total

% % % 7 o % % 0 - 5 0 0 1 0 . 6 7 . 7 9 . 8 1 7 . 8 1 9 . 0 1 8 . 2

5 0 1 - 1 , 0 0 0 2 2 . 7 3 8 . 5 2 7 . 2 24.4 2 8 . 6 2 5 . 8

1 , 1 0 1 - 1 , 5 0 0 2 4 . 2 7 . 7 1 9 . 6 20.0 2 3 . 8 2 1 . 2

2 , 0 0 1 - 2 , 5 0 0 1 5 . 2 1 5 . 4 1 5 . 2 15.6 9 . 5 1 3 . 6

Over 2 , 5 0 0 1 6 . 7 2 6 . 9 1 9 . 6 20.0 1 4 . 3 1 8 . 2

Total responding 6 6 2 6 9 2 45 2 1 6 6

47

by heads of departments of mathematics. The percentage of

colleges having five hundred or fewer students varied from

7.7 per cent in the case of Texas senior colleges to 17.8

per cent in the case of junior colleges in the national

sample. Of the junior colleges in Texas, 14.3 per cent had

an enrollment of over 2,500 while 26.9 per cent of the senior

colleges in the Texas sample had more than 2,500 students.

In the national sample, 16.7 per cent of the senior colleges

had an enrollment of over 2,500 while 20 per cent of the

junior colleges in this sample exceeded this figure. The

median size for all groups of colleges and for the combined

totals of senior and junior colleges lay in the interval

from 1,001 to 1,500.

The distribution of enrollment in mathematics classes

is given in Table III. Entries are again in percentages as

reported by mathematics department heads. Of the total num-

ber of senior colleges in both samples, 40.2 per cent had

two hundred fifty or fewer students in mathematics classes

while 34.8 per cent of all the junior colleges had two hun-

dred fifty or fewer mathematics students. The median enroll-

ment in mathematics classes in all categories was in the

interval from 251 to 500. Over all, 10.9 per cent of the

senior colleges and 6.1 per cent of the junior colleges

showed over 1,500 enrolled in classes in mathematics.

TABLE III

PERCENTAGE OF COLLEGES IN VARIOUS CATEGORIES AS TO ENROLLMENT IN MATHEMATICS CLASSES

48

Enrollment in

Mathematics Classes

Senior Colleges

National Sample

Senior Colleges

Texas Sample

Senior Colleges

Total

Junior Colleges

National Sample

Junior Colleges

Texas Sample

Junior Colleges

Total

°L % % % % %

0 - 250 39.4 42.3 40.2 33.3 38.1 34.8 251 - 500 27.3 23.1 26.1 33.3 28.6 31.8 501 - 750 15.2 7.7 13.0 15.6 9.5 13.6 751 - 1,000 3.0 7.7 4.3 8.9 9.5 9.1

1,001 - 1,500 6.1 3.8 5.4 4.4 4.8 4.5 Over 1,500 9.1 15.4 10.9 4.4 9.5 6.1

Total responding 66 26 92 45 21 66

The distribution of degrees with a major in mathematics

offered by the colleges is given in Table IV. Entries are

TABLE IV

PERCENTAGE OF COLLEGES OFFERING VARIOUS DEGREES IN MATHEMATICS

Senior Senior Degrees Colleges Colleges Senior Offered National Texas Colleges

Sample Sample Total

% % % Bachelor's 81.5 76.9 80.2 Master1s 18.5 23.1 19.8 DoctorT s • • • • • •

Total responding 65 26 91

49

in percentages as reported by mathematics department heads.

In each sample, approximately 80 per cent of the senior col-

leges offered the bachelor's degree with a major in mathema-

tics and about 20 per cent offered a master's degree with

major in mathematics.

The distribution of colleges as to number of mathematics

majors is shown in Table V. Entries are again in the form

TABLE V

PERCENTAGE OF COLLEGES IN VARIOUS CATEGORIES AS TO NUMBER OF MATHEMATICS MAJORS

Number Senior Senior of Colleges Colleges Senior

Mathematics National Texas Colleges Majors Sample Sample Total

% 7o % 0 - 100 76.6 73.1 75.6

101 - 200 12.5 23.1 15.6 201 - 300 4.6 3.8 4.4 301 - 400 6.3 • • 4.4 401 - 500 • • • • • •

Over 500 • • • • • •

Total responding 64 26 90

of percentages of the total number of department heads re-

sponding. None of the senior colleges reported over four

hundred mathematics majors and 91.2 per cent reported two

hundred or fewer.

Table VI summarizes certain information relative to

teacher preparation in the colleges of the four samples.

TABLE VI

PERCENTAGE DISTRIBUTION OF COLLEGES AS TO DEGREE OF IMPORTANCE ATTACHED TO

TEACHER PREPARATION

50

Item

Senior Colleges

National Sample

Senior Colleges

Texas Sample

Senior Colleges

Total

i Junior Colleges

National Sample

Junior Colleges

Texas Sample

Junior Colleges

Total

% % 7o % % 7o

Is preparation of secondary teachers of mathematics a major function of your school?

Yes Moderately important No

48.5 39.4 12.4

88.5 7.7 3.8

59.8 30.4 9.8

4.8 42.9 52.3

9.5 38.1 52.4

6.3 41.3 52.4

Total responding 66 26 92 42 21 63 Is preparation of elementary teachers of mathematics a major function of your school?

Yes Moderately important No

53.0 27.3 19.7

73.-1 23.1 3.8

58.7 16.1 15.2

16.3 53.5 30.2

19.0 38.1 42.1

17.2 48.4 34.4

Total responding 66 26 92 43 21 64

Entries to Table VI are in percentages of the total number

of mathematics department heads responding. This information

is helpful in assessing the general nature of the samples

used. From the answers-to the two questions in Table VI was

51

also derived the list of senior colleges in the national

sample which was used in testing hypothesis number three.

Of the total of sixty-six senior colleges in this sample,

thirty-eight reported that preparation of secondary teachers

was a major function of the school, that preparation of ele-

mentary teachers was a major function, or that both were

major functions. The list of the thirty-eight senior col-

leges which stressed teacher preparation is found in the

Appendix, page 237.

The junior colleges showed some interest in teacher

preparation in spite of the fact that this is largely a

function of the four-year college. Of all junior colleges,

47.6 per cent considered preparation of secondary mathematics

teachers to be either important or moderately important and

65.6 per cent considered the preparation of elementary teach-

ers to be either important or moderately important as a func-

tion of the school.

When the replies of heads of departments of mathematics

in senior colleges to this question are considered, a sur-

prising difference is noted in the figures for Texas colleges

and for colleges in the national sample. Of the heads of

departments of Texas senior colleges, 88.5 per cent reported

that preparation of secondary mathematics teachers was a

major function of their school as compared to 48.5 per cent

52

of heads of departments in the national sample. Ninety-six

and two-tenths per cent of Texas heads of departments held

preparation of secondary teachers to be either important or

moderately important while the same percentage for the na-

tional sample was 87.9 per cent. The corresponding percent-

ages for preparation of elementary teachers were 96.2 and

80.3 per cent respectively.

Most of the heads of departments of mathematics who

returned questionnaire number two answered the question,

"is there close cooperation between the department of mathe-

matics and the department of education in the preparation of

teachers?" Table VII summarizes the answers to this ques-

tion. Entries to Table VII are in percentages of the total

number of heads of departments responding. This question

was asked because it was felt that the acceptability of the

special doctorates would be related to the percentage of

colleges where a good degree of cooperation existed between

the departments of mathematics and education in the prepara-

tion of teachers of mathematics. Senior colleges in the

Texas sample reported very close cooperation in 53.8 per

cent of the schools as against 41.7 per cent in the national

sample. A total of 90.6 per cent of all senior college

heads of departments reported either very close cooperation

or moderately close cooperation. The heads of departments

53

of the combined sample of junior colleges reported very

close cooperation or moderately close cooperation in 59.4

per cent of the schools reporting. These responses seem to

indicate a degree of cooperation between mathematics depart-

ments and education departments which is unexpectedly high

to anyone who has had the opportunity to observe the rela-

tions between two such departments in actual practice.

TABLE VII

PERCENTAGE DISTRIBUTION OF COLLEGES AS TO DEGREE OF COOPERATION BETWEEN MATHEMATICS AND

EDUCATION DEPARTMENTS

CO <1) CO CO CO Q) CO CO

Is there close co- GJ i—I a,

<u <v W)r- i

<D 00

<D rH &o a

0) 0) to rH

CD 60

operation between the o) e i-H Ctf

cu ex. r-t g O

! - ! a). 6 rH Cd

<1) CX r~J £

Q) r-l

department of mathe- i—i CO 0

i—i cd O CO

i—! O r—1

i—1 CO o

t—i cd O CO

i—I O r - l

matics and the depart- O rH cd

o CO

o cd u

O r-i cd

o CO

o cd 4J

ment of education in U G U cd o x •H Q) a H

u o r~\ r .

u a r\ r\

U cd o x •H CD S H

u o O H •H S

preparation of teachers': •H £ 4J

U cd o x •H Q) a H £

•r-| .T-I

g 4J

U cd o x •H CD S H

u o O H •H S d) cd <L) 0) 0 Cd 0 3

CO CO CO 55

% 7o 7o % % %

Very close 41.7 53.8 45.3 13.0 11.1 12.5 Moderately close 48.3 38.5 45,3 47.8 44.4 46.9 Very little 10.0 7.7 9.3 39.1 44.4 40.9 Antagonism Total responding 60 26 86 23 9 32

Perhaps the respondents tend to see their own situation

through rose-colored glasses. Another possibility is that

department heads of mathematics who responded tended to

54

include an undue number who, for one reason or another,

were unusually interested in teacher preparation or in

mathematics education. Possibly, those who were not. failed

to respond to a greater degree.

The methods of handling special courses in mathematics

and in methods of teaching mathematics for teachers are sum-

marized in Table VIII. Entries are in percentages of the

total number of heads of departments of mathematics respond-

ing. The question of methods courses is of very little im-

portance in the case of the junior colleges since most of

them do not offer such courses. On the other hand, 57.3

per cent of all junior colleges reported special mathematics

courses for elementary teachers and 44.1 per cent reported

such courses for secondary teachers. In both cases, almost

all the special mathematics courses were conducted by the

mathematics department.

In the case of the senior colleges, over eighty per cent

in each category reported that both special courses in mathe-

matics for teachers and methods courses were taught. The

majority of special mathematics courses for teachers were

taught by members of the mathematics department, while the

methods courses were taught primarily by the department of

education.

55

TABLE VIII

PERCENTAGE OF COLLEGES IN VARIOUS CATEGORIES AS TO THE DEPARTMENT CONDUCTING SPECIAL COURSES FOR TEACHERS

Item

Senior Colleges

National Sample

Senior Colleges

Texas Sample

Senior Colleges

Total

Junior Colleges

National Sample

Junior Colleges

Texas Sample

Junior Colleges

Total

% % % % % %

Which department con-ducts methods courses for teachers of math-ematics? Elementary: Mathematics 13.6 23.1 16.3 21.3 19.0 20.6 Education 60.6 53.7 58.7 4.3 4.8 4.4 Both 9.1 15.4 10.9 • • • • • • Neither 16.7 7.7 14.1 74.5 76.2 75.0 Total responding ~66 26 92 47 21 68

Secondary: Mathematics 50.0 42.3 47.8 19.1 14.3 17.6 Education 21.2 34.6 25.0 f • • • • • Both 13.6 15.4 14.1 • • • • • • Neither 15.2 7.7 13.0 80.9 85.7 82.4 Total responding 66 26 92 47 21 68

Which department con-ducts special mathe-matics course for teachers? Elementary: Mathematics 65.2 73.1 67.4 53.2 57.1 54.4 Education 7.6 7.7 7.6 2.1 4.8 2.9 Both 9.1 11.5 9.8 « • • • • « Neither 18.2 7.7 15.2 38.1 38.1 42.6 Total responding 66 26 92 27 21 68

Secondary: Mathematics 72.7 88.5 77.2 40.4 52.4 44.1 Education 1.5 • « 1.1 Both Neither

. 7.6 18 * 2

3.8 7.7

6.5 15.2 59.6 47.6 55.9

Total responding 6~F~ 26 ~W2 "57 21 68

56

The Academic Preparation of Officials Responding

Certain information as to highest degree held and aca-

demic field was requested of each official to whom a ques-

tionnaire was sent. The distribution of highest degrees held

by senior college officials is shown in Table IX. Of the

total of 287 senior college officials responding, 191 held

doctorates. Of these there were 150 Ph. D.'s, thirty Ed.

D.'s, seven Ph. D.'s designed for teachers, and four Ed. D.'s

designed for teachers. Of the respondents, seventy-two re-

ported that they held either the M. A. or the M. S., while

only two held the M. Ed.

The corresponding data for officials of junior colleges

were given in Table X. Of the total of 270 respondents,

thirty held the Ph. D., forty-six the Ed. D., three the Ph. D.

designed for teachers, one the Ed. D. designed for teachers,

and the remaining 165 held a master's degree of some kind.

Thus, in neither group would the percentage of respondents

holding special doctorates for teachers seem to be large

enough to have prejudiced percentages shown to favor these

degrees.

The data concerning the academic fields of the respondents

from junior colleges are tabulated in Table XI and the corre-

sponding data for officials of senior colleges are tabulated

57

X

W i~3 §

Q hJ W as w w o w Q

H co W X o

o EH DD C oo •~3 3 o M pL< O w o w. J o o Pi o w 55 W CO

o !3 O M EH

6 w fx* M CO CO 5 o

cd 4J O H

CO -P a CD X) •r-(

CO a)

fu

CO a cd a) «

CO 4J

<+-1 a o <d

e CO 4J cd cd Q) Pj X <L> Q

a) cu 60 CD «

O o rs <t o CM <N 00 r ^ m co -sf* co r—J 00 i—( CM

rH cd • r ^ <fr • co LO 4J o

co • • • V0 V H CO cd 00 • • CO iH • r~i CM o> X • • • r-l CD H t—1 — CO • • CO • vD r—1 vO •P CNl • • • cd

i—i cd r- h*. CM \—I vO CO • m i—1 CM 4J v£> »—1 • o o rH H CO cd CO 00 • • r—1 • • CM r-H O X r—1 • • • • CO <D CO H r—i • - Ov ON CM r-4 in CO • CO • CM 4J <t • • cd

2 ;

r—! cd V0 v£> LO CO r m CM CM vt o 4J vt CM CM CM o r—i H CO cd CO r—1 • « O 00 • « vt v£> X r—1 • t r—! • • CO a) CO H T 1 — CO m LO CO r CM CM • <t 4J CO r-1 iH • 00 cd 00 53

60 50 a a •H •r-| & jd a a cd cd a> 0) Q) CO 4J 4J a I—1 o cd A ft a 4J « • • • • CO o

Q P « a • • *0 u <D H < CO w Q) U • • • • &

JG • • • 4J O PM w PM w s s s o &

58

X W •J PQ

S

o

w PC

w w P4 o w Q

H CO W 33 O M ffi

O H

CO <

CO <

M o M

f*4 O w o w 1-3 J o o

o

ptl o S3 o M EH

6

CO CO

a O

T—J cd 4J O H

CO 4J a CD

*D •H CO <D

CO C cd <D Q

cd cd <D a EC cu Q

a) 0)

&o CD o

CM O co i—4 o 00 r-s vO o CO r^ VO CM r-4

CM

r—J cd CM oo • • ON o LO <1* to 00 4J r-| CM • • r-4 v£> o H

CO cd V0 m • • CM m CO • r-4 CM X • • • CM <1) H

r-l • - v£> 00 • • CM vf v£> 4-> r-4 • • <t cd

i—i cd r>* 1—4 CM r-4 00 vD o CM r-4 00 4J r-4 CM CM r~4 r-4 ON o H

CO cd r>* • • Q\ hv CO CM • i n X • • • CO a) H

r-| • - o CM r-4 ON ON • \—1 CO u i—i r—| r-4 • vO cd 53

r-| cd CO CM i—1 • CO CM CM O i—I

• CO r-4 r-4 o o r-4 H

CO cd r-4 • • • CO 00 \D CM • o X • • • r-4 • CO <D H

r-| — CM CM i—1 • O \D 00 r-4 4J • CM co cd

to 50 0 a •H •r-4

£1 o O cd cd <D

) a) a) CO i—i •u u a cd

o 4J IS •V Cu o

• • • • • CO H Q Q p Q • • T) u CD

< CO W Q) U • • • * JX

rd X) XI *0 • • • 4J O PM w CU w s s 2 o &

M

X

w

1-3 PQ

IS

cd u o H

CO vO 00 CO o CO ON CM

CO •U a CD "D •H CO cu

PM

CO a cd a) ft

CO 4J

-w a O CD 6

CO 4J TJ M cd cd CD D. K CD

ft

^ O i O O C O i—I

o •H X3 6 ' • cd cd

T> *4 cd Pn o

CM O CO CO O r-l H CO H

00 O 00 CO N CM

CM CO CD LO 00 r-l CM in

fN <N N in ^ r—I

LT» H CO C st r-l <t

ON CO CD O CM <t 00 r-l O

\—I

r—I CD t—! t—I CM

CM CM O ^ H

kD

XJ W

CO a t-4 4J cd £ cd X ! 4J

a o •H 4J qj O 3

Cd *0 2 w

CD CO i—I & cd o u a o co EH <D

o 53

M M

X

w hJ PQ C H

ft

W M pL,

o M

s w ft

o

EH

CO C

CO

< M U M pt4

o

w o w 1-3 H-l o a

Pi o M IS w CO

Pm O

!3 O M

H

S M Pn M CO CO

a

!—I cd u o H

CM CO CO LO CM CM r-l CM

CO

a <D X) •r-l CO CD U cu

CO

C cd CD ft

cd cd o) a ffi CD

ft

v£> t—I 00 r-l ON

C M O C M H 4

sf H \D o m CO

00 O v f C O N r-l r>.

O VD r-l CM CM

N O 00 CM in m

00 CM o

H H 0 0

CD CD r-l r-l <f CO

a •H U £ r-l a) cd X) *r4 cd fn o <

00 CM O r-H

o <t

x) w

co a •r-l 4J

a o

Cd *r4 6 -M

cd o

Cti TJ 4J S w O

<u CO r—I a cd O 4J a o co H CD

O £5

59

60

in Table XII. Only a small number, in each case, reported

that either mathematics education or education was the major

field. Thus, again, it would not be expected that the offi-

cials would be predisposed to favorable consideration of the

special doctorates in mathematics and education by virtue of

training.

Present Composition of Mathematics Faculties

Sub-problem number one was as follows: to determine the

present composition of mathematics faculties of junior and

senior colleges as to graduate training in mathematics. The

data relevant to this sub-problem are found in the answers

to questions ten and eleven of questionnaire number two.

Question number ten requested information as to size of

mathematics staffs. These data are found in Table XIII.

Entries are in percentages of the total number of heads of

departments of mathematics reporting. It is evident that

the mathematics staffs were small since, in all categories,

almost ninety per cent of the staffs had not more than ten

members.

TABLE XIII

PERCENTAGE OF COLLEGES IN VARIOUS CATEGORIES AS TO SIZE OF MATHEMATICS FACULTIES

61

Number of members on mathematics

faculty

Senior Colleges

National Sample

Senior Colleges

Texas Sample

Senior Colleges

Total

Junior Colleges

National Sample

Junior Colleges

Texas Sample

Junior Colleges

Total

% % % 7o 7o % 0 - 5 62.1 62.5 62.0 61.7 76.2 66.2 6 - 10 21.2 26.9 22.8 27.7 9.5 22.1 11 - 15 4.5 3.8 4.3 8.5 9.5 8.8 16 - 20 6.1 7.7 6.5 • • 4.8 1.5 21 - 25 3.0 • • 2.2 • • • • • •

Over 25 3.0 • • 2.2 2.1 • • 1.5 Total responding 66 26 92 47 21 i~68

Question eleven asked for the number of staff members

holding various degrees as the highest earned degree. The

relevant data are tabulated in Table XIV. Entries are in

percentages of the total number of heads of departments of

mathematics reporting.

For the total of 583 senior college staff members re-

ported, there were 16.6 per cent who held the doctorate in

mathematics. A doctorate with major other than mathematics

was held by 4.6 per cent. For the master's degree with major

in mathematics the percentage was 64.3, and for the master's

degree with major other than mathematics the percentage was

TABLE XIV

PERCENTAGE OF MATHEMATICS FACULTIES HOLDING VARIOUS DEGREES

62

Highest Earned Degree

Senior Colleges

National Sample

Senior Colleges

Texas Sample

Senior Colleges

Total

Junior Colleges

National Sample

Junior Colleges

Texas Sample

Junior Colleges

Total

% % % 7o % %

Doctorate, mathematics 16.0 18.5 16.6 .4 • • .3

Doctorate, other major 5.2 3.2 4.6 1.2 3.9 2.0

Master's, mathematics 64.8 63.1 64.3 67.9 75.5 70.1

Master's, other major 9.2 13.4 10.3 23.5 16.7 21.4

Bachelor's 4.9 1.9 4.1 7.0 3.9 6.1

Total responding 426 157 583 243 102 345

10.3. The senior colleges reported 4.1 per cent of staff

to be holders of the bachelor's degree only. It is worthy

of note that the total of ninety-seven doctorates with a

major in the teaching field is almost exactly an average of

one and one-half doctorates per senior college reporting.

Of the 345 junior college staff members reported, .3

per cent held the doctorate in mathematics and 2 per cent

the doctorate with major other than mathematics. The

63

master's with major in mathematics was held by 70.1 per cent

and the master's with major other than mathematics by 21.4

per cent. The bachelor's degree was the highest degree held

by 6.1 per cent of all staff members reported by junior col-

leges.

Thus, for both senior and junior colleges, the percentage

of teachers with doctoral degrees is low. Offsetting this,

to some extent, is the fact that 80.9 per cent of the senior

college staff members and 70.4 per cent of the junior college

staff members held a graduate degree with major in their

teaching field of mathematics. This, of course, meant also

that approximately one-fifth of all senior college mathematics

teachers reported and approximately one-third of the junior

college teachers reported did not hold any graduate degree

with a major in their field.

Instructional Needs of the Colleges in Relation to Production of the Ph. D. .in Mathematics

Capability of the present system to supply instructional

needs of the colleges.--Sub-problem number two was as follows:

to determine the capability of the present system of doctoral

education in mathematics to supply the needs of junior and

senior colleges. The data bearing on this sub-problem are

found in Tables XV, XVII, XVIII, XIX, and XX.

6 4

Estimates made by the college heads of departments as

to their prospective needs for additional staff members in

mathematics are summarized in Table XV. This table groups

TABLE XV

PERCENTAGE OF COLLEGES IN VARIOUS CATEGORIES AS TO NUMBER OF STAFF MEMBERS IN MATHEMATICS

NEEDED WITHIN NEXT FOUR YEARS

(0 <D CO CO CO CD CO CO CD R-H CD CU CD CD rH CD CD CD W) a M r l 60 60 a, tD rH 00 CL) G CD CX a) CD B CD O, CD

Number of staff i—i cd *H |Ei rH r H Cd rH £Ei rH

Number of staff i—1 CO r—i cd rH tH C/D rH td rH Number of staff o O CO O rH O o W O rH members a rH o O cd O rH U o cd

cd CO 4J cd CO 4J £ U cd u o u £ >-T CD ^ o o o O X O H o o o K o H

•H «H •H CD •H •H *H • H CD •H C 4J C H c C 4 J C H c CD Ctf CD CD 3 cci 0 0

CO CO CO •"> 13 •"J

% 7o 7o % 7o %

0 - 5 8 3 . 3 8 8 . 5 8 4 . 8 9 1 . 5 9 0 . 5 9 1 . 1

6 - 1 0 1 0 . 6 3 . 8 8 . 7 6 . 4 9 . 5 7 . 4

1 1 - 1 5 3 . 0 • . 2 . 2 2 . 1 • . 1 . 5

1 6 - 2 0 3 . 0 7 . 7 4 . 3 * . . . . .

2 1 - 2 5

Over 25

Total responding 6 6 2 6 92 4 7 2 1 6 8

the colleges into categories as to number of staff members

needed in the next four years. Entries are in percentages

of the total number of mathematics department heads respond-

ing. These data became more meaningful when summarized in

terms of average needs, as is done in Table XVI. Thus, the

65

senior college department heads estimated their needs at

an average of slightly more than three new staff members

over the next four years. The junior college department

heads estimated their needs at between two and three addi-

tional staff members.

TABLE XVI

AVERAGE NUMBER OF STAFF MEMBERS NEEDED OVER FOUR YEAR PERIOD

Item

Senior Colleges

National Sample

Senior Colleges

Texas Sample

Senior Colleges

Total

Junior Colleges

National Sample

Junior Colleges

Texas Sample

Junior Colleges

Total

Average number needed next four years. 3.3 3.5 3.3 2.4 2.8 2.5

Total responding 66 26 92 47 21 68

In connection with the need of the colleges for mathe-

matics staff members it seemed pertinent to consider the

desires of the college heads of departments of mathematics

as to the percentage of Ph. D. holders that they would like

to have on their mathematics staffs. This information is

found in Table XVII. Entries are in percentages of the total

TABLE XVII

DISTRIBUTION OF COLLEGES AS TO PERCENTAGE OF PH. D.'S DESIRED

66

Percentage of Ph. D.'s Desired

Senior Colleges

National Sample

Senior Colleges

Texas Sample

Senior Colleges

Total

Junior Colleges

National Sample

Junior Colleges

Texas Sample

Junior Colleges

Total

% % % % % %

Less than 10% 6.3 3.8 5.6 52.8 33.3 46.3 11% - 15% 1.6 3.8 2.2 2.8 • • 1.9 16% - 20% • • 3.8 1.1 8.3 22.2 13.0 21% - 25% 4.7 19.2 8.9 8.3 11.1 9.3 26% - 30% 3.1 3.8 3.3 2.8 • • 1.9 31% - 35% 1.6 3.8 2.2 5.6 • • 3.7 36% - 40% 79.7 53.8 72.2 19.4 27.8 22.2

Total responding 66 26 92 47 21 68

number of mathematics department heads responding. Of the

department heads in the national sample of senior colleges,

79.7 per cent indicated that they would like to have over

40 per cent of their staff members with the Ph. D. degree.

Texas senior college department heads checked over 40 per

cent in 53.8 per cent of the cases. Of the junior college

department heads in the combined sample, 53.7 per cent

would like to have over 10 per cent of their mathematics

staff members with Ph. D. degrees. It seems reasonable to

67

set 40 per cent for senior colleges and 10 per cent for

junior colleges as desirable percentages of holders of the

Ph. D. for the colleges in the samples.

With these percentages of Ph. D.'s desired and the pro-

jected needs of the colleges for additional instructors, it

is possible to make an estimate of the number of Ph. D.

holders which would be needed by the colleges in the samples

to bring their mathematics staffs up to the desired standard.

The senior colleges would require 23.4 per cent of present

staff to increase the percentage of Ph. D.'s from 16.6 to 40

per cent. Since a total of 583 staff members was reported

by senior colleges, this would mean replacing 136 staff mem-

bers with holders of the Ph. D. The junior colleges would

require 9.7 per cent of present staff to increase the per-

centage of Ph. D.'s to 10 per cent. On the basis of the 345

staff members reported, this would require the replacement

of thirty-three present staff members with holders of the

Ph. D. Thus, to bring present mathematics staffs up to the

desired percentages would require a total of 169 Ph. D.'s

for the colleges in the samples.

In considering the total number of new instructors

needed over a four year period, a figure of three per school

for senior colleges and two per school for junior colleges

TTIP V - T Ti f l i o T -1 r r 1~> f - A ^4 -* nr»- 1- i - " T T T %

68

conservative. This would require 276 additional staff mem-

bers for the senior colleges in the samples and 136 additional

staff members for the junior colleges in the samples. To hold

new staff to 40 per cent Ph. D.fs for senior colleges would

mean a need for 110 holders of the Ph. D. over the four year

period. To hold the new staff for junior colleges to 10 per

cent Ph. D.'s would mean a need for thirteen holders of the

Ph. D. over a four year period.

In the study quoted in Chapter I, Young came to the con-

clusion that, over the twelve-year period from 1949 to 1960,

there was available approximately one-half of a Ph. D. for

each non-Ph. D. granting senior college, with none available

for junior colleges. - On the basis of this estimate, there

would be available for the ninety-two senior colleges and

the sixty-eight junior colleges in the samples approximately

one-sixth of a Ph. D. per school over a four-year period.

This would mean that these schools could probably count on

an available supply of Ph. D.'s, over a four-year period, of

fifteen to twenty for all 160 schools. When this projected

supply is compared with the need cited above for 123 holders

of the Ph. D. simply to hold new staff members to forty per

cent Ph. D.'s in senior colleges and 10 per cent in junior

•bfoung, "The Ph. D. Class of 1951," pp. 787-790.

69

colleges, it seems evident that demand far outstrips the sup-

ply. When the 169 additional holders of the Ph. D. who would

be required to bring present mathematics up to the desirable

40 per cent for senior colleges and 10 per cent for junior

colleges, the situation appears much darker. Of course, the

production of Ph. D.'s in mathematics may be expected to in-

crease, but the college enrollment in mathematics is also

growing by leaps and bounds.

One measure of the capability of the present system of

graduate education in mathematics to supply the needs of the

junior colleges and senior colleges was the degree of diffi-

culty which the heads of departments said that they had

experienced in securing such personnel. These data are

tabulated in Table XVIII. Entries are in percentages of the

total number of heads of departments of mathematics respond-

ing. At the senior college level, over 75 per cent of all

heads of departments in all samples reported both that they

had encountered great difficulty in securing staff members

at the doctoral level, and that they expected difficulty in

the future. Senior college heads of departments reported

great difficulty in securing staff members at the master's

level in 11.5 per cent of the responses and moderate diffi-

culty at this level in 41.4 per cent of the responses.

Junior college responses were comparable except that junior

70

TABLE XVIII

PERCENTAGE DISTRIBUTION OF COLLEGES AS TO DEGREE OF DIFFICULTY IN SECURING NEW STAFF

MEMBERS IN MATHEMATICS

Item

Senior Colleges

National Sample

Senior Colleges

Texas Sample

Senior Colleges

Total

Junior Colleges

National Sample

Junior Colleges

Texas Sample

Junior Colleges

Total

Difficulty in securing staff members at the doctoral level Great difficulty Moderate difficulty Little difficulty Total responding

% % % 7o % ' %

Difficulty in securing staff members at the doctoral level Great difficulty Moderate difficulty Little difficulty Total responding

77.0 19.7 3,3

83.3 16.7 • •

78.8 18.8 2.4

72.0 8.0 20.0

87.5 12.5 • •

78.0 9.8 12.2

Difficulty in securing staff members at the doctoral level Great difficulty Moderate difficulty Little difficulty Total responding 61 24 85 25 16 41

Is difficulty anticipated in the next few years at the doctoral level? Yes No No opinion Total responding

83.3 4.5 12.1

75.4 11.5 23.1

78.3 6.5 15.2

36.2 17.0 46.8

71.4 4.8 23.8

47.1 13.2 39.7

Is difficulty anticipated in the next few years at the doctoral level? Yes No No opinion Total responding 66 26 92 47 21 68

Difficulty in securing staff members at the master's level Great difficulty Moderate difficulty Little difficulty Total responding

13.1 37.7 49.2

7.7 50.0 42.3

11.5 41.4 47.1

13.6 45.5 40.9

9.5 57.1 33.3

12.3 49.2 38.5

Difficulty in securing staff members at the master's level Great difficulty Moderate difficulty Little difficulty Total responding 61 26 87 44 21 65

Is difficulty anticipated in the next few years at the master's level? Yes No No opinion Total responding

34.8 53.0 12.1

34.6 42.3 23.0

34.8 50.0 15.2

40.4 44.7 14.9

71.4 23.8 4.8

50.0 38.2 11.8

Is difficulty anticipated in the next few years at the master's level? Yes No No opinion Total responding 66 26 92 47 21 68

71

college heads of departments were slightly less pessimistic

concerning future difficulty at the doctoral level. The

junior college heads of departments reported slightly greater

difficulty at the master's level, and anticipated greater

future difficulty here than did senior college heads of de-

partments.

Further light was shed on the supply of Ph. D.'s by

data reflecting opinions of college officials, tabulated in

Tables XIX and XX. Entries are in percentages of the total

number of officials in each category responding. Because of

limited space, entries are given to the nearest one per cent.

Forty-five per cent of all junior college officials and 47

per cent of all senior college officials reported the belief

that, in the years ahead, the four-year colleges and the

junior colleges will be able to attract only the less able

Ph. D.'s in mathematics. An additional 30 per cent of senior

college officials and 32 per cent of junior college officials

thought that this would probably prove to be true in the fu-

ture. Thirty-two per cent of all senior college officials

and 43 per cent of all junior college officials thought it

was already true that there were almost no Ph. D.'s available

for junior and senior colleges. An additional 41 per cent of

officials of senior colleges and 40 per cent of junior col-

lege officials thought that this would probably be true in

72

TABLE XIX

PERCENTAGE DISTRIBUTION OF OPINIONS OF SENIOR COLLEGE OFFICIALS AS TO FUTURE SUPPLY OF MATHEMATICS PH. D.'S

Item

National Sample

M 'd to o PC

CO a <L> Q

CO •u C CD ra •ri £0 CD U pu

Texas Sample

cd

o H

CO T) cd cd Pd

CO a cd CD Q

CO •u C CD

•r-l CO CD P~<

r-l cd 4J o H

Combined Samples

CO -d cd CD X

CO C cd CD Q

CO 4J C CD

•r-l CO 0) P4

cd 4-> o H

% % % % % % % 7 /o %

Will junior and senior colleges be able to attract only less able Ph. D.'s? Already happening Probably will hap-pen

No sign now and little likelihood

No opinion Is it likely that there will be almost no Ph. D.'s for these col-leges in the future? Already happening Probably will hap-pen

No sign now and little likelihood

No opinion Total responding

56

23

6 15

43

35

7 15

35

39

9 17

47

31

6 16

61

17

6 16

43

43

3 11

37

32

31

49

29

4 18

57

21

6 16

43

37

6 14

35

37

6 22

47

30

6 17

35

38

14 13

34

43

14 9

30

37

15 18

34

40

14 12

33

42

8 17

23

53

17 7

32

37

5 26

29

45

11 15

34

39

13 14

31

46

15 8

31

37

12 2C

32

41

13 14

84 72 46 202 36 30 19 851 on 102 65 287

the future. In excess of 73 per cent of all officials, then,

thought that the supply of Ph. D.'s in mathematics was short

or would probably become short in the future. It seemed

reasonable to conclude, then, that sub-problem number two

could be answered by saying that there was a reasonable doubt

7 3

of the ability of the present system of doctoral education

in mathematics to supply the needs of the junior and senior

colleges.

TABLE XX

PERCENTAGE DISTRIBUTION OF OPINIONS OF JUNIOR COLLEGE OFFICIALS AS TO FUTURE SUPPLY

OF MATHEMATICS PH. D.'S

Item

National Sample

CO T) Gj <u

CO e cd CD

ft

CO •u e 0) X) *H CO CD U

r-J cd 4J O

Texas Sample

CO *0 cd a) EC

CO a cd CD Q

CO 4J a a) •H CO 0) PL,

Combined Samples

CO T) cd Q) K

CO a cd o> Q

CO 4J e a) x) •i-i CO <u J-l pLI

!—i cO 4J O H

Will junior and senior colleges be able to attract only less able Ph. D.'s? Already happening Probably will happen

No sign now and little likelihood

No opinion Is it likely that there will be almost no Ph. D.'s for these col-leges in the future? Already happening Probably will happen

No sign now and little likelihood

No opinion Total responding

4 7

26

8 H 9

4 5 3 2

12 11 7 4

% 7o % 7 /o

% %

4 3

3 2

16 9

3 7

4 3

11 9

4 3

3 2

12 1 3

5 7

1 7

7

1 9

4 3

4 3

6 8

5 0

2 7

1 4

9

4 9

3 0

8 1 3

5 0

2 3

8 1 9

5 3

3 6

12 9

4 1

3 8

12 9

3 5

4 8

11 6

3 9

4 4

1 3

4

4 0

4 0

12 8

5 3

3 3

7

7

4 9

4 3

3

5

4 0

4 6

5

9

4 8

4 0

5

7

4 7

3 3

11 9

4 0

4 6

8 6

4 0

4 4

10 6

4 5

3 2

10 1 3

4 3

4 0

10 7

6 3 4 6 1 3 3 3 0 3 5 22 8 7 L04 9 8 68 270

74

Satisfaction of college department heads with current

products of graduate schools.--Sub-problem number three was:

to determine the degree to which these colleges are satisfied

with current products of the traditional program for the doc-

torate. The data bearing on this sub-problem is found in

Table XXI. Entries are in percentages of the total respond-

ing. The heads of departments were asked to state degree of

satisfaction with teachers, who had come to them directly

from graduate school, with respect to knowledge of subject

matter, and with respect to their ability to teach. Of the

heads of departments of all senior colleges, 65.5 per cent

reported that they considered graduates to be highly satis-

factory with regard to knowledge of subject matter. An

additional 34.5 per cent regarded such graduates as moder-

ately satisfactory in this respect. The corresponding

percentages for junior colleges were respectively 48.2 per

cent and 51.8 per cent. Thus, no heads of departments con-

sidered the graduates of traditional programs to be unsatis-

factory as concerned knowledge of subject matter.

The degree of satisfaction with ability to teach of

recent graduates was not quite so marked, although still

high. Only 28.6 per cent of senior college department heads

and 26.8 per cent of junior college department heads con-

sidered graduates to be highly satisfactory in this respect.

TABLE XXI

PERCENTAGE DISTRIBUTION OF COLLEGES AS TO DEGREE OF SATISFACTION WITH CURRENT PRODUCTS

OF GRADUATE SCHOOLS

75

Item

W CD CD r—1 to a a) e

co r-4 r-4 o a r-4 8 o •r4 4J cd

u o •r4 c 0) CO

CO a) <D fcOr-4 <u a r-4 i—1 I o co o

03 u cd o x *r4 <D a H CD CO

CO <D 00 a) t—i I—i O r-4 O cd 4J u o

Q H •H C 0) CO

co a) &) i—i bO Ow a> e r—J Cd i—I CO o O r-4

cd C o •r4 4J cd ^ 53

co a> a) CL) cx r-4 JEj r-4 Cd O CO a u o •r-|

CO cd X CD C H

P

co <D to Q) r-4 r-4 O r-4 O Cd •U

^ o O H •r4 §

•->

7o % 7 /o

7 /o

Knowledge of subject matter Highly satisfactory Moderately satis-

factory Unsatisfactory Highly unsatisfac-

tory Ability to teach

Highly satisfactory Moderately satis-

factory Unsatisfactory Highly unsatisfac-tory Total responding

63.8

26.2

69.2

30.8

65.5

34.5

46.2

53.8

52.9

47.1

31.0

67.2 1.7

23.1

76.9

28.6

70.2 1.2

30.8

64.1 5.1

17.6

70.6 11.8

58 26 84 29 17

70

48.2

51.8

26.8

66.1 7.1

56

However, 70.2 per cent of senior college heads and 66.1 per

cent of junior college heads of departments considered grad-

uates to be moderately satisfactory in ability to teach. It

should be observed that the fact that department heads men-

tioned no teachers as having been unsatisfactory as to the

knowledge of subject matter and very few as unsatisfactory

76

in ability to teach does not necessarily mean that no unsatis-

factory teachers had been encountered. It is probable that

the department heads were thinking in terms of the typical

teacher they had received from graduate school. However, in

answer to sub-problem number three, it seemed reasonable to

conclude that officials of the colleges were very well satis-

fied with current products of the traditional program for the

doctorate.

The need for the development of special skills in the

doctoral student.--In the discussion of the traditional Ph.

D. versus the doctoral degree designed to prepare for college

teaching, the proponents of the Ph. D., as the sole vehicle

for such preparation, have argued that the prime requisite

for the college teacher is training in research and the

ability to produce original research. On the other hand,

some have held that special preparation for teaching was of

equal or even greater importance and that special doctorates

were necessary to fill this need.

Questions twenty-two through twenty-six of questionnaire

number two, and the identical questions three through seven

of questionnaire number one, were designed to sample the

opinion of college officials as to the importance of training

for research and of special preparation for college training.

77

The data relative to the responses to these questions are

tabulated in Tables XXII and XXIII. Entries are percentages

of the total number of college officials responding. Because

of limited space, entries are given to the nearest one per

cent. Table XXII summarizes the responses of senior college

officials, and Table XXIII summarizes the responses of junior

college officials. As might have been expected, there was

a considerable difference in the degree of importance which

senior college and junior college heads of departments of

mathematics, deans, and presidents attached to the active

production of research as a qualification for teaching under-

graduate mathematics. About 1 per cent of all officials

felt that it was necessary that teachers at the undergraduate

level be productive research mathematicians. However, 61 per

cent of all senior college officials considered active re-

search to be desirable as opposed to 22 per cent of all

junior college officials. Thus, a total of 62 per cent of

senior college officials and 23 per cent of junior college

officials felt that active production of research was either

necessary or desirable. The percentage favoring training in

research methods in mathematics was somewhat higher. Seventy

seven per cent of senior college officials and 46 per cent

of junior college officials considered such training either

necessary or desirable. Officials in all categories were

78

TABLE XXII

PERCENTAGE DISTRIBUTION OF OPINIONS OF SENIOR COLLEGE OFFICIALS AS TO NEED FOR PREPARATION IN RESEARCH

METHODS AND TEACHING METHODS

National Texas Combined Sampli o Sami ole Sample

Item CO 4-> £

CO 4-> c

CO 4~> e

CO CO O T—1 w CO a) !—! CO CO <D r-4 x) C T) cd ••a a X) cd T> G XJ cd cd cd •r-f 4J cd cd •P-| 4J cd cd •H 4-1 <D CD CO o CL) CD CO O <D o CO 0 EC P <D H Ed « a) H Ed Q d) H

u Ed

eu i % % % % % % 7

to % % % % % 1

Is it necessary that a 1 teacher of undergrad- I uate mathematics be a i productive research i

i mathematician? 1

Necessary 1 • • • • 1 • • 3 • • i 1 1 • • 1 Desirable 63 65 48 60 78 60 42 64 67 64 46 61 Not necessary and 1 not desirable 35 29 41 34 22 30 42 29 31 29 42 33

No opinion 1 6 11 5 • • 7 16 6 1 6 12 5 ! Is research training 1 at the doctorate le\el necessary for the teacher of undergrad-uate mathematics? Necessary 5 14 2 7 3 10 • • 5 4 13 2 6 Desirable 75 68 63 70 81 73 58 73 77 69 61 71 Not necessary and not desirable 17 15 22 17 14 10 26 15 16 14 23 17

No opinion 3 3 13 6 2 7 16 7 3 4 4 6 Is it necessary for the prospective teach-er of undergraduate mathematics to have special preparation for teaching? Necessary 17 21 30 21 8 23 21 17 14 22 28 20 Desirable 60 59 48 56 70 60 53 62 63 59 49 58 Not necessary and not desirable 21 12 11 16 22 10 10 15 21 12 11 16

No opinion 2 8 11 7 • * 7 16 6 2 7 12 6 . Total responding 84 72 46 202 36 30 19 85 120 102 65 287

79

TABLE XXIII

PERCENTAGE DISTRIBUTION OF OPINIONS OF JUNIOR COLLEGE OFFICIALS AS TO NEED FOR PREPARATION IN RESEARCH

METHODS AND TEACHING METHODS

Item

National Sample

CO X3 cd CD X

CO C cd cd Q

CO 4J a 0) X) •H CO CD P-4

r—J cd 4J o H

Texas Sample

CO xj cd CD

CO C cd cd Q

CO 4J a CD

"O •r-|

CO CD U cu

r~l cd

O H

Combined Sample

CO XI cd

CD 33

CO u a <D

XJ •r-l W O CM

r - l d 4J o H

Is it necessary that a teacher of under-graduate mathematics be a productive re-search mathematician? Necessary-Desirable Not necessary and not desirable

No opinion Is research training at the doctoral level necessary for the teacher of undergrad-uate mathematics? Necessary Desirable Not necessary and not desirable

No opinion Is it necessary for the prospective teach-er of undergraduate mathematics to have special preparation for teaching? Necessary Desirable Not necessary and not desirable

No opinion Total responding

18

76 6

4 32

60 4

30 63

% % %

2 .. 1 19 76 20

75 24 4 . .

3 46

46 5

44 51

74 63

52

46 2

37 57

46

75 4

3 42

51 4

37 57

5 1

27

66 7

183

7 43

43 7

23 60

13 4

28

69 3

6 43

48 3

23 74

30 35

22

73 5

50

41 9

41 45

9 5

26

69 5

4 45

45 6

28 62

9 1

20

73 7

22 87

5 35

55 5

28 62

9 1

1 22

72 5

4 45

47 4

37 59

1 3

25

74 1

104 98

52

38 53

7 2 68

1 22

73 4

3 43

44 49 4 5

34 59

5 2

270

80

strongly in favor of the provision of some form of special

preparation for teaching in the programs for preparing teachers

of undergraduate mathematics. Seventy-eight per cent of all

senior college officials and 93 per cent of all junior college

officials thought that this was either necessary or desirable.

It seemed reasonable to conclude that, in the opinion of these

officials, it would be desirable for doctoral program designed

for preparation of teachers of undergraduate mathematics to

include seminars or other courses in which methods of research

in mathematics were encountered, and that they also should

include some form of special preparation for teaching over

and above courses in subject matter.

As an indication of the form which college officials

thought that the special preparation for teaching should

take, officials were asked to rank three methods of giving

this preparation. The results are summarized in Table XXIV.

Officials were also asked to indicate their preference for

one of two fields in education from which courses might be

drawn as preparation for teaching. These data are summarized

in Table XXV. The entries to Table XXIV are given in the

form of weighted scores. The computation of the weighted

score for formal instruction in methods, as ranked by heads

of departments of mathematics of senior colleges in the

national sample, is given here to illustrate the method of

s

w •J

S

o fa w

PQ

CP CD

h a

•9 e 6 cd o co o

CO CD cd i x £i <d 6 H cd

CO

rH cd a) £i rH o a]

§ -u cd cd co 53

T ^ ^ o x

s ^ u a p i s a a ^

S U B 0 Q

S p F 0 H

T B ^ O I

s ^ u a p i s a a j

S U F 0 Q

sp-eaH

W o i

s ^ u a p x s a ^

sireaQ

s p p a n

6 cd •u

vD vD • •

rH CM

00

rH

vD ON * i

rH CM

vf

rH

•st oo « •

rH CM

00

rH <t • •

CM CM

CM

i—1

vO vD • •

r~| CM

<r

rH

CM O « •

rH 00

vD

0O O • •

r—I CM

vO CM • •

CM CM

0O

t—I

vo • •

rH CM

oo

in • t

rH CM

OO

m r-• «

rH CM

00

vo v£> • •

i—' CM

CM

rH

vjd r-. • •

i—I CM

vD • •

rH CM

vl> 00 « •

i—I CM

vO 00 • •

r—I CM

vD 00 • •

i-i CM

vD O • •

rH 00

VD 0\ • •

r—I CM

in r . • •

rH CM

\0 in • •

rH CM

m oo • •

rH CM

vo r^ • •

rH CM

vo • •

rH rH

rH

r~i

rH

rH

0O

rH

CM

OO

00

rH

UO

rH

in

rH

m

CD CD 60 4J 60 4J C cd a cd •H 3 •H ^

co rd x5 CO jd x> XJ O cd x> o cd o cd U o cd u jc a) 60 CD 60 «P 4J 4J •M CD cd CD cd e 6 rQ

CD CO 6

CD CO C CO cd 0 co cd •H *H •H •H

> 60 > 60 a ^ £ c ^ a O CD •H o CD #H •H •H 4J P o 4J 3 a

•• O CO cd * • o CO Cd co 0 a CD CO 3 a cd CD U 0 4J CD M 2 4J 60 4J 60 4J

2 4J

CD CO J^XJ CD CO P^XJ rH Pi t—I CD 4~> rH £ rH CD 4J rH *H CD CO £ t—1 »H CD CO O > •H CD O > *H CD O H H > X* C3 rH •H > X)

cd 4J cd 4J V4 3 U & cd CD 4J M E cd a) 4J O U rH Cu CO O p rH Oh CO •H O CD 3 •H O CD 3 a fa c4 co fa fa' CO CD 3 C/3

81

82

computing the scores. Fifty-nine department heads of senior

colleges in the national sample answered this question.

Thirty of these department heads ranked formal instruction

in methods as number one; twenty ranked it second; and nine

ranked it third as a method of giving preparation for teach-

ing. The number of department heads checking each ranking

was multiplied by the rank assigned this method. These pro-

ducts were then added and divided by fifty-nine, the total

responding, to arrive at the weighted score. Thus, in this

case, this method produced a sum of thirty plus forty plus

twenty-seven, or a total of ninety-seven. Dividing by fifty-

nine gave a weighted score of one and sixth-tenths.

The weighted scores for the combined samples of officials

of both senior colleges and junior colleges ranked the three

mathods in the following order: supervised teaching as a

graduate student, formal instruction in methods, and rela-

tively unsupervised teaching as a graduate student. In only

three categories of officials was a different ranking from

that above assigned to the three methods. Heads of depart-

ments of Texas senior colleges ranked them as follows:

supervised teaching as a graduate student, relatively un-

supervised teaching as a graduate student, and formal instruc-

tion in methods. Deans and presidents of Texas senior colleges

ranked the methods in the following order: formal instruction

83

in methods, supervised teaching as a graduate student, and

relatively unsupervised teaching as a graduate student.

The entries to Table XXV are in percentages of the total

number of college officials responding. Because of the limi-

tations of space entries are given to the nearest one per

TABLE XXV

PERCENTAGE DISTRIBUTION OF OPINIONS OF COLLEGE OFFICIALS AS TO DESIRABILITY OF TWO TYPES

OF INSTRUCTION IN EDUCATION

National Sample

Item CO X? cd CD K

CO a cd <D «

CO 4J a <L) •r4 CO a) u P-,

Texas Sample

cd o H

CO cd CD K

CO a cd 0) Q

CO 4J e 0) r0 •H CO CU (U

I—I cd 4J o H

Combined Sample

CO -a cd CL)

CO a cd <D Q

CO 4J a CL) •H CO cu

cd u o

7o 7 (o

7 to Z

Senior Colleges: Methods of teaching History, philosophy, and problems

Equally desirable No opinion Neither

Total responding

28

26 26

7 13

33

29 24

8 6

28

26 28 18

30

27 26 10

7

31

22 19

3 25

47

20 20 10

3

47

11 11 21 10

40

19 18 10 13

28

25 24

6 17

37

27 23

9 4

34

22 23 18

3 84 72 46 202 36 30 19 85 120 102 65

33

25 23 10

9 287

Junior Colleges: Methods of teaching History, philosophy, and problems

Equally desirable No opinion Neither

Total responding

51

15 24 10

48

16 33

2 1

50

13 33

4

50

14 30

2 4

43

7 17 10 13

63

14 20

3

68

9 14

9

58

14 17

7 4

49

15 22

3 11

53

15 29

2 1

46

12 26

6

52,

14 26

3 5

74 63 46 183 30 35 22 87 104 98 68 270

84

cent. Officials were asked to express a choice between in-

struction in methods of teaching and instruction in the

history, philosophy, and problems of higher education, as

part of the preparation of teachers of college mathematics.

In all categories, officials placed methods of teaching first.

In the combined sample of senior colleges 33 per cent of all

officials preferred instruction in methods of teaching; 25

per cent preferred instruction in history, philosophy and

problems of higher education; and 23 per cent said that they

were equally desirable. The corresponding figures for offi-

cials of junior colleges in the combined sample were respec-

tively, 52 per cent, 14 per cent, and 26 per cent.

Doctoral Degrees in Mathematics and Education in the Junior and Senior Colleges

Present use of faculty members with such degrees.--Sub-

problem number four was to determine to what extent colleges

are already using people with training comparable to that

proposed in the new programs. The data relevant to this

sub-problem are tabulated in Tables XXVI and XXVII. Heads

of departments of mathematics were asked the question, "Does

your school have a mathematics staff member with a doctorate

similar to the Ph. D., math. ed., or the Ed. D. math. ed.?,T

The responses to this question are summarized in Table XXVI.

Entries are in percentages of the total number of department

85

heads responding. Percentages varied in the different cate-

gories of colleges, as reflected in the table, but it was

found that 23.8 per cent of all senior colleges in the com-

bined sample and 8.8 per cent of all junior colleges had such

staff members.

TABLE XXVI

PERCENTAGES OF COLLEGES HAVING STAFF MEMBERS IN MATHEMATICS WITH PROFESSIONAL DOCTORATES

Response

Senior Colleges

National Sample

Senior Colleges

Texas Sample

Senior Colleges

Total

Junior Colleges

National Sample

Junior Colleges

Texas Sample

Junior Colleges

Total

% % % % % %

Yes 27.3 15.4 23.8 11.2 4.8 8.8

No 72.7 84.6 88.8 88.8 95.2 91.2

Total responding 66 26 92 47 21 68

Heads of departments of mathematics who reported staff

members with professional doctorates were asked to say how

many they had. Responses to this question are summarized in

Table XXVII. Entries are in terms of percentages of the

total number of department heads responding. Of the total

86

number of department heads of senior colleges, 19.5 per cent

reported one staff member with a professional doctorate; 1.1

per cent reported two; and 3.3 per cent reported three.

TABLE XXVII

PERCENTAGE DISTRIBUTION OF COLLEGES AS TO NUMBER OF MATHEMATICS STAFF MEMBERS WITH

PROFESSIONAL DOCTORATES

Number of Staff Members Holding Professional Doctorates

Senior Colleges

National Sample

Senior Colleges

Texas Sample

Senior Colleges

Total

Junior Colleges

National Sample

Junior Colleges

Texas Sample

Junior Colleges

Total

7o % % % % 1

One 21.2 15.4 19.5 10.6 5.0 8.8

Two 1.5 • • 1.1 • • t 9 • •

Three 4.5 • • 3.3 • • • • • •

None 72.8 84.6 76.1 89.4 95.0 91.2

Total responding 66 26 92 47 21 68

In question thirty of questionnaire number two, heads

of departments of mathematics were asked to comment on the

desirability of having a staff member with preparation both

in mathematics and education. These responses are summarized

87

in Table XXVIII. Entries are in percentages of the total

number of heads of departments of mathematics responding.

TABLE XXVIII

PERCENTAGE DISTRIBUTION OF OPINIONS OF DEPARTMENT HEADS AS TO DESIRABILITY OF HAVING A STAFF MEMBER

PREPARED IN MATHEMATICS AND EDUCATION

Response

Senior Colleges

National Sample

Senior Colleges

Texas Sample

Senior Colleges

Total

Junior Colleges

National Sample

Junior Colleges

Texas Sample

Junior Colleges

Total

% % \ % 7o % % Highly desirable 33.3 38.5 34.8 38.3 28.6 35.3 Desirable 42.4 34.6 40.2 38.3 33.3 36.8 No opinion 19.7 15.4 18.5 19.1 33.3 23.5 Undesirable 4.5 11.5 6.5 4.3 4.8 4.4

Total responding 66 26 92 47 21 68

The heads of departments responded in a manner that indicated

a considerable degree of approval of the idea of having a

staff member with preparation both in mathematics and in

education. In no category did more than 11.5 per cent of

the department heads indicate that they considered this to

be undesirable. And in all categories more than 72 per cent

of all heads of departments responded that they considered

it neither highly desirable or desirable to have such a

staff member. It was possible, of course, that those heads

88

of departments who were more interested in mathematics educa-

tion or in teacher preparation tended to respond more readily

than those who were less interested. This possibility is

decreased by the fact that responses of heads of departments

of Texas colleges were also favorable. The Texas colleges

represented a much greater percentage of the population than

did the colleges in the two national samples.

Sub-problem number four may be answered by saying that

23.8 per cent of all senior colleges and 8.8 per cent of all

junior colleges in the combined samples were using faculty

members with special doctorates in mathematics and education

designed for the preparation of college teachers of mathema-

tics. Further, the fact that a majority of heads of depart-

ments regarded such preparation as either highly desirable

or desirable for at least some staff members indicated a

likelihood that these percentages could be expected to in-

crease.

Type of work for which college officials consider the

new degrees to be adequate preparation.--Sub-problem number

five was to determine the type of work for which college

officials consider the proposed degrees to be appropriate

ti*aining. The data pertinent to this sub-problem were taken

from the responses of college officials to question eight of

89

questionnaire number one and question twenty-seven of ques-

tionnaire number two. In these identical questions college

officials were asked to check any of seven positions for

which they felt these special doctorates to constitute ade-

quate preparation.

The responses of senior college officials are summarized

in Table XXIX and those for junior college officials are sum-

marized in Table XXX. Entries to both tables are in percent-

ages of the total number of department heads responding. The

highest degree of approval was registered by the heads of

departments of mathematics of senior colleges in the national

sample. In general, the greatest degree of approval was

given to this preparation, for all positions listed, by heads

of departments, the lowest by presidents. For the heads of

departments of senior colleges in the national sample, the

percentages of approval were above 65 per cent for all posi-

tions listed. The percentages of approval on the part of

deans and presidents fell below 50 per cent in the case of

research in the teaching of mathematics.

The responses of junior college officials were very

similar to those of senior college officials. Here, again,

a majority of all officials approved of the special doctorates

as preparation for the positions listed, in all cases. The

90

X M

w

CO •4 C M O M to to O •4 <

W 53 O O W w •J CO >4 CO a O w o O pM !—!

O H Pi Pi <d o h~! ^ 9 53 ffi P-« W u w CO M

ffi p^ pL* & o w

Pi H CO O <J 53 to CD O c M CO w

^ p M o < to H O H W

l-H od to CO < o o

pL4 CO a w o PL, EH M O <tf H pq £3 CO o PQ W H M P^ O Pi O H H Q CO M O Q H

w CO O < <

w u Pi w p^

<d r~i a

i CO

cu C

•H

'i o o

0) r—I a §

CO

CO cd X CU H

CU r—I Ou

I CO

I—I cd e o

•rH 4J cd

s q u a p i s a a j

S U B 9 Q

S p B 9 H

T B ^ o x

s ^ u a p i s a a j

S U B 9 Q

S p B 9 H

W O I

s q u a p i s a . ! ^

s u B a a

S p B 9 H

CO a o •rH 4J •rH CO o p^

M-H o CO 0) Ou

H

6^

\o co r-* oo

CO as -vi-vo in

vt r~l o vO

o\ m

CM vO

O 00 vO <t

<t >3-oo

vO vO

vO f*

CM r^

CO vo

O 00 00 00

«n 00 00

CM 00

vO <f-vo

r~H O oo

1—I CM r^

CM r^. vo VO IT)

ON r^. r-.

as CO CM vo in

o oo

co vO

oo o o uo

c* m vo

oo vO

r^ r^

oo IH

o o in

o <r 00 00

CO r^.

m r^ r^

o oo in

r -r-v vo in

CM in in m oo

m co oo

r^ rH

m rH h- a\ vD

m <t oo a \

as oo oo

00 00

o in oo vO

00 CM

m vO

CM O

O CM

in oo

os r-H

o oo

vO oo

CM o CM

vO xf

CM r-x

00

<D W) CO CU a

1-1 1 •r-f I—1 <U

rd u

o a <U

rd cd cd u •r-i c 4J 6 a) •H O cd cu

VI o a) C

cw 6 X u

b •H jd O CO u cd g o •rH CU o 6 o cd 4J CO CU

CM •r~i cu 4J

cd u CO

cw O

a a cd o <U •H •H

or a

CL) o CO 60

a 50 CO CO CO •r-i a a O a a O X •rH

•H •r-l u •r a a 4J o u cd a cd cd CO <u cd CO cu o 6 e •H X 6 X) CO 4J a CD 0) > o CU o CO

rd r£ U r-4 cd X X CU cu cu 4J 4J 0) O cu u 4J X X cd cd a o 4J CO cd CU o 4J S 6 3 xi o e g cd

4J 1—1

cw co o cw •r-l cu a cd cw cw CO o 4J CO 4J •H u

o <D o r\ cd o o o 50 C a u 6 CU CO E H CI) u Cd o CL> U X u a o

a) rH <D 6 rH 4J X <D a CU •rH «H rH M X a 4-i X cd X 4J cd

o o a •H 3 0) cd a Q) o cd cu cd o cd cd a 6 cd 4J cd 6 CO <D Q) XI •H cu a)

6 CU

EH H o Q EH H Pi

9 1

x

w

o

a)

a Ch r->. 8

6

VD 74

73

vD LO

27

0

C/3

a) a

*T~{

-8

s ^ u a p t s e a j 81

1 06

I 6

6 r ^ iH r>.

CO O vD to

00 vD

C/3

a) a

*T~{

-8

S U P 9 Q vD

86 vD

vD 71

CO h-

ON VD i n 98

u s p B 9 H 81

83 CO

r^. 74 CO 00 CO

vo in

104

a> rH a

W o i 82 06

99 ON vD 70

ON ON vD <t 87

E cd C/D s ^ u a p T s a a j oo

86

55 CO ON

LO 00 vD vD Nj- 22

CO cd X <D r i •

S U B 9 Q 86

91

09

09 71

vD CT\ vD v t 35

S p B 9 H 83

i 06 80 r ^ co co

in 30

. S

am

ple

I ^ 3 0 £ s-s CO <t

oo 71

76

74 V D

vo i n

183

. S

am

ple

s r j u e p T s a a j 85

!

91

CM 00 r - 7

6 r-A CM VD M 4

6

r - l cd a o

S U B 9 Q 70 co

00 70

78 IT) r-1 CM

VD CO vD

•r-l

4J cd S3

S p B 9 H 80

80

70

73

72 vD CO

VD i n 74

CO a o

•r-l 4J T-L CO O PM

O

CO CD a

H

CD 0 0 CO CD o

r—I 1 •r-| r- i CD 4 J

V-s o a X I cd cd O T-i A -u 6 CD • H o cd <D

o CD a TW 6 JZ

4J •H x2 o CO cd

3 g a •r-l CD o B O 5 cd 4J CO m • r -> (P

4 J cd U 2 CO o

a a cd O CD •r-i •H ^ A a CO to

CO O 0 ) A GJO

CO CO CO *r4 A a O * A O o rC •r-i •r-l • H M •r-l a o - P 4~> O 4 J cd A cd Cd CO CD cd CO CD o 6 B x : 6 X) CO 4J A A) 0 ) > o CD o CO

x : J C M rH cd x : rC <D CD <D 4J 4 J <D O CD u CO 4 J J C j d u cd cd A o 4 J CO cd CD a 4 J 6 E 3 x ; o B CD 6 cd

4 J r- l

<4-1 CO A «4-I • H CD a cd

<4-1 4~I CO O 4J M-I a TM 4J •H 4J o CD O cd O CD O O txO a o 6 CD CO x : H

u CD M CD •H O CD U O o CD r-l CD g i—1 -u x i CD <D •H

XI rH XI V4 X> a 4J JC U JZ 4 J cd o o a «h 0 a; cd O o O cd CD cd U cd cd a u 6 cd cd e CO CD 0 ) • H CD CD CD EH H o Q H H

92

percentage of approval fell below fifty per cent in only two

cases. Forty-nine per cent of the deans in the Texas sample

of junior colleges and 46 per cent of the presidents in the

same sample approved of the special doctorates as preparation

for research in the teaching Of mathematics. Sub-problem

number five, then, could be answered by inferring that the

majority of the college officials considered the proposed

degrees to be adequate preparation for all positions listed

except for that of research in the teaching of mathematics.

In every category there was a high percentage of approval

of the degrees as preparation for teaching undergraduate

mathematics either in senior college or in junior college.

Attitude of college officials toward proposed degree

problems.--Sub-problem number six was to determine the

attitude of presidents, deans, and heads of departments of

mathematics in junior and senior colleges toward proposed

doctoral programs designed primarily for college teachers.

Two questions were asked of all college officials, the

primary purpose of which was to determine the answer to the

above sub-problem. In question nine of questionnaire number

one and question thirty-one of questionnaire number two,

officials were asked to rank six graduate degrees in order

of preference in filling vacancies. The responses to this

93

question are summarized in Table XXXI. Entries are in the

form of weighted scores. These scores are simple, weighted

arithmetic averages. The computation of the score for the

Ph. D., as ranked by heads of departments of mathematics of

senior colleges in the national sample, is described here to

illustrate the method of computing the scores. Of the

eighty-four presidents in the national sample who responded

to this question, sixty-eight ranked the Ph. D. in mathema-

tics one; five ranked it two; seven ranked it three; three

ranked it four; and one ranked it six. The number of depart-

ment heads assigning each rank to the degree was multiplied

by the rank assigned by them to this degree. These products

were then added and the sum was divided by eighty-four, the

total responding to arrive at the weighted score. Thus, in

the case of the Ph. D. in mathematics, this method produced

the sum of sixty-eight, ten, twenty-one, twelve, and six for

a total of 117. This total was then divided by eighty-four

to give the score of one and four-tenths, which is the first

score to appear in the table. For all categories of senior

college officials, the weighted scores for the degrees

ranked the degrees in the following order: Ph. D. in mathe-

matics; Ph. D., math. ed.; Ed. D., math, ed.; M. A. or M. S.

in mathematics; M. A. or M. S. in education; and M. Ed.

These rankings followed the pattern which might have been

94

M

w

PQ

s

CO

< 3 M O M pLi fx* O

w o w 1-3 J

o o

I n PQ

Q W

CO <

CO w w PS o w Q

X M CO

P«H o Pn

CO w P4 o o CO

cu 1—I a

i CO

* 0 a) a

•r-i g

o o

a> r -4 a §

CO

CO cd X cu

H

CU i—I a §

CO

r—1 Ctf a o

•r-i 4 J cd

a

r—I cd 4 J O

•r-l CO CO 4 J cu a ^ a.) PM X> CO a cd 0

Q

CO x l cd cu

K

cd 4 J o

¥ -• H CO CO 4 J cu a ^ cu

CO a cd CU

Q

CO X J cd cu

ffi

r - l cd

4 J O

H "T * H CO CO u <D C k a)

PL) X )

CO a cd CU

Q

CO X > cd cu

ffi

CO <L) CU U to CU

o

< t ON ON CO N N

H H CM CO v t l O

l A ON 0 > CO vO i f j • • • • • •

r~4 r—I CM CO -<J" i n

^ 0 0 LO 0 0 0 0 < f " • • • • • •

I—I t—I CO <f~ L/0 CM

CO CO ON H v o 0 0

H H CM C O s f i n

C O O > ON CM N i n

H H CM CO \ f LT)

v o ON ON ON CM

H H CM CM v j u o

co oo o n in o oo H H CM CO LT) i n

i—! i—I ON l O O 0 0 • • • • • •

h cm cm co i n i n

v f 0 0 0 0 CO N CO * • • • « «

r l I—I CM 0 0 \ f " i n

ON 0 0 vO h v 0 0 • • t • • •

H H CM CO s j - i n

CO N N s j 0 0 0 0

p—i r -4 CM CO < j " i n

^ ON ON CM vO ON

H H CM CO i n

m o o i n N v o v o

CM r - l CM CM <J" i n

v o o o i n h . o n n • • • • • •

CM H CM CM ^ i n

\ f N < t CO VD N « • • • • «

CM i—I CM CM i n

v D 0 0 r s N s f < r • • • • • •

CM H CM CM i n

CM N vD 00 N in CM H N CM vt in

H N f \ O v O • • • • • •

CM r~ l CM CM •<}" i n

CM N in 00 vO vO • • • • • #

CM H CM CM i n

\T M n oo vo^ CM H CM CM in

N 00 in N v O vO

CM r H CM CM in

O 0 0 CO vO ON 0 0 • • • • • •

CO r H CM CM < t in

in N CM 00 vO 00 CM rH CM CM <t in

oo o n v o co -3* • • • • • •

CM tH CM CM <t in

CO X J CU 4J 6 0 Cd <u e

X J x > cu cu

o o

u o a CU CO

rC 4 J • cd x) 6 cu

*\ r\ CO CO

P O P « • •

r£ r£ X) CU Pm W

u CU 4 J CO cd

s

u cu • 4J X) CO W cd •

S 2

CO & CU 4J 60 cd cu 6

o u

u o

• H

§ * - )

x> CU 4J

cd x) £ CU

cd co co 6 - -

* ^

cu Q Q 4-J

• • CO

rd XJ P~i PM W

Cd s

J-l cu * 4J XJ CO W cd •

s a

95

expected. It. should be noted that, in this ranking, both

the Ph. D., math, ed., and the Ed. D., math, ed., were rated

higher than the master's degree with major in mathematics.

The responses of junior college officials to this ques-

tion followed a different pattern. Responses from heads of

departments in the national sample yielded weighted scores

which ranked the degrees as follows: Ph. D., math, ed.;

M. A. or M. S. in mathematics; Ed. D., math. ed.; Ph. D. in

mathematics; M. A. or M. S. in education; M. Ed. The responses

of department heads of Texas junior colleges yielded scores

which ranked the degrees in the following order: Ph. D.,

math. ed.; Ed. D., math. ed.; Ph. D. in mathematics; M. A.

or M. S. in mathematics; M. A. or M. S. in education; M. Ed.

It is striking that both sets of responses ranked the Ph. D.,

math. ed.,and the Ed. D. , math, ed., ahead of the Ph. D. in

mathematics and that the responses of heads of departments

in the national sample of junior colleges also ranked the

M. A. or M. S. in mathematics ahead of the Ph. D. in mathema-

tics. The responses of college presidents in the national

sample ranked the degrees in the following order: Ph. D.,

math. ed.; Ed. D., math. ed.; M. A. or M. S. in mathematics;

Ph. D. in mathematics; M. S. or M. S. in education; M. Ed.

The responses from deans in the national sample ranked the

degrees as follows: Ph. D., math. ed., Ed. D., math. ed.;

96

Ph. D. in mathematics; M. A. or M. S. in mathematics; M. A.

or M. S. in education; M. Ed. Responses of deans, and presi-

dents of junior colleges in the Texas sample produced weighted

scores which ranked the degrees in the following order: Ph.

D., math, ed.; Ph. D. in mathematics; Ed. D., math, ed.; M.

A. or M. S. in mathematics; M. A. or M. S. in education; M.

Ed. Thus, in every category, at least one of the special

doctoi-ates in mathematics and education was ranked ahead of

both the Ph. D. in mathematics and the M. A. or M. S. in

mathematics.

The results of the rankings of the degrees obtained from

the responses of officials both in senior and junior colleges

indicated a rather high degree of acceptance of the new

degrees. It should be pointed out that to say officials

displayed acceptance for the new degrees does not mean that

they would, in most cases, employ a teacher with an Ed. D.,

math, ed., if a holder of the Ph. D. in mathematics were

available at the same time as an applicant for the position.

At least in the case of most senior colleges, the Ph. D. in

mathematics was preferred over all other degrees. Some of-

ficials, by their own statements in answer to this question,

would prefer the Ph. D., math. ed.,or the Ed. D., math, ed.,

over the Ph. D. in mathematics. In the national sample of

senior colleges, sixteen-heads of departments ranked Ph. D.,

97

math, ed., first; and one ranked the Ed. D., math, ed., first.

A much greater number of junior college officials could be

expected to give preference to a holder of one of the pro-

fessional doctorates over a holder of the traditional Ph. D.

It seems advisable to stress, in this connection, that

it was not a part of any of the purposes of this study to

attempt to establish superiority of the professional doc-

torates over the traditional Ph. D. in mathematics. Although

the degrees have some common purposes, they have a different

primary emphasis and it would hardly be possible to undertake

to prove the superiority of one over the other. The chief

purpose of the study was, instead, to try to see if there is

a place for the newer degrees in mathematics education side

by side with the traditional Ph. D. in mathematics. It is

undoubtedly true that the Ph. D. in mathematics will con-

tinue to be the principal degree both for training mathema-

ticians and teachers. It is fitting that every Ph. D. in

mathematics that can be produced be produced. Without re-

search in mathematics, mathematics as a living and growing

branch of knowledge could not maintain its rightful place

as the queen of sciences. For this reason, the production

of Ph. D.'s will remain one of the paramount needs of mathe-

matics.

9 8

In question ten of questionnaire number one and question

thirty-two of questionnaire number two, officials were asked

to express the degree of their approval or disapproval of

the offering of the Ph. D., math, ed., and the E. D., math,

ed., by checking one of five responses for each degree. The

five responses were agree strongly, agree, no opinion,

disagree, disagree strongly. The data derived from responses

to this question are tabulated in Tables XXXII and XXXIII.

Entries to both tables are in percentages of the total number

of college officials responding. Because of the limitations

of space, entries are given to the nearest one per cent.

The responses of senior college officials are tabulated

in Table XXXII. A rather high percentage of senior college

officials felt that the present situation in mathematics

education justified the offering of such degrees as the Ph.

D., math, ed., and the Ed. D., math. ed. For the Ph. D.,

math, ed., the percentage checking either "agree strongly"

or "agree" ran from a low of 75 per cent of all heads of

departments in Texas senior colleges to a high of 82 per

cent of all presidents of colleges in the national sample.

For the Ed. D., math, ed., the percentage who checked either

"agree strongly" or "agree" ran from a low of 62 per cent for

heads of departments in the national sample of senior colleges

to a high of 71 per cent for presidents in this sample.

99

TABLE XXXII

PERCENTAGE DISTRIBUTION OF OPINIONS OF SENIOR COLLEGE OF-FICIALS AS TO THE DESIRABILITY OF OFFERING SUCH

DEGREES AS THE PH. D., MATH. ED. AND THE ED. D., MATH. ED.

Response

National Sample

CO tti cu

CO G cd CD Q

co 4J C 0

T) •r~|

CO CD u

fU

Texas Sample

r-l cd 4 J O H

CO X) cd 0) K

CO C cd <D Q

CO •u C 0) X) •H CO CD

P-<

i—I cd

4 J O H

Combined Sample

CO T) cd 0) EC

CO a cd CD Q

CO 4J a <U X) •H CO 0)

r - l cd 4 J o H

% % % % 7 /o % % 7o % 7o %

Ph.D., math.ed.: Agree strongly Agree No opinion Disagree Disagree strongly

Ed.D., math.ed.: Agree strongly Agree No opinion Disagree Disagree strongly Total responding

45 33 12

6 4

29 33 23 12 3

36 45

8 7 4

22 47 13 15 3

54 28 9 4 5

30 40 17 9

44 36 10

6 4

27 36 18 12 3

39 36

6 11

8

28 37

8 14 14

37 43 3 13 4

33 37 7

20 3

32 47 16

32 37 21 5 5

37 41 7 9 6

30 34 11 14

8

43 34 10

8 5

28 44 18 13 7

36 44 7 9 4

25 40 11 17 3

48 34 11 3 4

31 40 18

8 3

%

42 38 9 7 4

28 39 1.6 13 4

.84 ,46 72 202 36 30 19 85 120 102 65 2.87

The responses of junior college officials to this ques-

tion are tabulated in Table XXXIII. For the Ph. D., math,

ed., the percentage checking either "agree strongly" or

"agree" ran from a low of 70 per cent for deans in the national

sample of junior colleges to a high of 91 per cent for deans

in the Texas sample. For the Ed. D., math, ed., the percentage

checking either "agree sti*ongly" or "agx ee" ran from a low of

100

68 per cent for deans in the national sample of junior colleges

to a high of 89 per cent for presidents in this sample.

It is noteworthy that for each degree the upper range of

approval was higher on the part of junior college officials.

TABLE XXXIII

PERCENTAGE DISTRIBUTION OF OPINIONS OF JUNIOR COLLEGE OF-FICIALS AS TO THE DESIRABILITY OF OFFERING SUCH

DEGREES AS THE PH. D., MATH. ED. AND THE ED. D., MATH. ED.

National Texas Combined Sample Sam pie Sami Die

Response

Heads

Deans

Presidents

| Total

Heads

Deans

|

Presidents

Total

r i

j Heads

1

Deans

Presidents

Total

% % % % % 7o % -% % % % %

Ph.D., math.ed.: Agree strongly Agree

5 0

3 5 3 5 3 5

4 3

3 7

4 3 3 6

5 3 3 7

5 4 3 7

4 0

3 2

5 1

3 6

5 1

3 6 4 2 3 6

4 3

3 5 4 6 3 6

No opinion Disagree Disagree strongly

Ed.D., math.ed.:

7 4

4

1 6

1 3

1

9 1 1 • •

1 0

9 2

1 0 • •

6

3 1 4

1 4

9 4

8

3 2

1 2

9 1

1 0

1 2 • •

1 0

7 1

Agree strongly Agree

4 3

3 7

3 6

3 2 4 6

4 3 4 2

3 7

3 7 3 7

4 0

4 6

3 7 4 1

3 8 4 1

4 1

3 6

3 8

3 7 4 2 4 3

4 0

3 8

No opinion Disagree

1 0

5 1 3

1 7 4 7

9 1 0

2 3

3

6 8

9 1 3

1 3 8

1 4 5

1 0

1 4

6 9

1 1 9

Disagree strongly 5 2 • * 2 4 1 • * 2 Total responding 7 4 6 3 4 6 1 8 3 3 0 3 5 2 2 r 8 7 1 0 4 98 6 8 2 7 0

The highest percentage of approval for the Ph. D., math, ed.,

was 91 per cent for deans of the national sample of junior

colleges as opposed to a high of 82 per cent for presidents

101

of senior colleges in the national sample. For the Ed, D.,

math. ed., the highest percentage of approval was 89 per cent

for presidents in the national sample of junior colleges as

opposed to a high of 71 per cent for presidents in the na-

tional sample of senior colleges. In general, the percentages

of junior college officials and senior college officials who

checked either "agree strongly" or "agree" for the Ph. D.,

math, ed., were almost the same. In the case of the Ed. D.,

math, ed., however, the percentage of junior college officials

checking either "agree strongly" or "agree" ran considerably

higher than the corresponding percentage of senior college

officials. For example, the percentage of junior college

officials in the combined samples who checked either "agree

strongly" or "agree" for the Ed. D., math, ed., was 78 per

cent as opposed to 67 per cent for senior college officials.

It seemed reasonable to answer sub-problem number six

by saying that the attitude of presidents,.deans, and heads

of departments of mathematics in both junior and senior col-

leges toward proposed doctoral program designed primarily for

college teachers of mathematics was quite favorable. The

percentages of approval for the Ph. I)., math, ed., were approxi-

mately the same in the case of officials of both junior and

senior colleges. In the case of the Ed. D., math, ed., how-

ever, junior college officials expressed a considerably higher

102

percentage of approval than did senior college officials.

It should be emphasized that the expression of approval for

the offering of these degrees by an official did not mean

that he would prefer them for his college mathematics depart-

ment over any other doctoral degree. It meant that he

thought that the situation in mathematics education, as he

saw it, justified the offering of such degrees.

Sub-problem number seven was to determine to what

extent the need of colleges for teachers and their willing-

ness to accept those trained under the new programs justify

intensifying the offering of such degrees. It has been

shown that there was a need on the part of the colleges for

staff members in mathematics with advanced training which

was not likely to be filled for some time by the present

system of doctoral education in mathematics. This condition

appeared to be likely to continue or to become worse. It

has also been shown that college officials were, to a con-

siderable extent, in favor of the offering of special doc-

torates in mathematics and education designed for preparing

teachers of undergraduate mathematics. It seemed reasonable

to conclude, then, in answer to sub-problem seven, that the

need of the colleges for teachers and their willingness to

accept those trained under the new programs justified inten-

sifying the offering of such degrees.

103

Analysis of Returns from Graduate Schools

Analysis of Returns to Questionnaire Number Four

Questionnaire number four was designed to supply data

concerning graduate offerings in mathematics and in mathema-

tics ediication. The primary purpose of this questionnaire

was to determine which graduate schools offered doctoral

degrees in mathematics and education designed for preparing

college teachers of mathematics, what schools might offer

these degrees in the future, and what the attitude of the

graduate schools was toward these special doctorates.

Doctoral degrees offered in mathematics and mathematics

education.--Sub-problem number eight was to determine the

extent to which doctoral degrees designed for the specific

purpose of preparing teachers of college mathematics are

now being offered by graduate schools. Responses of gradu-

ate school officials concerning doctoral degrees offered in

mathematics and in mathematics education are summarized in

Table XXXIV. Entries are in percentages of the total re-

sponding. It should be noted, again, that only one return

from each graduate school was utilized in compiling data from

questionnaire four.

Of the 108 graduate schools from which a return was

received for questionnaire number four, eighty-one, or 75

104

per cent, stated that the traditional Ph, D. in mathematics

was offered. Thirty-two, or 29.6 per cent, reported that

another doctoral degree was offered, which was primarily in

mathematics, but which had a dissertation requirement differ-

ing from that of the research degree in mathematics. These

degrees were, in most cases, similar to the degree proposed

TABLE XXXIV

PERCENTAGES OF GRADUATE SCHOOLS OFFERING VARIOUS DOCTORAL DEGREES IN MATHEMATICS AND

MATHEMATICS EDUCATION

Degree

Schools Offer-ing Special

Doctorates for Teachers

Other Graduate Schools

Total

Ph.D., in mathematics 81.3 72.4 75.0

Ph.D., with dissertation requirement different from the Ph.D. in math. 40.6 27.6 29.6

Ph.D., math.ed. 46.9 • • 13.9

Ed.D., math.ed. 56.2 • • 18.5

Other doctoral degree fox* teachers 15.6 • « • 4.6

Total responding 32 76 108

by the Mathematical Association of America and the Mathemati-

cal Society, which was tentatively titled the Doctor of Arts

105

degree, and which was to have differed from the Ph. D. in

mathematics in the type of dissertation required. In general,

these degrees have very much the same requirements as to

course work, as the Ph. D., but the dissertation may be expo-

sitory in nature. Thirty-two schools, or 29.6 per cent,

reported the offering of a special doctorate for teachers.

A total of thirty-eight different doctorates in mathematics

and education for teachers were reported by these thirty-two

schools. Several schools offered two such degrees and two

schools offered three different doctorates designed for pre-

paring teachers of undergraduate mathematics. This accounts

for the fact that of the total number of 108 graduate schools,

13.9 per cent offered the Ph. D., math, ed., 18.5 per cent

the Ed. D., math, ed., and 4.6 some other special doctorate,

for a total of 37 per cent instead of 29.6 per cent. These

were the degrees with which this study was concerned. It

was possible to answer sub-problem eight, then, by saying

that thirty-two of 108 graduate schools, or 29.5 per cent,

offered degrees which they considered to be doctoral degrees

in mathematics and education designed for the specific pur-

pose of preparing teachers of college mathematics. These

thirty-two schools offered a total of thirty-eight degrees.

It was considered desirable to know how many graduates

of the programs for special doctorates had been produced and

106

how many of these graduates wei-e engaged in teaching mathema-

tics. The data relevant to the first of these two questions

are summarized in Table XXXV. Entries are in numbers of

graduates reported. The thirty-two schools offering the

TABLE XXXV

NUMBER OF GRADUATES OF SPECIAL DOCTORAL PROGRAMS IN THE PAST TEN YEARS

Degree Number of

Graduates

Ph. D., math, ed 82

Ed. D., math. ed. 104

Other doctoral degrees 15

Total 201

special doctorates reported a total of 201 graduates of such

programs over a ten-year period. Actually, these 201 gradu-

ates were reported by sixteen out of the thirty-two schools.

Table XXXVI gives the distribution of these sixteen schools

as to the percentage of graduates of special doctoral pro-

grams estimated to be engaged in teaching of mathematics.

Entries are in number of schools in each category as to per-

centage of graduates engaged in teaching. Eleven schools,

or 68.7 per cent, estimated that over 90 per cent of all

graduates of special doctoral programs were engaged in teach-

ing college mathematics.

107

TABLE XXXVI

DISTRIBUTION OF GRADUATE SCHOOLS AS TO PERCENTAGE OF GRADUATES OF SPECIAL DOCTORAL PROGRAMS

ENGAGED IN TEACHING

Percentage Number of Schools

Under 25 per cent 1 26 per cent- to 50 per cent 1 51 per cent to 70 per cent 2 71 per cent to 80 per cent . . . . . . . . . . . . 0 81 per cent to 90 per cent 1 Over 90 per cent 11

Total responding 16

Attitude of graduate schools as to future offerings of

doctoral degrees in mathematics and education.--Sub-problem

number nine was to determine the willingness of graduate

schools to initiate such degree programs. The data relevant

to this sub-problem are found in Tables XXXVII and XXXVIII.

Table XXXVII contains the data concerning those schools which

had definite plans for offering special doctorates in mathe-

matics and education. Entries are in percentages of the total

TABLE XXXVII

PERCENTAGE OF GRADUATE SCHOOLS PLANNING TO OFFER SPECIAL DOCTORATES

Response Percentage

Yes 11.8 No 67.1 No opinion . . . . . 21.1

Total responding . . . . . . . . 76

108

number responding. Thus, 11.8 per cent of the seventy-six

schools which reported that no special doctorates were

offered, or nine schools, reported that they planned to offer

such doctorates in the future. Graduate school officials

were asked, "if you have no plans for the offering of special

doctorates in mathematics and education, would your school

consider such offerings if a demand should develop for these

degrees on the part of the colleges?" Table XXXVIII contains

the data derived from this question. Entries are in percent-

ages of the total responding. Of the sixty-seven schools

TABLE XXXVIII

PERCENTAGE OF GRADUATE SCHOOLS WHICH WOULD CONSIDER OFFERING SPECIAL DOCTORATES IF A DEMAND

SHOULD DEVELOP

Response Percentage

Yes 53.7 No 20.9 No opinion 15.4

Total responding . . . . . . . 67

which did not report that they planned to offer special doc-

torates, as shown in Table XXXVII, 53.7 per cent, or thirty-

six schools, reported that they would consider initiating

such degree programs if a demand for them on the part of

the junior and senior colleges should become evident. Thus,

the findings showed that of the seventy-six schools which

109

did not offer special doctorates in mathematics and education,

nine had definite plans for offering such degrees in the fu-

ture, and an additional thirty-six schools would consider such

offerings if a demand for them should become evident.

Attitude of graduate schools toward special doctorates.--

Sub-problem number ten was to determine whether the tradi-

tional Ph. D. is the only terminal degree acceptable to

departments of mathematics in Ph. D.-granting universities

and colleges. Graduate school officials were asked three

questions bearing directly on this sub-problem. The first

question asked in this connection was, "in your opinion,

would the Ph. D. and the Ed. D. in mathematics and education

constitute adequate preparation for some positions on the

staff of a university which confers the Ph. D. in mathema-

tics?" The data derived from the responses to this question

are tabulated in Table XXXIX. Entries are in percentages of

the total responding. Seventy-two per cent of all graduate

school officials checked yes in response to this question.

The responses from officials of schools which offered a

professional doctorate indicated a higher percentage of

affirmative response than did those of officials of schools

not offering such degrees.

110

TABLE XXXIX

PERCENTAGE OF GRADUATE OFFICIALS CONSIDERING PROFESSIONAL DOCTORATES TO EE ADEQUATE PREPARATION FOR

STAFF OF PH. D. GRANTING SCHOOL

Are Professional Schools Offering Other Doctorates Special Doctorates Graduate Total adequate? for Teachers Schools

% % %

Yes 84.4 67.1 72.2 No 12.5 22.4 19.4 No opinion 3.1 10.5 8.4

Total responding 32 76 108

Graduate officials were also asked to check each of

seven types of positions which they thought could be satis-

factorily filled by teachers holding professional doctorates

in mathematics and education. Responses to this question

are summarized in Table XL. The only positions out of the

seven which were checked by fewer than fifty per cent of

those responding were graduate courses in the teaching of

mathematics and direction of research in the teaching of

mathematics. The first was checked by 41.7 per cent of all

graduate school officials and by 34.2 per cent of graduate

officials of schools which did not offer a professional

doctorate. The second, direction of i-esearch in the teaching

Ill

TABLE XL

PERCENTAGE DISTRIBUTION OF OPINIONS OF GRADUATE OFFICIALS AS TO TYPES OF POSITIONS FOR WHICH PROFESSIONAL

DOCTORATES ARE ADEQUATE PREPARATION

Schools Offering Other Position Special Doctorates Graduate Total

for Teachers Schools % % %

Teacher of undergraduate mathematics 65.3 52.6 56.5

Teacher of mathematics courses for teachers 90.6 64.5 72.2

Teacher of math, or methods courses in school of ed. 78.1 57.9 63.9

Teacher of methods courses offered by math. dept. 78.1 52.6 60.2

Graduate courses in teaching of math. 59.4 34.2 41.7

Direction of research in teaching of math. 68.8 38.2 47.2

Direction of teacher v

preparation in math. 81.3 55.3 62.9 Total responding 32 76 108

of mathematics, was checked by 47.2 per cent of all graduate

school officials and 38.2 per cent of graduate officials of

schools which did not offer a professional doctorate. This

response possibly arose from a feeling that the type of

work involved here required more of a background in education

than envisioned in the programs for the professional doctor-

ates in mathematics and education.

112

The final question asked in this immediate connection

was "do you at present have on your staff a member with a

doctorate similar to the Ph. D., math, ed., or the Ed. D.,

math. ed.?n Responses to this question are summarized in

Table XLI. Entries are in percentages of the total number

TABLE XLI

PERCENTAGE OF GRADUATE SCHOOLS HAVING STAFF MEMBERS WITH PROFESSIONAL DOCTORATES

Does your School Have Schools Offering Other a Staff Member with a Special Doctorates Graduate Total Professional Doctorate? for Teachers Schools

7o % % Yes 62,5 18.5 31.5 No 37.5 81.6 68.5

Total responding 32 76 108

responding. Of the total of 108 respondents, thirty-four or

31,5 per cent checked yes. Again, as might have been expected,

those graduate schools which offered professional doctorates

reported staff members with professional doctorates in a

higher percentage of the cases than did the other graduate

schools. The percentage for these schools was 62.5 per cent

as against 1.8.5 per cent for graduate schools which offered

no professional doctorate.

It seemed reasonable to answer sub-problem number ten

by saying that, in the opinion of a considerable majority of

113

all graduate school officials, the traditional Ph. D„ was

not the only terminal degree acceptable to departments of

mathematics of Ph. D.-granting universities and colleges *

Further, almost a third of all graduate schools were using

such staff members at the time of the study. The actual

percentage was 31.5 as compared with 27.3 per cent of all

senior colleges in the national sample and 15.4 per cent of

all senior colleges in the Texas sample which reported such

staff members.

Two other questions dealt with the attitude of graduate

school officials toward the professional doctorates as prep-

aration for teaching undergraduate mathematics. The officials

of graduate schools were asked to check the one statement of

three given statements which best described their feelings

as to the status of doctoral degrees in mathematics and edu-

cation as preparation for teachers of undergraduate mathema-

tics. The data derived from the responses to this question

are tabulated in Table XLII. Entries are in percentage of

the total number responding. A majority of all graduate

school officials in both types of graduate schools checked

one of the last two statements indicating a feeling that the

professional doctorates should be offered.

114

TABLE XLII

PERCENTAGE DISTRIBUTION OF ATTITUDES OF GRADUATE SCHOOL OFFICIALS TOWARD PROFESSIONAL DOCTORATES

Schools Other Statement Offering Graduate Total

Special Schools Doctorates

% % % The research Ph.D. should be

the only degree for training teachers of college math. 9.4 41.2 31.0

The present situation makes it desirable that professional doctorates be offered. 62.5 39.7 47.0

The offering of professional doctorates is justified by the need for people prepared for teaching as well as in subject matter. 28.1 19.1 22.0

Total responding 32 68 100

Graduate school officials were also asked to rank the

Ph. D., math, ed., and the Ed. D., math. ed., in order of pref-

erence if such degrees were to be offered. The rankings for

the Ph. D., math, ed., are given in Table XLIII. This, in

effect, also gives the rankings for the Ed. D., math, ed.,

since a second place for the Ph. D. was equivalent to a

first place for the Ed. D., math. ed. Entries are in percent'

ages of the total number responding. Of all graduate school

officials, 72.8 per cent ranked the Ph. D., math, ed., first

and 27.2 per cent ranked it second. In view of the prestige

which adheres to the Ph. D., it was probably surprising that

27 per cent ranked the Ed. D. in first place.

TABLE XLIII

PERCENTAGE DISTRICUTION OF RANK ASSIGNED THE PH. D., MATH. ED. BY GRADUATE SCHOOL OFFICIALS

115

Schools Other Rank Assigned Ph.D., Offering Graduate Total

Math. Ed. Special Doctorates

Schools

% % °L

1 74.1 70.9 71.9 2 25.9 29.1 28.1

Total responding 27 55 82

It could be concluded, then, that a majority of graduate

school officials felt that the professional doctorates were

acceptable for certain positions on the staff of a Ph. D.-

granting institution. Also, a majority of officials felt

that the situation existing in mathematics education was such

as to make it desirable for the degrees to be offered. Of

the two,degree titles used in the study, the Ph. D., math,

ed., was preferred about three to one over the Ed. D., math.,

ed.

Analysis of Returns to Questionnaire Number Five

Sub-problem number eleven was to determine the compo-

sition of current doctoral programs designed specifically for

preparing college teachers of mathematics. Questionnaire

number five was designed to provide data concerning this sub-

problem. As outlined in Chapter II, the degree programs

116

offered by twenty-seven graduate schools were judged, on the

basis of the information available, to be degree programs of

the type with which this studjy was concerned. A list of these

schools together with the titles of the professional doctor-

ates in mathematics and educajtion offered by each school is |

found in the Appendix. The twenty-seven schools offered a i !

total of eighteen Ph. D. degrees in mathematics education and

a total of twenty Ed. D. degrees in mathematics education. j

!

Prerequisites for the decree programs.--The data con-

cerning prerequisites for entrance to programs for the Ph.

D., math. ed., and the Ed. D., math. ed., are summarized in j

Table XLIV. A bachelor's degree of some type is, of course,

assumed. Entries are in term^ of the number of degree pro-

grams reporting each specific jprerequisite in mathematics !

and education. Since the study was concerned with the degree

programs as consisting of all work above the bachelor's level, |

|

the requirement of a master's idegree as a prerequisite may

be translated into terms of anj undergraduate major followed

by a master's degree, as part pf the over-all graduate pro-

gram for the degree. Thus, this x'equirement is essentially

the same as that of an undergrkduate major in mathematics.

Since only one school required fewer than thirty semester

hours of mathematics and one other required thirty, it seemed

117

reasonable to conclude that the customary prerequisite in

mathematics for the Ph. D., math. ed., was an undergraduate

major in mathematics consisting of thirty or more semester

hours. Since fifteen .out of twenty programs required thirty

or more semester hours of mathematics as a prerequisite, the

mathematics prerequisites for the Ed. D., math, ed., were

set at an undergraduate major in mathematics.

TABLE XLIV

NUMBER OF PROGRAMS FOR PROFESSIONAL DOCTORATES IN VARIOUS CATEGORIES AS TO PREREQUISITES IN

MATHEMATICS AND EDUCATION

Prerequisites Number of

" 11 i Number of ; Prerequisites Ph.D. Programs Ed.D. Programs

Mathematics: 1 Undergraduate major 7 1

8 Master's degree 6 6 ; 15-20 semester hours 1 * • 1 20 semester hours • « 1 30 semester hours 1 1 36 semester hours 1 • «

40 semester hours 1 • •

Unspecified 1 4 Education:

8 semester hours • • 1 12 semester hours 1 1 15-20 semester hours 1 i 18 semester hotirs 1 1 20 semester hours 1 • •

30 semester hours « • 2 Minor 1 • •

Unspecified 13 15 Total number of degree programs 18 20

118

Only five programs specified prerequisites in education

for either the Ph. D., math. ed., or the Ed. D., math. ed.

Thus, it seemed reasonable to conclude that, in general, no

specific requirement was made in education for entrance to

the program for either doctoral degree. In the five cases

where such a prerequisite was given, the median was eighteen

semester hours of education.

Mathematics requirements for the Ph. D., math, ed., and

the Ed. D., math, ed.--The requirements in mathematics for

the two doctoral degrees are summarized in Tables XLV and

XLVI. Entries to Table XLV are in terms of the number of

degree programs, for each degree, specifying each number of

semester hours of mathematics. Table XLVI is a summary of

Table XLV in terms of averages. The data were more meaning-

ful when looked at in this manner. The requirements in

mathematics, in semester hours, for the Ph. D., math. ed.,

ranged from a low of twenty-six semester hours to a high of

sixty semester hours. The distribution was bi-modal with a

mode at forty hours and one at sixty hours. The mean number

of hours required was 44.8 and the median was forty-eight

semester hours. The requirements in mathematics, in semester

hours, for the Ed. D., math. ed., ranged from a low of twenty-

four semester hours to a high of seventy-five hours. There

119

TABLE XLV

NUMBER OF PROGRAMS FOR PROFESSIONAL DOCTORATES IN VARIOUS CATEGORIES AS TO MATHEMATICS REQUIREMENTS

Semester Hours of Number of Number of Mathematics Ph.D. Pi~ograrns Ed.D. Programs

24 • • 1 26 1 • •

24-32 • • • •

30 2 1 27-42. « * 1 36 * « 2 40 3 3 45 • • 2 48 2 « *

48-60 • * 1 50 2 • •

55 1 • •

60 3 3 70 • • 1 75 • « 1 Unspecified 4 4

Total, number of programs 18 20

TABLE XLI

AVERAGE MATHEMATICS REQUIREMENTS FOR THE DEGREES IN SEMESTER HOURS

Type of Average Ph.D.,Math.Ed. Ed.D.,Math.Ed. Low 26 24 Mean 44.8 46.7 Median 48 40 Mode 40 and 60 40 and 60 High 60 75

were two modes which were, again, forty hours and sixty hours.

The mean was 46.7 hours and the median forty hours. Thus,

it seemed reasonable to conclude that the average requirements

120

in mathematics for the Ph. D. , math. eel., were from forty-five

to forty-eight semester hours, The average requirements in

mathematics for the Ed. D., math, ed., were from forty to

forty-seven hours.

Requirements in education for the Ph. D., math, ed.,

and the Ed. P., math, ed.--The requirements in education, in

semester hours, for the two professional doctorates are sum-

marized in Tables XLVII and XLVIII. Entries to Table XLVII

TABLE XLVII

NUMBER OF PROGRAMS FOR PROFESSIONAL DOCTORATES IN VARIOUS CATEGORIES AS TO EDUCATION REQUIREMENTS

Semester Hours of Number of Number of Education Ph.D. Programs -Ed.D. Programs

6 • « 1 8 2 1 9 2 • •

10 • • 1 12 • a 1 15 • • 3 18 1 1 20 • • 2 21 1 • •

24 2 2 20-35 1 « •

30 1 1 35 2 1 30-40 1 « •

28-42 • * 1 36 1 1 42 • * 1 40-48 • • 1 Unspecified 4 3

Total number of programs 18 20

121

are again in numbers of degree programs specifying each num-

ber of. semester hours. Table XLVIII is a summary of the data

in Table XLVII in terms of averages. The requirements in

education for the Ph. D., math, ed., ranged from a low of eight

semester hours to a high of thirty-six hours. The mean was

19.9 semester hours and the median was twenty-four semester

hours. The requirements in education for the Ed. D., math,

ed., ranged from a low of six semester hours to a high of

forty-eight semester hours. The mode was fifteen semester

hours, the mean 22.8 hours, and the median eighteen hours.

Thus, on the average, it was concluded that the requirements

in education for both degrees lay between eighteen and twenty-

four semester hours.

TABLE XLVIII

AVERAGE EDUCATION REQUIREMENTS FOR THE DEGREES IN SEMESTER HOURS

Type of Average Ph.D.,Math.Ed. Ed.D.,Math.Ed. Low 8 6 Mean 19.9 22.8 Median 24 18 Mode • • • 15 High 36 48

Credit allowed for dissertation for the Ph. D., math,

ed., and the Ed. D., math. ed„~~The data regarding the number

of semester hours credit, allowed for the dissertation in the

122

programs for the two doctoral degrees are found in Table XLIX.

Entries are in terms of the number of degree programs for each

degree falling into each category. Again, Table L is a sum-

mary of the data in Table XLIX in terms of averages. For the

TABLE XLIX

NUMBER OF PROGRAMS FOR PROFESSIONAL DOCTORATES IN VARIOUS CATEGORIES AS TO CREDIT ALLOWED FOR DISSERTATION

Number of Number of Semester Hours Credit Ph.D. Programs Ed.D. Programs

6 1 • •

9 1 • *

10 1 2 12 1 1 15 1 1 12-24 1 1 18-24 • • 1 15-25 1 • •

30 1 2 Unspecified 10 12

Total number of programs 18 To i

Ph. D., math. eds, credit for the dissertation ranged from a

low of nine semester hours to a high of thirty semester hours.

There was no mode. The mean was fifteen semester hours and

the median was 13.5 semester hours. For the Ed. D., math,

ed., credit for the dissertation ranged from a low of ten

semester hours to a high of thirty semester hours. There

were two modes at ten hours and thirty hours. The mean was

18.2 semester hours and the median was 16.5 hours. Thus, the

123

credit for the dissertation for both degrees lay between

twelve and eighteen hours.

TABLE L

AVERAGE CREDIT, IN SEMESTER HOURS, FOR DISSERTATION

Type of Average Ph.D., Math.Ed. Ed.D., Math.Ed. Low 9 10 Mean 15 18.2 Median 13.5 16.5 Mode • • 10 and 30 High 30 30

Total requirements for the Ph. D., math, ed., and the

Ed. P., math, ed., in semester hours.--The data concerning the

total requirements for the two doctoral degrees are tabulated

in Table LI. Entries are in terms of the number of degree

TABLE LI

NUMBER OF PROGRAMS FOR PROFESSIONAL DOCTORATES IN VARIOUS CATEGORIES AS TO TOTAL CREDIT REQUIRED

Semester Hours Number of Number of Credit Required Ph.D. Programs Ed.D. Programs

60 • • 1 70 1 • •

72 2 3 75 1 • •

84 • 9 1 90 1 9 85-97 • • 1 99 1 • •

Unspecified 6 5 Total number of programs 18 20

124

programs which fell into each category. Table LII is a sum-

mary of the data in Table LI in terms of averages. For the

Ph. D., math, ed., total requirements ranged from a low of

seventy semester hours beyond the bachelor's degree hours

to a high of ninety-nine hours. Those for the Ed. D., math,

ed., ranged from sixty semester hours beyond the bachelor's

degree to ninety-seven hours. From the averages, it seemed

reasonable to conclude that the most frequent requirement

for the total number of semester hours required for both

degrees was ninety semester hours beyond the bachelor's degree.

TABLE LII

AVERAGE TOTAL REQUIREMENTS FOR THE DEGREES

Type of Average Ph.D., Math.Ed. Ed.D., Math,Ed. Low 70 60 Mean 87.4 80.4 Median 90 90 Mode 90 90 High 99 97

Mathematics courses required for the Ph. D., math, ed.,

and the Ed. D., math, ed.--The data concerning specific

courses in mathematics, beyond the bachelor's degree, which

are required for the Ph. D., math, ed., are summarized in

Table LIII. Entries to the tables are given in terms of the

number of schools reporting and the modal number of hours

reported for each course. The six courses most often mentioned

125

TABLE LIII

MATHEMATICS COURSES REQUIRED FOR THE PH. D. , MATH. ED. ' ARRANGED IN ORDER OF FREQUENCY OF MENTION

Modal Number Title of Number of Degree of Semester Course Programs Reporting Hours Required

Abstract Algebra 6 3-6 Statistics 6 3 Geometry 5 3 Analysis 4 6 Topology 4 3 Linear Algebra 3 3 Advanced Calculus 2 6 Numerical Analysis 2 3 Logic 1 3 Applied Mathematics 1 12 Functional Analysis ]. 3 Seminar 1 2 Readings in Masterworks 1 6 Unspecified 7

Total responding 18

for the Ph. D., math, ed., with the number of semester hours

most frequently mentioned as required, were as follows:

Abstract Algebra, three to six; Statistics, three; Geometry,

three; Analysis, six; Topology, three; and Linear Algebra,

three.

The data concerning specific courses in mathematics,

beyond the bachelor's degree, required for the Ed. D., math,

ed., are summarized in Table LIV. The six courses most com-

monly mentioned for the Ed. D., math, ed., with the modal

numbers of semester hours for each, were Topology, three;

126

TABLE LIV

MATHEMATICS COURSES REQUIRED FOR THE ED. D., MATH. ED, ARRANGED IN ORDER OF FREQUENCY OF MENTION

Modal Number Title of Course Number of Degree of Semester

Programs Reporting Hours Required Topology 6 3 Abstract Algebra 6 6 Geometry 6 3 Statistics 5 3 Analysis 3 12 ! Foundations 3 3 ! Probability 3 3 Logic 2 3 Linear Algebra 2 3 Advanced Calculus 2 6 | Applied Mathematics 2 6 Numerical Analysis 2 9 Number Systems 1 6

|

Functional Analysis 1 3 Unspecified 10

Total responding 20

Abstract Algebra, six; Geometry, three; Statistics, three;

Analysis, twelve; and Foundations, three. A seventh course

might be added to the list of courses most commonly men-

tioned for the Ed. D., math. ed. Probability received the

same number of mentions as Foundations of Mathematics.

Education courses required for the Ph. D., math, ed., and

the Ed. D., math-, ed. - -The data concerning specific courses

in education, beyond the bachelor's degree required for the

Ph. D., math, ed., are summarized in Table LV. Entries are

127

TABLE LV

EDUCATION COURSES REQUIRED FOR THE PH. D., MATH. ED., ARRANGED IN ORDER OF FREQUENCY OF MENTION

Title of Course Number of Degree

Programs Reporting

Modal Number of Semester

Hours Required

Mathematics Education Educational Psychology Methods of Research Tests and Measurements Statistics Philosophy of Education Curriculum Higher Education Secondary Education History of Education Theory of Learning Education and Government Advanced Psychology Elementary Methods History of American Ed. Seminar Social Foundations of Ed. History & Philosophy of

Education Unspecified

Total responding

3 3 3 3 6 3 3 3 3 3 3 3 3 3 3 3 6

given in terms of the number of schools reporting each

course and the modal number of semester hours reported for

each course. Twelve schools listed specific requirements in

education for the Ph. D., math. ed. The. seven courses which

were mentioned the greatest number of times together with

the modal number of hours for each were Mathematics

128

Education, three; Educational Psychology, thiee; Methods of

Research, three; Tests and Measurements, three; Statistics,

six; Philosophy of Education, three; and Curriculum, three.

The data concerning specific courses required for the Ed. D.,

math. ed., beyond the bachelor's degree, are summarized in

Table LVI. Fifteen schools listed specific requirements in

TABLE LVI

EDUCATION COURSES REQUIRED FOR THE ED. D., MATH. ED., ARRANGED IN ORDER OF FREQUENCY OF MENTION

Title of Course Number of Degree Programs Reporting

Modal Number of Semester

Hours Required Mathematics Education Methods of Research Higher Education Statistics Seminar Foundations of Education Philosophy of Education Curriculum Educational Psychology Theory of Learning History of Education Philosophy of American Education

Comparative Education History and Philosophy of Education

Improvement of College Teaching

Theory of Instruction Elementary Methods .Secondary Methods Tests and Measurements History of American Ed. Leadership in Education

5 4 4 4 4 3 3 3 3 2 1

1 1

1 1 1 1 1 1 1

15 3 3 3 3 3 3 3 6 3 3

3 3

3 3 3 3 3 3 3

129

TABLE LVI--Continued

Title of Course Number of Degree Programs Reporting

Modal Number of Semester

Hours Required Sociological and Aesthe-tic Foundations of Education

Unspecified Total responding

1 5

3

Sociological and Aesthe-tic Foundations of Education

Unspecified Total responding 20

3

education for the Ed. D., math. ed. The nine courses which

were mentioned the greatest number of times for the Ed. D.,

math, ed., together with the modal number of semester hours

required for each, were Mathematics Education, fifteen;

Methods of Research, three; Higher Education, three; Statis-

tics, three; Seminar, three; Foundations of Education, three;

Philosophy of Education, three; Curriculum, three; and Educa-

tional Psychology, six.

Types of dissertation regarded as acceptable for the

Ph. D., math, ed., and the Ed. D., math, ed.--The data regard-

ing the type of dissertation accepted for the two doctoral

degrees are found in Table LVII. Entries are in terms of the

percentages of degree programs for which certain types of

dissertations were checked as acceptable. Since most schools

checked several types for each degree program and a few

schools checked all types listed, there is an overlap. Since

130

this table seems to be self-explanatory the data are not re-

peated.

TABLE LVII

PERCENTAGE OF DEGREE PROGRAMS FOR WHICH VARIOUS TYPES OF DISSERTATION WERE APPROVED

Type of Dissertation Ph.D.,Math.Ed. Ed.D.,Math.Ed.

% %

Research in mathematics 33.3 45.0 Research in the teaching

of mathematics 66.7 65.0 Statistical 50.0 60.0 Historical 44.4 70.0 Critical or Expository 44«4 65.0 Other • • • •

Total responding

Examinations required for the Ph. D., math, ed., and the

Ed. D., math, ed.--The data regarding examinations required

for the two doctoral degrees are found in Table LVIII. En-

tries are given in percentages of programs for which each

type of examination was reported as required. Of the eight-

een schools offering the Ph. D., math. ed., 61.1 per cent

required an entrance examination', 100 per cent required a

qualifying examination; and 100 per cent required a final

examination. Of the twenty schools offering the Ed. D.,

math, ed., 75 per cent required an entrance examination; 100

131

per cent required a qualifying examination; and 100 per cent

required a final examination.

TABLE LVIII

PERCENTAGE OF DEGREE PROGRAMS FOR WHICH VARIOUS TYPES OF EXAMINATIONS WERE REQUIRED

Type of Examination Ph.D.,Math.Ed. Ed.D.,Math.Ed.

% % Entrance examination 61.1 75.0 Qualifying examination 100.0 100.0 Final examination 100.0 100.0

Total responding 18 20

Foreign language requirements for the Ph. D., math, ed.,

and the Ed. D., math, ed.--The data concerning foreign lan-

guage requirements for the two doctoral programs are found

in Table LIX. Entries are in terms of the percentage of

programs for each degree, in each category, as to foreign

language requirements. For the Ph. D., math. ed., 88.9 per

cent of the total of eighteen schools required two languages,

while 11..1 per cent required one. For the Ed. D., math, ed.,

75 per cent of the total of twenty schools required no foreign

language; 5 per cent required two; and 20 per cent required

one. This was the most striking difference between the pro-

grams for the Ph. D., math, ed., and those for the Ed. D.,

math. ed.

132

. TABLE L1X

PERCENTAGE OF DEGREE PROGRAMS IN VARIOUS CATEGORIES AS TO REQUIREMENT OF FOREIGN LANGUAGES

Number of Languages Required Ph.D.,Math.Ed. Ed.D.,Math.Ed.

% %

One 11.1 20 Two 88.9 5 None • • 75

Total responding 18 20

Special knowledge or special skills required for the

Ph.D., math. edM and the Ed. D., math. ed.--The data concern-

ing requirement of special knowledge or skills for the two

doctoral programs are summarized in Table LX. Entries are

in percentage of degree programs in various categories as to

TABLE LX

PERCENTAGE OF DEGREE PROGRAMS REQUIRING SPECIAL KNOWLEDGE OR SKILLS

Special Knowledge or Skill Ph.D.,Math.Ed. Ed.D.,Math.Ed. % %

Statistics 27.8 50.0 Methods of Educational Research 44.4 50.0

Methods of Teaching College Mathematics 5.6 5.0

Higher Education 5.6 5.0 Total responding 18 20

133

requirement of each special knowledge or skill listed. Only

two of the special skills listed were required by any consid-

erable number of degree programs. Fifty per cent of the

programs for the Ed. D., math, ed., required both a knowledge

of statistics and of methods of educational research. Twenty-

seven and eight-tenths per cent of the programs for the Ph.

D., math, ed., required a knowledge of statistics, and 44.4

per cent of these programs required a knowledge of methods

of educational research. These special skills were to be

acquired by the taking of appropriate courses or, in some

cases, demonstrated by the passing of an examination.

The requirement of a practicuum and experience for the

Ph. P., math, ed., and the Ed. D., math, ed.--The data con-

cerning requirement of a practicuum and/or experience for the

two types of doctoral programs are tabulated in Table LXI.

The term practicuum meant the completion of some type of

special project or problem related to the teaching of mathe-

matics. The word experience was used to mean actual experi-

ence in teaching mathematics, either as a teacher in a college

or public school or as a graduate assistant. Entries to

Table LXI are in percentages of degree programs for the two

types of degrees requiring a practicuum or experience. Fifty

per cent or more of all degree programs required some type

134

TABLE LXI

PERCENTAGE OF DEGREE PROGRAMS REQUIRING A PRACTICUUM OR EXPERIENCE

Item Ph.D., Math.Ed. Ed.D., Math.Ed.

% % Practicuum 16.7 35.0 Experience 55.6 50.0

Total responding 18 2.0

of experience in teaching. Thirty-five per cent or less of

all programs required a practicuum.

The above data, derived from an analysis of questionnaire

number five, constitute an outline of the requirements for

the Ph. D., math, ed., and the Ed. D., math, ed., as they

existed at the time of the study. This outline when con-

sidered as a whole constituted an answer to sub-problem

number eleven by delineating the composition of current

doctoral programs designed specifically for preparing college

teachers of mathematics.

Analysis of Returns from Panel of Experts

Questionnaire number three was designed to determine the

attitude of the members of the panel specialists in mathema-

tics education toward the special doctoral programs for pre-

paring teachers of undergraduate mathematics. A second

135

purpose of the questionnaire was to secure an expression of

the views of the panel concerning desirable programs for such

degrees.

Prerequisites in Mathematics for Entrance to Special Doctoral Programs

Members of the panel were asked to choose among seven

statements of prerequisites in mathematics to be required

for entrance to programs leading to the professional doctor-

ates. The data derived from their answers are summarized in

Table LXII. Entries are in terms of the percentage of the

TABLE LXII

PERCENTAGE DISTRIBUTION OF OPINIONS OF PANEL AS TO PREREQUISITES IN MATHEMATICS

Prerequisite Percentage

Twelve semester hours beyond elementary calculus . . . 0 Eighteen semester hours beyond elementary calculus . . 0 Eighteen semester hours beyond elementary calculus

including advanced calculus and abstract algebra . . 10,3 Twenty-four semester hours beyond elementary

calculus . . . . . 24.1 Twenty-four semester hours beyond elementary

calculus including advanced calculus and abstract algebra 34.5

Thirty semester hours beyond elementary calculus . . . 0 Thirty semester hours beyond elementary calculus

including advanced calculus and abstract algebra . . 31.0 Total responding 29

panel members checking each statement of prerequisites.

Table LXIII is a summary of the responses to this question

136

in terms of averages. The data seemed to be more meaningful

when regarded in this manner. The lowest requirement check

was "eighteen semester hours beyond elementary calculus in-

cluding advanced calculus and abstract algebra." Both the

median and the mode were "twenty-four semester hours beyond

elementary calculus including advanced calculus and abstract

algebra." It was possible to compute an arithmetic mean in

terms of the number of semester hours beyond elementary

calculus as suggested by the panel. This mean was 25.24

semester hours.

TABLE LXIII

AVERAGE MINIMUM REQUIREMENTS IN MATHEMATICS FOR ENTRANCE TO DOCTORAL PROGRAMS

Average Requirement

Low Eighteen semester hours beyond elementary calculus including advanced calculus and abstract algebra

Median . . . . Twenty-four semester hours beyond ele-mentary calculus including advanced calculus and abstract algebra

Mode Same as median

High Thirty semester hours beyond elementary calculus including advanced calculus and abstract algebra

Mean . . . . .25.24 semester hours beyond elementary calculus

137

Requirements in Mathematics and Education for the Special Doctoral Degrees

Sub-problem number twelve was to determine what train-

ing in mathematics and education should be included in the

new programs. The answer to this sub-problem required a

consideration of the requirements in mathematics and educa-

tion, as suggested by the panel, in terms of the number of

semester hours of each and a consideration of specific

courses suggested in mathematics and education. The data

concerning the number of semester hours in mathematics and

education suggested by the panel are summarized in Tables

LXIV and LXV. It seemed more meaningful to express the re-

quirements in semester hours in terms of numbers of

specialists suggesting each number of semester hours in

mathematics and education than to use percentages. Thus the

entries to Table LXIV are in terms of the number of special-

ists checking each response. Then, in Table LXV, these same

data are expressed in terms of averages in'Table LXV. Entries

to Table LXV are in semester hours. These data seemed most

meaningful when regarded in the light of Table LXV. The

requirements in mathematics suggested by the panel ranged

from a low of thirty semester hours beyond the bachelor's

degree to a high of sixty-six hours. The median and the

mode were each sixty semester hours and the mean was 60.4

138

TABLE LXIV

NUMBER OF PANEL MEMBERS CHECKING VARIOUS REQUIREMENTS IN MATHEMATICS AND EDUCATION

Requirements in Semester Hours Mathematics Education

12 • • 9

18 • • 8

24 9 • 2

30 1 4

36 2 3

42 3 2

48 4 1

54 4 • •

60 9 • •

66 6 • •

Total responding 29 29

semester hours. The requirements in education ranged from

a low of twelve semester houi-s beyond the bachelor's degree

to a high of forty-eight semester hours. The median was

eighteen semester hours, the mode twelve semester hours, and

the mean 22.7 semester hours. Thus it seemed reasonable to

conclude that, in the opinion of the panel, the requirement

139

in mathematics should be about sixty semester hours and that

in education from twelve to twenty-four semester hours.

TABLE LXV

AVERAGE REQUIREMENTS IN MATHEMATICS AND EDUCATION, IN SEMESTER HOURS, AS SUGGESTED BY PANEL

Subject Low Mean Median Mode High

Mathematics 30 60.4 60 60 66

Education 12. 22.7 18 12 48

Required courses in mathematics suggested by the panel.

The courses in mathematics, beyond the bachelor's degree,

suggested by the panel as required courses for the profes-

sional doctorates are listed in Table LXVI. Entries are in

terms of the number of panel members mentioning each course

and the modal number of semester hours suggested for each

course. A total of seventeen different courses were men-

tioned. The eight courses which were most frequently men~

tioned, together with the modal number of hours suggested

for each, were Real Analysis, six; Topology, three to six;

Geometry, six; Abstract Algebra, six; Number Theory, three;

and History of Mathematics, three. Each of these courses

was mentioned by nineteen or more members of the panel.

140

TABLE LXVI

MATHEMATICS COURSES SUGGESTED BY THE PANEL FOR THE PROFESSIONAL DOCTORATES

Title Number of Panel Modal Number of of Members Men- Semester Hours

Course tioning Suggested

Real Analysis 29 6 Topology 27 3-6 Probability & Statistics 26 6 Complex Analysis 24 6 Geometry 24 6 Abstract Algebra 24 6 Number Theory 23 3 History of Mathematics 19 3 Logic 9 3 Foundations 7 3 Applied Mathematics 7 6 Numerical Analysis 5 3 Differential Equations 3 6 Vector Analysis 1 3 Theory of Equations 1 3 Graph Theory 1 3 Game Theory 1 3

Total responding 29

Required courses in education suggested by the panel.

The courses in education, beyond the bachelor's degree, sug-

gested by the panel as required courses for the professional,

doctorates,are listed in Table LXVII. Entries are in terms

of the number of panel members mentioning each course and

the modal number of semester hours suggested for each course,

A total of fifteen different courses was suggested. The

five courses which were most frequently mentioned, together

141

TABLE LXVII

EDUCATION COURSES SUGGESTED BY THE PANEL FOR THE PROFESSIONAL DOCTORATES

Title Number of Panel Modal Number of of Members Men- Semester Hours

Course tioning Suggested

Educational Psychology 20 3 Learning Theory 19 3 Curriculum and Method in Higher Education 15 3

Statistics 13 6 Improvement of College Teaching 13 3

Adolescent Psychology 8 3 Organization and Admin-istration of Higher Education 8 3

Mathematics Education 6 3 Human Growth and Develop-ment 6 3

Philosophy of Education 4 3 Curriculum Development 4 3 Research Methods 3 3-6 Personality Theory 3 3 History of Education 2 3 History and Development

of the American College 1 3-6 Sociology of Education 1 3 Guidance 1 3 Tests and Measurements 1 3

Total responding 29

with the modal number of semester hours suggested for each,

were Educational Psychology, three; Learning Theory, three;

Curriculum and Method in Higher Education, three; Statistics,

142

six; and Improvement of College Teaching, three. Each of

these courses was mentioned by thirteen or more members of

the panel.

It may be noted that there are two chief differences in

the course work suggested for the professional doctorates

and that commonly suggested for the traditional Ph. D. in

matViemati.es. The first is, of course, the inclusion of

course work in education. The second is that of a lesser

degree of specialization in mathematics. In general, there

would not be a great deal of difference between the fields

of mathematics suggested for the professional doctorates and

those which might be found in the program of a candidate for

the Ph. D. in mathematics. The candidate for the professional

doctorate would probably not take as intensive work in any one

branch of mathematics. The work in mathematics for the pro-

fessional doctorates is, in other words, somewhat broader and

less intensive than that for the traditional doctorate.

Special Requirements for the Professional Doctorates

Training in methods of mathematical research.--The mem-

bers of the panel were asked the question, "Do you think the

work in mathematics for these degrees should include some

training in methods of mathematical research through seminars

143

or courses providing for independent mathematical work?"

The data derived from the responses to this question are

summarized in Table LXVHI. Entries are percentages of the

total responding. Of the twenty-nine members of the panel

who returned the questionnaire, twenty-two, or 76.1 per cent,

answered yes to this question, six said no and one expressed

no opinion.

TABLE LXVIII

PERCENTAGE DISTRIBUTION OF OPINIONS OF PANEL AS TO TRAINING IN METHODS OF MATHEMATICAL RESEARCH

Response Percentage

Yes 76.1

No 20.6

No opinion 3.3

Total responding 29

Language requirements for the professional doctorates.--

The members of the panel were asked to state whether they

thought one foreign language, two foreign languages, or no

foreign language should be required for doctoral degrees of

the type under consideration. The data derived from the re-

sponses to this question are summarized in Table LXIX. Entries

are in percentages of the total responding. Eleven of the

panel members, or 37.9 per cent, said two foreign languages

144

TABLE LXIX

PERCENTAGE DISTRIBUTION OF OPINIONS OF PANEL AS TO FOREIGN LANGUAGE REQUIREMENTS

Languages Percentage Required Favoring

One 34.4

Two .37.9

None 10.5

No opinion 17.2

Total responding 29

should be required; ten, or 34.4 per cent, said one; arid the

remainder, 27.7 per cent, either said no foreign language

should be required or expressed no opinion.

Standards for Doctoral Programs in Mathematics

and Education

Sub-problem number thirteen was to suggest standards

for doctoral programs in mathematics and education designed

for preparation of college teachers of mathematics at the

undergraduate level. In the light of the data from question-

naire number five, which outlined the composition of current

doctoral programs, and from questionnaire number three which

outlined the opinions of the panel of experts, it was possi-

ble to draw some inferences concerning this sub-problem.

145

In the first place it should be kept in mind that it is

difficult to attempt to specify exact requirements for any

doctoral degree. These degrees would, as in the case of

other doctoral degrees, be based on demonstration of mastery

of a field or fields, the attainment of a certain level of

maturity in these fields, and the production of a credible

dissertation. The statement of suggested standards by

panel members or any conclusions drawn here should be re-

garded only as setting certain limits to the doctoral programs

under study.

It seemed reasonable to conclude, on the basis of the

above data, that programs for the professional doctorates

should involve graduate work amounting to the equivalent of

ninety semester hours of work at a true graduate level. The

principal difference between the two degrees, in practice,

seemed to be a difference in the foreign language requirements.

Since it was intended here to set rather broad limits to the

programs, the two degrees were treated in the same manner with

respect to other requirements.

It seemed reasonable to conclude that, for entrance to

the programs, a student should be expected to have the equi-

valent of an undergraduate major in mathematics with approxi-

mately twenty-four semester hours beyond elementary calculus.

146

This should include some introduction to abstract algebra

and six semester hours in advanced calculus or other courses

in analysis at the same level, or at a higher level.

Since the current programs had an average requirement

of approximately forty-five semester hours in mathematics and

the average requirement in mathematics suggested by the panel

members was sixty semester hours, it seemed reasonable to set

the lower limit on the amount of mathematics to be required

at forty-five semester hours. Similar reasoning gave a fig-

ure of approximately eighteen hours in education to be

required. Assuming a dissertation carrying twelve semester

hours credit, this left fifteen hours of electives. Con-

sidering that these degrees were being considered as prepara-

tion for college teaching of mathematics, it seemed advisable

to suggest that the candidate be encouraged to choose these

electives in mathematics.

The forty-five semester hours of required mathematics

should include at least those courses which are found both

in the list of courses most commonly found in current degree

programs and in the list of courses most frequently mentioned

by the panel. This would mean that the following should prob-

ably be included: Analysis, real and complex, twelve hours;

Abstract Algebra, six hours; Geometry, three to six hours;

Topology, three to six hours; and Probability and Statistics,

147

six hours. Since a considerable majority of all college

officials expressed the opinion that training in methods of

research in mathematics was necessary or desirable, there

should also be included three to six semester hours of

seminar or independent; work in mathematics designed to

develop this ability. The remainder of the forty-five semes-

ter hours, together with additional electives in mathematics,

could be chosen from these or other fields of mathematics.

In the case of the required courses in education, there

was not such a close correspondence between actual require-

ments in current degree programs and courses frequently men-

tioned by members of the panel. Two courses, which were

common to both lists of education courses, should probably

be included in the eighteen hours or required education

courses. These are Educational Psychology and Statistics.

Methods of Research should also be included because of its

relationship to the applications of statistics and because

it represents one of the special skills emphasized by current

programs. Three other courses frequently mentioned deserved

strong consideration as a part of the education requirements.

These were; Learning Theory, Curriculum and Method in Higher

Education, and Improvement of College Teaching. The last

two courses mentioned were included not only because of the

148

fact that they were stressed by members of the panel, biit,

also, because of the fact that a majority of college officials

felt that it was either necessary or desirable that some work

bearing on methods of instruction be included.

For the Ph. D., math, ed., one or two foreign languages

should probably be required. The Ed. D., math, ed., would

probably not require a foreign language unless the problem

selected for the dissertation required a knowledge of a

foreign language.

It seemed desirable to include in the program for either

degree a practicuum and/or actual experience in teaching.

Because of the feeling on the part of many college officials

that the best was to develop the ability to teach was through

supervised teaching as a graduate student, consideration

might well be given to permitting the candidate to substitiite

such experience for the practicuum or the teaching experience.

Type of Work for Which Members of the Panel Considered the Degrees to be Adequate Preparation

Members of the panel were asked to check all of a list

of seven types of positions for which they felt that the pro-

fessional doctorates to be adequate preparation. The data

derived from the responses to this question are summarized

in Table LXX. Entiries are in terms of the percentages check-

ing each position. Of the twenty-nine panel members, .

149

twenty-seven, or 93.4 per cent, checked "teacher of mathema-

tics, junior college." Twenty panel members, or 68.9 per

cent, checked "chairman, supervisor, or teacher in public

school" and "director of teacher training in mathematics;"

The percentages for the other five positions lay between these

two extremes.

TABLE LXX

PERCENTAGE DISTRIBUTION OF OPINIONS OF PANEL MEMBERS AS TO TYPES OF POSITIONS FOR WHICH PROFESSIONAL

DOCTORATES ARE ADEQUATE PREPARATION

Position Percentage

Teacher of mathematics, four year college 89.7

Teacher of mathematics, junior college . . . . . . . 93.4

Chairman, supervisor, or teacher in public school 68.9

Director of teacher training in mathematics 68.9

Teacher of special courses in mathematics for teachers . . . . . 86.2

Teacher of methods courses for public school mathematics teachers 75.9

Research in the teaching of mathematics 72.4

Total responding 29

Attitude of Panel Members toward Proposed Degree Programs

In question eight of questionnaire number three, members

of the panel were asked to express the degree of their approval

150

or disapproval of the offering of the Ph. D., math. ed.,and

the Ed. D., math, ed.? by checking one of five responses for

each degree. The five responses provided were agree

strongly, agree, no opinion, disagree, and disagree strongly.

The purpose of this question was two-fold: to determine the

attitude of the panel members toward the professional doctor-

ates, and to provide the necessary data for testing hypotheses

one through eight.

The data derived from the responses of the panel members

to this question are tabulated in Table LXXI. Entries are in

TABLE LXXI

PERCENTAGE DISTRIBUTION OF OPINIONS OF PANEL MEMBERS AS TO THE DESIRABILITY OF OFFERING SUCH DEGREES AS THE PH.D., MATH. ED. AND THE ED.D.,'MATH. ED.

Response Ph.D.,Math.Ed. Ed.D.,Math.Ed.

% % Agree 72.4 41.4 Agree strongly 20.6 44.8 No opinion 3.5 3.4 Disagree • • 10.4 Disagree strongly 3.5 • •

Total responding 29 29

percentage of the total responding who checked each possible

response. For the Ph. D., math, ed., twenty-one, or 72.4

per cent, checked "agree strongly"; and six, or 20.6 per cent

151

checked "agree". For the Ed. D., math, ed., twelve, or 41.4

per cent, checked "agree strongly"; and thirteen, or 44.8 per

cent, checked "agree". Thus, 92.4 per cent of the panel mem-

bers could be said to favor the offering of professional

doctorates such as the Ph. D., math, ed., and 86.2 per cent

could be said to favor the offering of degrees such as the

Ed. D., math, ed.

Testing of Hypotheses

In the final question of each of questionnaires number

one, two, and three, officials of colleges and specialists

in mathematics education were asked to select one of five

responses indicating agreement or disagreement with each of

two proposals for a new doctoral degree in mathematics and

education. The question,which was identical in all question-

naires, was as follows:

Taking into consideration the present situation in mathematics as you see it and considering the degrees as designed primarily for preparation of teachers of undergraduate mathematics in junior colleges and four year colleges, do you agree that it is desirable for such degrees as the Ph. D., math, ed., and the Ed. D., math, ed., to be offered?

The five possible responses were as follows:

Ph.D., math. ed.: Agree strongly Agree No opinion Disagree Disagree strongly

Ed.D., math. ed.: Agree strongly Agree No opinion Disagree Disagree strongly

152

In every case, the covering letter made plain that the

degrees to be considered were degrees such as those defined

in the description of the degrees which was enclosed with

each mailing. The following hypotheses were used to test

the distribution of responses of officials and specialists,

in various categories, to the above question for each of the

two degrees. The chi-square distribution was used to test

the hypotheses.

Four by five contingency tables would ordinarily have

been used for testing each of the hypotheses. However, be-

cause the theoretical frequency in one or more cells of each

table did not reach five, four by four contingency tables

were used. The observed frequencies for "disagree" and

"disagree strongly" were combined into a single category.

Because of the fact that theoretical frequencies in one or

more cells in each table still remained at five or less,

Yates' correction consists of increasing by .5 each observed

frequency that is less than expected and decreasing by .5

each observed frequency that is larger than expected.-*- Hypo-

theses were tested at the five per cent level of significance,

which required a chi-square of 16.919 for rejection. Entries

•'"Guilford, Fundamental Statistics in Psychology and Education.

153

to each of the sixteen four by four contingency tables were

in observed frequencies and expected frequencies. In each

cell the number representing the observed frequency is given

first. Immediately below it, in parentheses, is given the

number representing the expected frequency for that cell.

Hypothesis number one was that there is no difference in

the distribution of responses of specialists in mathematics

education, presidents, deans, and heads of departments of

mathematics in the national sample of junior colleges.

Table LXXII and Table LXXIII contain the data which were

used in computing chi-square for hypothesis number one.

Table LXXII was used to test this hypothesis for the Ph. D.,

math, ed., and Table LXXIII was used to test it for the Ed.

TABLE LXXII

CONTINGENCY TABLE FOR COMPUTATION OF CHI-SQUARE TO TEST HYPOTHESIS ONE FOR PH. D., MATH. ED.

Ph.D., Math.Ed. Heads Deans Pres. Panel Total

Agree strongly 37 22 20 21 100 (34.9) (29.7) (21.7) (13.7)

Agree 26 22 17 6 71 Agree (24.8) (21.1) (15.4) ( 9.7)

No opinion 5 10 4 1 20 ( 6.9) ( 5.9) ( 4.3) ( 2.7)

Disagree or dis-agree strongly 6 9 5 1 21

( 7.3) ( 6.3) ( 4.6) ( 1.4)

Total 74 63 46 29 212

Chi-square 10.067

154

D., math, ed., For Table LXXII, chi-square was 10.067, and

for Table LXXIII, it was 5.466, Thus, hypothesis number one

TABLE LXXIII

CONTINGENCY TABLE FOR COMPUTATION OF CHI-SQUARE TO TEST HYPOTHESIS ONE FOR ED. D., MATH. ED.

Ed. D., Math. Ed. Heads Deans Pres. Panel Total

Agree strongly 32 23 21 12 88 (30.7) (26.2) (19.1) (12)

Agree 27 20 20 13 80 (27.9) (23.8) (17.3) (10.9)

No opinion 7 8 2 1 18 ( 6.3) ( 5.4) ( 3.9) ( 2.5)

Disagree or dis-agree strongly 8 12 3 3 26

( 9 ) ( 7.7) ( 5.7) ( 3.6)

Total . 74 63 46 29 212

Chi-square 5 .466

was accepted for both degrees because the five per cent level

of significance was not reached. The non-significant chi-

squares meant that the distribution of responses for each

group did not differ with regard to their agreement as to the

desirability of offering each of the two professional doctor-

ates.

Hypothesis number two was There is no difference in

the distribution of responses of specialists in mathematics

education, presidents, deans, and heads of departments of

mathematics in the national sample of senior colleges.

155

Tables LXXIV and LXXV contain the data from which chi-

square was computed. Table LXXIV was used to test hypothesis

TABLE LXXIV

CONTINGENCY TABLE FOR COMPUTATION OF CHI-SQUARE TO TEST HYPOTHESIS TWO FOR THE PH. D., MATH. ED.

Ph.D., Math.Ed. Heads Deans Pres. Panel Total

Agree strongly 38 26 25 21 110 (40) (34.3) (13.8) (13.8)

Agree 28 32 6 6 79 (28.7) (24.6) ( 9.9) ( 9.9)

No opinion 10 6 1 1 21 ( 7.6) ( 6.5) ( 2.6) ( 2.6)

Disagree or dis-agree strongly 8 8 1 1

( 7.7) ( 6.5) ( 2.8) ( 2.8)

Total 84 72 46 29 231

Chi-square 9.802

number two for the Ph. D., math. ed.,and Table LXXV was

used to test it for the Ed. D., math. ed. For Table LXXIV,

chi-square was 9.802, and, for Table LXXV, it was 9.242.

Thus hypothesis number two was accepted for both degrees

because the five per cent level of significance was not.

reached. The non-significant chi-squares meant that the

distribution of responses for each group did not differ

with regard to their agreement as to the desirability of

offering each of the two professional doctorates.

156

TABLE LXXV

CONTINGENCY TABLE FOR COMPUTATION OF CHI-SQUARE TO TEST HYPOTHESIS TWO FOR THE ED. D., MATH. ED.

Ed. D., Math. Ed. Heads Deans Pres. Panel Total

Agree strongly 24 16 14 12 66 (24) (20.6) (13.1) ( 8.3)

Agree 28 34 19 13 94 Agree (34.2) (29.3) (18.7) (11.8)

No opinion 19 9 8 1 37 (13.5) (11.5) ( 7.6) ( 4.6)

Disagree or dis-agree strongly 13 " 13 5 3 28

(12.4) (10.6) ( 6.8) ( 4.3)

Total 84 72 46 29 231

Chi-square 9 .242

Hypothesis number three was that there is no difference

in the distribution of responses of specialists in mathematics

education, presidents, deans, and heads of departments of

mathematics in colleges in the national sample of senior

colleges which stress teacher education. Tables LXXVI and

LXXVII contain the data from which chi-square was computed.

Table LXXVI was used to test hypothesis number three for the

Ph. D., math, ed., and Table LXXVII was used to test it for

the Ed. D., math. ed. For Table LXXVI, chi-square was 7.090,

and, for Table LXXVII, it was 6.023. Thus, hypothesis number

three was accepted for both degrees because the five per cent

level of significance was not reached. The non-significant

157

TABLE LXXVI

CONTINGENCY TABLE FOR COMPUTATION OF CHI-SQUARE TO TEST HYPOTHESIS THREE FOR THE PH. D. , MATH. ED.

Ph. D., Math. Ed. 'Heads Deans Pres. Panel Total Agree strongly 20 11 13 21 65

(21.1) (14.5) (11.6) (16.2) Agree 9 11 5 6 31

(10.6) ( 6.9) ( 5.5) ( 8.2) No opinion 6 1 1 1 9

( 3.1) ( 2.0) ( 1.6) ( 2.3) Disagree or dis-agree strongly 2 1 1 1 7

( 2.5) ( 1.6) ( 1-2) ( 1.8) Total 38 25 ~~1 20 29 112

Chi-square 7 .090

chi-squares meant that the distribution of responses for each

group did not differ with regard to their agreement as to the

desirability of offering each of the two professional doctorates.

TABLE LXXVII

CONTINGENCY TABLE FOR COMPUTATION OF CHI-SQUARE TO TEST HYPOTHESIS THREE FOR THE ED. D., MATH. ED.

Ed. D., Math. Ed. Heads Deans Pres. Panel Total Agree strongly 13 6 9 12 40

(15.8) ( 8.2) ( 6.6) ( 9.5) Agree 18 13 8 13 52

(20.4) (10.7) ( 8.5) (12.4) No opinion 10 3 2 1 16

( 6.3) ( 3.3) ( 2.6) ( 3.8) Disagree or dis-agree strongly 7 3 1 3 14

( 5.5) ( 2.9) ( 2.3) ( 3.3) Total 38 25 20 29 112

Chi-square 6, .023

158

Hypothesis number four was that there was no difference

in the distribution of responses of specialists in mathema-

tics education, presidents, deans, and heads of departments

of mathematics in Texas junior colleges. Tables LXXVIII

and LXXIX contain the data from which chi-square was computed,

Table LXXVIII was used to test hypothesis number four for

TABLE LXXVIII

CONTINGENCY TABLE FOR COMPUTATION OF CHI-SQUARE TO TEST HYPOTHESIS FOUR FOR THE PH. D., MATH. ED.

Ph.D., Math. Ed. Heads Deans Pres. Panel Total

Agree strongly 16 19 9 21 65 (16.8) (19.6) (12.3) (16.2)

Agree 11 13 7 6 37 ( 9.6) (11.2) ( 7.0) ( 9.2)

No opinion 3 2 6 1 9 ( 2.3) ( 2.7) ( 1.7) \ 2.3)

Disagree or dis-agree strongly 0 1 0 1 5

( 1.3) ( 1.5) ( 1.0) ( 1.3)

Total 30 35 22 29 116

Chi-square 12.407

the Ph. D., math, ed., and Table LXXIX was used to test it

for the Ed. D., math. ed. For Table LXXVIII, chi-square was

12.407, and, for Table LXXIX, it was 5.932. Thus, hypothesis

number four was accepted for both degrees because the five

per cent level of significance was not reached. The non-

significant chi-squares meant that the distribution of

159

responses for each group did riot differ with.regard to their

agreement as to the desirability of offering each of the two

professional degrees.

TABLE LXXIX

CONTINGENCY TABLE FOR COMPUTATION OF CHI-SQUARE TO TEST HYPOTHESIS FOUR FOR THE ED. D., MATH. ED.

Ed.D., Math. Ed, Heads Deans Pres. Panel Total

Agree 11 14 8 12 45 Agree (11.6) (13.6) ( 8.6) (11.2)

Agree strongly 11 16 9 13 49 (12.7) (14.8) ( 9.3) (12.2)

No opinion 7 2 2 1 12 ( 3.1) ( 3.6) ( 2.8) ( 3.0)

Disagree or dis-agree strongly 1 3 3 3 10

( 2.6) ( 3.0) ( 1.9) ( 2.5)

Total 30 35 22 29 116

Chi-square 5.932

Hypothesis number five was: there is no difference in

the distribution of responses of specialists in mathematics

education, presidents, deans, and heads of departments of

mathematics in Texas senior colleges. Tables LXXX and LXXXI

contain the data from which chi-square was computed. Table

LXXX was used to test hypothesis number five for the Ph. D.,

math., ed., and Table LXXXI wasused to test it for the Ed. D.,

math. ed. For Table LXXX, chi-square was 12.609, and, for

160

TABLE LXXX

CONTINGENCY TABLE FOR COMPUTATION OF CHI-SQUARE TO TEST HYPOTHESIS FIVE FOR THE PH. D., MATH. ED.

Ph. D., Math. Ed. Heads Deans Pres. Panel Total

Agree 14 11 6 21 52 (16.4) (13.7) ( 8.7) (13.2)

Agree strongly 13 13 9 6 41 (12.9) (10.8) ( 6.8) (10.4)

No opinion 2 1 3 1 7 ( 2.2) ( 1.8) ( 1.2) ( 1.8)

Disagree or dis-agree strongly 7 5 1 1 14

( 4.5) ( 3.7) ( 2.3) ( 3.5)

Total 36 30 19 29 114

Chi-square 12 .609

Table LXXXI, it was 5.087. Thus, hypothesis number five

was accepted for both degrees because the five per cent level

TABLE LXXXI

CONTINGENCY TABLE FOR COMPUTATION OF CHI-SQUARE TO TEST HYPOTHESIS FIVE FOR THE ED. D., MATH. ED.

Ed.D.j Math.Ed. Heads Deans Pres. Panel Total Agree strongly 10 10 6 12 38

(12.0) (10.0) ( 6.3) ( 9.7) Agree 13 11 7 13 44

(13.9) (11.6) ( 7.3) (11.2) No opinion 3 2 4 1 10

( 3.2) ( 2.6) ( 1.7) ( 2.5) Disagree or dis-agree strongly 10 7 2 3 22

( 6.9) ( 5.7) ( 3.7) ( 5.6) Total 36 30 19 29 114

Chi-square 5, .087

161

of significance was not reached. The non-significant chi-

squares meant that the distribution of responses for each

group did not differ with regard to their agreement as to

the desirability of offering each of the two professional

degrees.

Hypothesis number six was that there is no difference in

the distribution of response of presidents in the national

samples of junior and senior colleges and of Texas junior

colleges and senior colleges. Tables LXXXII and LXXXIII

contain the data from which chi-square was computed. Table

LXXXII was used to test hypothesis number six for the Ph. D.,

TABLE LXXXII

CONTINGENCY TABLE FOR COMPUTATION OF CHI-SQUARE TO TEST HYPOTHESIS SIX FOR THE PH. D., MATH. ED.

Ph.D., Math.Ed. Sr.Col. Sr.Col. Jr.Col. Jr.Col. Opinions of National Texas National Texas Total Presidents Sample Sample Sample Sample

Agree strongly 25 6 20 9 60 (20.8) ( 8.6) (20.2) ( 9.9)

Agree 13 9 17 7 46 (15.9) ( 6.6) (15.9) ( 7.6)

No opinion 4 3 4 3 14 ( 4.8) ( 2.0) ( 4.8) ( 2.3)

Disagree or dis-agree strongly 4 1 5 3 13

( 4.5) ( 1.8) ( 4.5) ( 2.2)

Total 46 19 46 22 133

Chi-square 3.: 330

162

math, ed., and Table LXXXIII was used to test it for the Ed.

D., math. ed. For Table LXXXII, chi-square was 3.330, and,

for Table LXXXIII, it was 4.449. Thus, hypothesis number six

was accepted for both degrees because the five per cent level

of significance was not reached. The non-significant chi-

squares meant that the distribution of responses for each

group did not differ with regard to their agreement as to

the desirability of offering each of the two professional

degrees.

TABLE LXXXIII

CONTINGENCY TABLE FOR COMPUTATION OF CHI-SQUARE TO TEST HYPOTHESIS SIX FOR THE ED. D., MATH. ED.

Ed.D., Math.Ed. Sr.Col. Sr.Col. Jr.Col. Jr.Col. Opinions of National Texas National Texas Total Presidents Sample Sample Sample Sample

Agree strongly 14 6 21 8 49 (16.9) ( 7.0) (16.9) ( 8.1)

Agree 19 7 20 9 55 (19.0) ( 7.9) (19.0) ( 9.1)

No opinion 8 4 2 2 16 ( 5.6) ( 2.3) ( 5.5) ( 2.6)

Disagree or dis-agree strongly 5 2 3 3 13

( 4.5) ( 2.3) ( 4.5) ( 2.1)

Total 46 19 46 22 133

Chi-square 4 .449

Hypothesis number seven was that there is no difference

in the distribution of responses of deans in the national

163

samples of junior colleges and senior colleges and of Texas

junior colleges and senior colleges. Tables LXXXIV and LXXXV

contain the data from which chi-square was computed. Table

LXXXIV was used to test hypothesis number seven for the Ph.

D., math, ed., and Table LXXXV was used to test it for the Ed.

D., math. ed. For Table LXXXIV, chi-square was 9.708, and,

TABLE LXXXIV

CONTINGENCY TABLE FOR COMPUTATION OF CHI-SQUARE TO TEST HYPOTHESIS SEVEN FOR THE PH. D., MATH. ED.

Ph.D., Math.Ed. Sr.Col. Sr.Col. Jr.Col. Jr.Col. Opinions of National Texas National Texas Total Presidents Sample Sample Sample Sample

Agree strongly 26 11 22 19 78 (22.7) (11.7) (24,6) (13.6)

Agree 32 13 22 13 (29.2) (12.0) (25.2) (14.0)

No opinion 6 1 10 2 19 ( 7.6) ( 2.8) ( 6.0) ( 3.3)

Disagree or dis-agree strongly 8 5 9 1 23

(13.6) ( 3.5) ( 7.3) ( 4.0)

Total 72 30 63 35 200

for Table LXXXV, it was 6.666. Thus, hypothesis number seven

was accepted for both degrees because the five per cent level

of significance was not reached. The non-significant chi~

squares meant that the distribution of responses for each

group did not differ with regard to their agreement as to

the desirability of offering each of the two professional degrees.

164

TABLE LXXXV

CONTINGENCY TABLE FOR COMPUTATION OF CHI-SQUARE TO TEST HYPOTHESIS SEVEN FOR THE ED.D., MATH. ED.

Ed.D., Math.Ed. Sr.Col. Sr.Col. Jr.Col. Jr.Col, Opinions of National Texas National Texas Total

Deans Sample Sample Sample Sample

Agree strongly 16 10 23 14 63 (22.7) ( 9.4) (19.8) (ii.o)

Agree 34 11 20 16 81 Agree (29.1) (12.1) (2.5.5) (14.2)

No opinion 9 2 8 2 21 ( 7.6) ( 3.1) ( 6.6) ( 3.7)

Disagree or dis-agree strongly 13 7 12 3 35

(12.6) ( 5.2) (11.1) ( 6.1)

Total 72 30 63 35 200

Chi-square 6. 666

Hypothesis number eight was that there is no difference

in the distribution of responses of heads of departments of

mathematics in the national samples of junior colleges and

senior colleges and of Texas junior and senior colleges.

Tables LXXXVI and LXXXVII contain the data.from which chi-

square was computed. Table LXXXVI was used to test hypothesis

number eight for the Ph. D., math. ed., and Table LXXXVII was

used to test it for the Ed. D., math. ed. For Table LXXXVI,

chi-square was 6.629, and, for Table LXXXVII, it was 13.370.

Thus, hypothesis number eight was accepted for both degrees,

because the five per cent level of significance was not

165

TABLE LXXXVI

CONTINGENCY TABLE FOR COMPUTATION OF CHI-SQUARE TO TEST HYPOTHESIS EIGHT FOR THE PH. D., MATH. ED.

Ph. D., Math. Ed. Sr.Col. Sr.Col. Jr.Col. Jr.Col. Opinions of Heads National Texas National Texas Total of Departments Sample Sample Sample Sample

Agree strongly 38 14 37 16 105 (38.7) (16.6) (34.1) (13.8)

Agree 29 13 26 11 (29.2) (12.6) (24.8) (10.4)

No opinion 10 2 5 3 20 ( 7.5) ( 3.2) ( 6.7) ( 2.7)

Disagree or dis-agree strongly- 8 7 6 0 21

( 7,9) ( 3.3) ( 6.9) ( 2.8)

Total 84 36 74 30 224

Chi-square 6, .629

TABLE LXXXVII

CONTINGENCY TABLE FOR COMPUTATION OF CHI-SQUARE TO TEST HYPOTHESIS EIGHT FOR THE ED. D., MATH. ED.

Ed. D.j Math. Ed. Sr.Col. Sr.Col. Jr * Col. Jr.Col. Opinions of Heads National Texas National Texas Total of Departments Sample Sample Sample Sample

Agree strongly 24 10 32 11 77 (28.9) (12.4) (25.4) (10.3)

Agree 28 13 27 11 79 (29.7) (12.7) (26.0) (10.6)

No opinion 19 3 7 7 36 (13.5) ( 5.8) (11.9) ( 4.8)

Disagree or disagree strongly 13 10 8 1 32

(12.0) ( 5.1) (10.5) ( 4.3)

Total 84 36 74 30 224

166

reached. The non-significant chi-squares meant that the

distribution of responses for each group did not differ with

regard to their agreement as to the desirability of offering

each of the two professional degrees.

All eight hypotheses were accepted because the five per

cent level of significance was not reached. The non-signifi-

cant chi-squares meant that in every grouping of specialists

and college officials, for which the distribution of responses

were compared, the distribution of responses did not differ

with regard to their agreement as to the desirability of

offering each of the professional degrees.

It was particularly noteworthy that the distribution of

responses of officials of Texas junior and senior colleges

did not differ significantly from the distribution of re-

sponses of officials of colleges in the national samples.

The heads of departments of mathematics in Texas senior

colleges constituted a sample which made up 92.3 per cent

of the total population of Texas senior college heads of

departments. The heads of departments of mathematics of

Texas junior.colleges constituted a sample which made up

71.4 per cent of the total population of Texas junior college

heads of departments. This could be regarded as increasing

the degree of confidence with which generalizations of

167

favorable opinions tox ard the new doctorates were made from

the samples to the population of colleges outside Texas.

Since the attitude of Texas heads of departments toward the

offering of the new doctorates was highly favorable, the

heads of departments of Texas colleges responding constituted

a large percentage of all such heads of departments, and

since no significant differences were found between these

groups and other groups, it seemed likely that the attitude

in the population of colleges outside Texas could also be

presumed to be quite favorable to the new degrees.

CHAPTER IV

SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS

Summary

The problem of the study was to analyze doctoral pro-

grams in mathematics and education for the preparation of

teachers of undergraduate mathematics. The purpose of the

study was to determine (1) the need for such programs,

(2) the attitude of college and university officials toward

them, (3) the composition of present offerings, and (4)

recommendations as to the future course their development

should take.

The nature of the problem required that data be col-

lected from officials of junior colleges and senior colleges,

from officials of graduate schools, and from a panel of

specialists in mathematics education. For the data from

officials of colleges, four samples were used. One sample

consisted of all the junior colleges in the state of Texas.

A second sample was made up of all senior colleges and

universities in the state of Texas except for Arlington

State College and for those colleges whose graduate catalog

showed that any type of doctoral degree was offered. Arling-

ton State College was not used in the sample because the

168

169

candidate was a member of the mathematics staff at this

school. The third list consisted of one hundred junior col-

leges outside the state of Texas, and the fourth consisted

of one hundred senior colleges outside the state of Texas.

The national samples were drawn from the list of junior

colleges published by the American Council on Education-'- and

from the list of senior colleges and universities published

O

by the same organization. All junior colleges on the list,

excluding those in Texas, were numbered consecutively. One

hundred junior colleges were then selected at random through

the use of a table of random digits. From the list of senior

colleges and universities, those which were shown to offer

any type of doctoral degree were first removed. The remain-

ing colleges, excluding those in Texas, were numbered conse-

cutively. One hundred senior colleges and universities were

then selected at random by use of a table of random digits.

The panel of specialists in mathematics education was

selected from three sources. The first source consisted of

present and past officers and directors of the National Council

of Teachers of Mathematics who were engaged in college teaching

^American Council on Education, American Junior Colleges, pp. 491-503.

O ''American Council on Education, American Universities

and Colleges, pp. 1283-1304.

170

of mathematics or in teacher preparation. The second con-

sisted of present and past members of the Committee on the

Undergraduate Program of the Mathematical Association of

America. A third list was compiled by searching the files

of the Mathematics Teacher and the American Mathematical

Monthly for the past ten years for names of frequent contri-

butors of articles on mathematics education. Since the names

on the third list also appeared on the first two lists, the

final list was, in effect, selected from the first two

sources. A list of forty-three specialists in mathematics

education was compiled from all sources. Those who responded

to the questionnaire mailed to them, were used as the panel

of specialists in mathematics education.

A list of graduate schools offering doctoral degrees

was compiled from the following sources: (1) the list of

colleges and universities published by the American Council

O

on Education, (2) the list of colleges and universities in

Lovejoy's College Guide,^ and (3) individual graduate catalogs.

A total of 139 graduate schools were identified as doctoral

institutions. From this list, North Texas State University

3 Ibid., pp. 1283-1304.

^Lovejoy, Love joy's College Guide.

171

was deleted because the candidate was a graduate student at

this school. The remaining list of 138 schools was used for

mailings to graduate school officials. A final list consisted

of graduate schools thought to offer professional doctorates

of the type under study. Of the 138 schools in the graduate

school sample, thirty-two reported the offering of such doc-

toral degrees. A list of nine additional schools was obtained

from the list given by Lindquist^ and from catalogs of indivi-

dual schools. North Texas State University was included in

this group of nine schools and information concerning the

program for the Ed. D. in College Teaching of Mathematics was

obtained from official publications of the graduate school.

This list of forty-one graduate schools constituted the sam-

ple used in securing data concerning the composition of

current programs for the professional doctorates.

Questionnaires were used to secure data from the various

sources. Questionnaires were sent to presidents, deans, and

heads of departments of mathematics of all colleges. A

questionnaire was sent to graduate deans and heads of depart-

ments of mathematics of the 138 graduate schools. A question-

naire went to members of the panel of specialists. Finally

a questionnaire was mailed to graduate deans, heads of

^Lindquist, Mathematics in Colleges and Universities p. 69.

172

departments of education, and heads of departments of the

forty-one graduate schools which offered a Ph, D., an Ed. D.,

or any other doctoral degree in mathematics and education

specifically for the purpose of preparing teachers of under-

graduate mathematics. The data from the questionnaires was

tabulated and presented in tables to be used as a basis for

drawing conclusions concerning the problem of the study.

Sub-problems

The primary problem of the study was sub-divided into

thirteen sub-problems. These sub-problems, together with a

summary of the findings or the conclusions reached in each

case, were as follows:

1. To determine the present composition of mathematics '

faculties of junior and senior colleges as to graduate train-

ing in mathematics.

For the total of 583 senior college staff members re-

ported, 16.6 per cent held the doctorate in mathematics; 4.6

per cent held doctorates with other majors; 64.3 per cent

held a master's degree in mathematics; and 10.3 per cent

held a bachelor's degree. Of the total of 345 junior college

staff members reported, .3 per cent held the doctorate in

mathematics; 2 per cent held a doctorate with other major;

70.1 per cent held a master's degree in mathematics; 21.4

173

per cent held a master's degree with other major; and 6.1

per cent held only a bachelor's degree. On the basis of

these findings, it seemed reasonable to conclude that, for

both junior and senior colleges, the percentage of teachers

with doctoral degrees was low. Also, approximately one-

fifth of all senior colleges mathematics teachers and approxi-

mately one-third of all junior college mathematics teachers

held no graduate, degree with a major in their teaching field

of mathematics.

2. To determine the capability of the present system

of doctoral education in mathematics to supply the needs of

junior and senior colleges.

The findings showed that the desire on the part of col-

lege officials for holders of the Ph. D. in mathematics and

their projected need for staff members with this degree ex-

ceeded the prospective supply by a wide margin. Over 75 per

cent of senior college beads of departments in all samples

reported both that they had experienced either great diffi-

culty or moderate difficulty in securing staff members at the

doctoral level and that they expected this difficulty to con-

tinue. The findings showed junior college officials to be

slightly less pessimistic but a majority of all such officials

had experienced difficulty and expected this difficulty to

continue. In addition, over 73 per cent of all officials

174

thought that the supply of Ph. D. ' s in mathematics was short

or would probably become short in the future. In the light

of these findings, it seemed reasonable- to conclude that

there was a doubt of the ability of the present system of

doctoral education in mathematics to supply the needs of

junior and senior colleges.

3* To determine the degree to which these colleges are

satisfied with current products of the traditional program

for the doctorate.

In all samples of junior and senior colleges, 100 per

cent of officials reported that their experience with current

products of the graduate schools as staff members had been

either highly satisfactory or moderately satisfactory with

regard to subject matter. In excess of 87 per cent of offi-

cials in all samples reported that current products of the

graduate schools had been either highly satisfactory or mod-

erately satisfactory with regard to ability to teach. In

the light of these findings, it seemed reasonable to con-

clude that officials of the colleges were, in general, very

well satisfied with current products of the traditional pro-

gram for the doctorate in mathematics.

4. To determine to what extent colleges are already

using people with training comparable to that proposed in the

new programs.

175

The findings showed that approximately 23.9 per cent of

senior colleges and approximately 8.8 per cent of junior

colleges were using people with degrees comparable to the

professional doctorates considered in the study.

5. To determine the type of work for which college

officials consider the proposed degrees to be appropriate

training.

It seemed reasonable to conclude that officials of junior

and senior colleges considered the proposed degrees to be ade-

quate preparation for the following types of positions:

teacher of mathematics in four-year college; teacher of mathe-

matics in junior college; chairman, supervisor, or teacher in

public schools; director of teacher preparation in mathematics;

teacher of special courses in mathematics for teachers; and

teacher of methods course for public school mathematics

teachers. For these six positions, the degree of approval

in the combined samples ranged from 67.4 per cent to 85.6 per

cent. Research in the teaching of mathematics could also have

been included in this list, since the degree of approval for

this type of work was 53.7 per cent.

6. To determine the attitude of presidents, deans, and.

heads of departments of mathematics in junior and senior col-

leges toward proposed doctoral programs designed primarily

for college teachers.

176

It seemed reasonable to conclude that the attitude of

presidents, deans, and heads of departments of mathematics

in junior and senior colleges toward the proposed doctoral

programs designed primarily for college teachers of mathema-

tics was quite favorable. For the Ph. D., math. ed., the

degree of approval ranged from a low of 75 per cent of heads

of departments in Texas senior colleges, who checked either

"agree strongly" or "agree" when asked to signify the degree

of their approval of the offering of such degrees, to a high

of 82.6 per cent of presidents of senior colleges in the

national sample. For the Ed. D., math, ed., the degree of

approval ranged from a low of 61.9 per cent of heads of de-

partments of mathematics in the national sample of senior

colleges to a high of 71,7 per cent for presidents in this

sample.

7. To determine to what extent the need of colleges for

teachers and their willingness to accept those trained under the

new programs justify intensifying the offering of such degrees.

It seemed reasonable to conclude that the need of the

colleges for teachers and their willingness to accept those

trained under the new programs justified intensifying the

offering of such degrees.

8. To determine the extent to which doctoral degrees

A R. .

177

college mathematics are now being offered by graduate

schools.

The findings showed that thirty-two of the 108 graduate

schools, or 29.5 per cent of all graduate schools responding,

offered degrees which they considered to be doctoral degrees

in mathematics and education designed for the specific purpose

of preparing teachers of college mathematics.

9. To determine the willingness of graduate schools to

initiate such degree programs.

The findings showed that, of the seventy-six graduate

schools which reported no special doctorates in mathematics

and education, nine had plans to initiate such offerings in

the future. Thirty-six additional schools reported that they

would consider offering such doctoral degrees if it should

become evident that there was a demand for holders of such

degrees on the part of the junior and senior colleges.

10. To determine whether the traditional Ph. D. is the

only terminal degree acceptable to departments of mathematics

in Ph. D. granting universities and colleges.

In the light of the data, it seemed reasonable to con-

clude that the traditional Ph. D. was not the only terminal

degree acceptable to departments of mathematics in the Ph.

D. granting universities and colleges. On the contrary, a

majority of graduate school officials felt that holders of

178

such degrees as the professional doctorates have a place on

the staff of Ph. D. granting institutions. Of all graduate

school officials who responded, 31.4 per cent reported staff

members holding such degrees, as compared to 23.9 per cent

of all senior colleges which had such staff members.

11. To determine the composition of current doctoral

programs designed specifically for preparing college teachers

of mathematics.

This sub-problem could be answered only by summarizing

briefly the findings concerning current degree programs.

The customary requirement for entrance to programs for either

the Ph. D., math, ed., or the Ed. D., math. ed., was the

equivalent of an undergraduate major in mathematics.

Average requirements in mathematics for the Ph. D.,

math. ed., were from forty-five to forty-eight semester hours.

The six fields most commonly required were: Abstract Algebra,

Statistics, Geometry, Analysis, Topology, and Linear Algebra.

Average requirements in mathematics for the Ed. D., math, ed.,

were from forty to forty-seven hours. The six fields most

commonly required were Topology, Abstract Algebra, Geometry,

Statistics, Analysis, and Foundations of Mathematics.

Average requirements in education for both degrees ranged

from eighteen to twenty-four semester hours. There was little

general agreement as to specific courses, but courses which

179

were frequently mentioned as being required were Mathema-

tics Education, Educational Psychology, Methods of Research,

Tests and Measurements, Statistics, Philosophy of Education,

Curriculum and Method in Higher Education, and Foundations

of Education.

The average total requirement in semester hours for

both degrees was ninety semester hours. The credit allowed

for the dissertation, as part of these ninety hours, averaged

from twelve to eighteen semester hours. Types of disserta-

tion which were acceptable for both degrees included research

in the teaching of mathematics, research in mathematics,

statistical studies, historical studies, and critical or

expository studies. In the majority of programs, no foreign

language was required for the Ed. D., math. Ed., while two

were generally required for the Ph. D., math., ed. The most

common requirements, as to special knowledge or special

skills, were the requirement of a knowledge of statistics

and of methods of educational research. Approximately one-

half the programs for both degrees required a practicuum

and experience in teaching. Almost all programs for the two

degrees required an entrance examination, a qualifying

examination, and a final oral examination over the disserta-

tion.

180

12. To determine what training in mathematics and edu-

cation should be included in the new programs.

In the light of the responses of the panel of specialists

in mathematics education, it seemed reasonable to conclude

that the programs for these degrees should include up to

sixty semester hours of mathematics and from twelve to twenty-

four hours in education. Mathematics courses required should

probably include the following: Real Analysis; Topology;

Probability and Statistics; Complex Analysis; Geometry; Ab-

stract Algebra; and possibly, History of Mathematics and

Number Theory. Education courses required should probably

include Educational Psychology, Learning Theory, Curriculum

and method in Higher Education, Statistics, and Improvement

of College Teaching.

13. To suggest standards for doctoral programs in

mathematics and education designed for preparation of college

teachers of mathematics at the undergraduate level.

In the light of the data from questionnaire number five,

which outlined the composition of current doctoral progi-ams,

and from questionnaire number three, which outlined the

opinions of the panel of experts, conclusions were drawn

concerning this sub-problem. The programs for the Ph. D.,

math, ed., and the Ed. D., math, ed,, should involve graduate

181

study amounting to the equivalent of ninety semester hours

of work at a true graduate level. The chief difference

between the two degrees, in practice, seemed to be a differ-

ence in the foreign language requirement. Since it was in-

tended in the study to set rather broad limits to the programs,

the two degrees were treated in the same manner with regard

to other requirements.

For entrance to the programs a student should be expected

to have the equivalent of an undergraduate major in mathematics,

with approximately twenty-four semester hours beyond elementary

calculus. This should include'"some introduction to abstract

algebra and six semester hours in advanced calculus or othei-

courses in analysis at the same level or at a higher level.

Since the current programs had an average requirement of

approximately forty-five semester hours in mathematics and

the average requirement in mathematics suggested by the panel

was sixty semester hours, it seemed reasonable to set the

lower limit on the amount of mathematics, to be required, at

forty-five semester hours. Similar reasoning gave a figure

of eighteen semester hours in education to be required. As-

suming a dissertation requirement of twelve semester hours,

this left fifteen hours of electives. Since these degrees

were being considered as preparation for the college teaching

of mathematics, the. candidate should probably be encouraged

to choose these electives in mathematics.

182

The forty-five semester hours of required mathematics

should include the following: Analysis, real and comples,

twelve semester hours; Abstract Algebra, six hours; Geometry,

three to six hours; Topology, three to six hours; and Proba-

bility and Statistics, six hours. There should probably also

be included three to six hours of seminar or independent work

in mathematics designed to develop an understanding of methods

of research in mathematics.

The required courses in education might be selected from

Educational Psychology, Statistics, Methods of Research,

Learning Theory, Curriculum and Method in Higher Education,

and Improvement of College Teaching. The last two courses

were included not only because of the fact that they were

stressed by members of the panel, but, also, because of the

fact that a majority of college officials felt that it was

either necessary or desirable that some work bearing on

methods of instruction be included.

For the Ph. D., math. ed., one or two foreign languages

would probably be required. The Ed. D., math, ed., would

probably not require a foreign language unless the problem

selected for the dissertation required a knowledge of a

foreign language.

It seemed desirable to include in the program for either

degree a practicuum and/or actual experience in teaching.

183

Because of the feeling on the part of college officials that

the best way to develop the ability to teach is through super-

vised teaching, consideration might be given to permitting

the candidate to substitute such experience for the practi-

cuum or the teaching experience. For either degree, a series

of three examinations would be required; an entrance examina-

tion, a qualifying examination, and a final oral examination

over the dissertation. The dissertation might be a statisti-

cal study, an historical study, a critical or expository

study, or it might consist of the results of research in

mathematics or in the teaching of mathematics.

Hypotheses

In the final question of each of questionnaires number

one, two, and three, officials of colleges and specialists

in mathematics education were asked to select one of five

responses indicating agreement or disagreement with each

of two proposals for a new doctoral degree in mathematics

and education. The question, which was identical in all

questionnaires, was as follows:

Taking into consideration the present situation in mathematics as you see it and considering the degrees as designed primarily for preparation of teachers of undergraduate mathematics in junior colleges and four year colleges, do you agree that it is desirable for such degrees as the Ph. D., math, ed., and the Ed. D., math, ed., to be offered?

184

The five possible responses were as follows:

Ph.D., math. ed.: Agree strongly Agree _No opinion Disagree Disagree strongly

Ed.D., math. ed. : Agree strongly Agree No opinion

Disagree Disagree strongly

In every case, the covering letter made plain that the

degrees to be considered were degrees such as those defined

in the description of the degrees which was enclosed with

each mailing. The following hypotheses were used to test

the distribution of responses of officials and specialists,

in vax-ious categories, to the above question for each of the

two degrees. The chi-square distribution was used in testing

the hypotheses. Because the theoretical frequency in one or

more calls of each contingency table fell below five, the

categories "disagree" and "disagree strongly" were combined.

This resulted in four by four contingency tables for use in

computing chi-square, in each case. Because theoretical fre-

quencies still remained small, Yates' correction was applied

in computing chi-square. Hypotheses were tested at the five

per cent level of significance, which required a chi-square

of 16.919 for rejection. The eight hypotheses and the results

of the test of the distribution of responses for each of the

two degrees, in each case, appear below.

Hypothesis number one was that there is no difference in

the distribution of responses of specialists in mathematics

185

education, presidents, deans, and heads of departments of

mathematics in the national sample of junior colleges. For

the Ph. D., math, ed., chi-square was 10.067, and, for the

Ed. D., math, ed., it was 5.466. Thus, hypothesis number one

was accepted for both degrees because the five per cent level

of significance was not reached. The non-significant chi-

squares meant that the distribution of responses for each

group did not differ with regard to their agreement as to

the desirability of offering each of the two professional

doctorates.

Hypothesis number two was that there is no difference in

the distribution of responses of specialists in mathematics

education, presidents, deans, and heads of departments of

mathematics in the national sample of senior colleges. For

the Ph. D., math. ed., chi-square was 9.802, and, for the

Ed. D., math. ed., it was 9.242. Thus, hypothesis number

two was accepted for both degrees because the five per cent

level of significance was not reached. The non-significant

chi-squares meant that the distribution of responses for each

group did not differ with regard to their agreement as to the

desirability of offering each of the two professional degrees.

Hypothesis number three was that there is no difference

in the distribution of responses of specialists in mathematics

education, presidents, deans, and heads of departments of

186

mathematics in colleges in the national sample of senior col-

leges which stress teacher education. For the Ph. D., math,

ed., chi-square was 7.090, and, for the Ed. D., math, ed.,

it was 6.023. Thus, hypothesis number three was accepted for

both degrees because the five per cent level of significance

was not reached. The non-significant chi-squares meant that

the distribution of responses for each group did not differ

with regard to their agreement as to the desirability of

offering each of the two professional degrees.

Hypothesis number four was that there is no difference

in the distribution of responses of specialists in mathematics

education, presidents, deans and heads of departments of

mathematics in Texas junior colleges. For the Ph. D., math,

ed., chi-square was 12.407, and for the Ed. D., math, ed.,

it was 5.932. Thus, hypothesis number four was accepted for

both degrees because the five per cent level of significance

was not reached. The non-significant chi-squares meant that

the distribution of responses for each group did not differ

with regard to their agreement as to the desirability of

offering each of the two professional degrees.

Hypothesis number five was that there is no difference

in the distribution of responses of specialists in mathematics

education, presidents, deans, and heads of departments of

187

mathematics in Texas senior colleges. For the Ph. D., math,

ed., chi-square was 12.609, and, for the Ed. D., math, ed.,

it was 5.087. Thus, hypothesis number five was accepted for

both degrees because the five per cent level of significance

was not reached. The non-significant chi-squares meant that

the distribution of responses for each group did not differ

with regard to their agreement, as to the desirability of

offering each of the two professional degrees.

Hypothesis number six was that there is no difference in

the distribution of responses of presidents in the national

samples of junior and senior colleges and of Texas junior

colleges and senior colleges. For the Ph. D., math. ed.,

chi-square was 3.330, and, for the Ed. D., math, ed., it was

4.449. Thus, hypothesis number six was accepted for both

degrees because the five per cent level of significance was

not reached. The non-significant chi-squares meant that the

distribution of responses for each group did not differ with

regard to their agreement as to the desirability of offering

each of the two professional degrees.

Hypothesis number seven was that there is no difference

in the distribution of responses of deans in the national

samples of junior colleges and senior colleges and of Texas

junior colleges. For the Ph. D., math, ed., chi-square was

188

9.708, and, for the Ed. D., math, ed., it was 6.666. Thus,

hypothesis number six was accepted for both degrees because

the five per cent level of significance was not reached.

The non-significant chi-squares meant that the distribution

of responses for each group did not differ with regard to

their agreement as to the desirability of offering each of

the two professional degrees.

Hypothesis number eight was that there is no difference

in "the distribution of responses of heads of departments of

mathematics in the national samples of junior colleges and

senior colleges and of Texas junior and senior colleges. For

the Ph. D., math, ed., chi-square was 6.629, and, for the

Ed. D., math, ed., it was 13.370. Thus, hypothesis number

eight was accepted for both degrees because the five per

cent level of significance was not reached. The non-signifi-

cant chi-squares meant that the distribution of responses

for each group did not differ with regard to their agreement

as to the desirability of offering each of the two profes-

sional degrees.

General Conclusions

On the basis of the data derived from responses to the

five questionnaires, and, on the basis of the conclusions

drawn concerning the thirteen sub-problems, general conclusions

189

were drawn for each of the.four primary purposes of the study.

These four purposes, together with the conclusions reached

for each, are

1. To determine the need for such programs. On the

basis of the findings concerning sub-problems number one and

number two, it seemed reasonable to conclude that there was

a need for such doctoral programs as those for the Ph. D,,

math, ed., and the Ed. D., math. ed. The percentage of mem-

bers of the mathematics staffs of junior and senior colleges

who were trained at the doctoral level was far below that

desired by the colleges. The present system of doctoral

education in mathematics, in the opinion of a majority of

all college officials, could not be depended upon to supply

a sufficient number of holders of the Ph. D. in mathematics

to fill the needs of the junior colleges and senior colleges.

In addition, a majority of college officials indicated that

preparation for teaching was desirable as well as preparation

in subject matter. There was a need for the special doctor-

ates, then, to help lessen the shortage of adequately pre-

pared teachers and to supply some teachers with specific

preparation for teaching of mathematics.

2. To determine the attitude of college and university

officials toward them. On the basis of the conclusions con-

190

ten, it seemed reasonable to conclude that there was a very

favorable attitude toward these degrees on the part of junior

and senior college officials, and, also, on the part of

graduate school officials. Not only did a majority of col-

lege officials agree that the degrees should be offered, but,

also, approximately 23.9 per cent of all senior colleges and

1.8 per cent of all junior colleges were already using holders

of such degrees. A majority of graduate school officials

responding felt that the offering of the degrees was justified

by the present state of affairs in mathematics education.

Seventy-two per cent of graduate school officials felt that

there was a place for such people on the staffs of Ph. D.

granting institutions. Approximately 30 per cent of all

graduate schools were already offering such degrees, and an

additional 41.6 per cent either planned to offer them or were

willing to consider doing so if a demand for them should be-

come apparent. Of all college and university officials

responding, a majority considered these degrees to be adequate

preparation for teaching mathematics both in junior colleges

and in senior colleges.

3. To determine the composition of present offerings.

The conclusions concerning this purpose were identical with

those summarized under sub-problem number eleven. In brief,

it seemed reasonable to answer this sub-problem by summarizing

191

the findings concerning current degree programs. The pro-

grams, in general, required an undergraduate major in mathe-

matics or the equivalent for entrance. Average requirements

in mathematics were from forty-five to forty-eight semester

hours for the Ph. D., math. ed.; and from forty to forty-seven

semester hours for the Ed. D., math. ed. The mathematics

courses required were such as to give a fairly extensive

preparation in mathematics. Average requirements in educa-

tion for both degrees ranged from eighteen to twenty-four

semester hours. The average total requirement in semester

hours for both degrees was ninety semester hours. The credit

allowed for the dissertation, as part of these ninety hours,

averaged from twelve to eighteen semester hours. Types of

dissertations which were acceptable for both degrees included

research in the teaching of mathematics, research in mathema-

tics, statistical studies, historical studies, and critical

or expository studies.

In the majority of programs, no foreign language was re-

quired for the Ed. D., math, ed., while two were generally

required for the Ph. D., math. ed. The most common require-

ments, as to special knowledge or special skills, were the

requirement of a knowledge of statistics and of methods of

educational research. Approximately one-half the programs

for both degrees required a practicuum and experience in

192

teaching. Almost all programs for the two degrees required

an entrance examination, a qualifying examination, and a

final oral examination over the dissertation.

4. To determine recommendations as to the future course

their development should take. It seemed reasonable to con-

clude. that the programs for the doctoral degrees in mathema-

tics should evolve in the direction of a program such as that

outlined under sub-problem thirteen. With regard to general

requirements and to division of work between mathematics and

education, the programs would be very similar to those out-

lined in three, above. There would be slightly greater

emphasis on mathematics. The mathematics required for the

two degrees would consist of about the same number of semes-

ter hours as usually required for the Ph. D. in mathematics.

It would, however, be more extensive in nature. It would be

a mistake to set forth such specific course requirements as

to lose the flexibility which is needed in a doctoral program.

The exact requirements for each candidate would, of course,

be determined by his previous preparation and his future aims.

The tentative program outlined under sub-problem thirteen

left room for fifteen hours of electives. These elective

courses could be used to fit the program to the needs of the

individual. The candidate whose primary interest lay in

193

college teaching of mathematics would probably need to take

these electives in mathematics. This, of course, was the

group with which this study was chiefly concerned. The

individual whose primary interest was in teacher preparation,

in school mathematics, or in research in the teaching of

mathematics would probably be advised to select education

electives in line with his objective.

In addition to specific requirements for the Ph. D.,

math, ed., or the Ed. D., math, ed., certain other standards

should be kept in mind in setting up a program for any such

degree. These standards include the following: (1) the

quality of scholarship required should be equal to that

required for the traditional Ph. D.; (2) research training

should be provided; (3) sufficient preparation in the candi-

date's major field of mathematics should be included to

enable him to teach most of the courses commonly offered at

the undergraduate level; and (4) attention should be given

to the nature, structure, and problems of higher education

and to instructional procedures and resources.

Recommendations ^

The following recommendations are made:

1. It is recommended that graduate schools which do

not offer professional doctorates in mathematics and education

194

for the preparation of teachers of undergraduate mathematics,

give serious consideration to the institution of such programs.

2. It is recommended that graduate schools, which are

now offering professional doctorates in mathematics and edu-

cation , re-examine the programs for these degrees with a

view to making them such as to attract and hold greater num-

bers of capable students.

3. It is recommended that, in selecting education courses

to be required for the professional doctorates, care be used

to select courses which will give insight into the problems

of higher education, methods of educational research, and

instructional methods and procedures at the college level.

4. It is recommended that requirements in mathematics

for the professional doctorates be set up in such a manner

as to insure that each candidate has a broad knowledge of

several fields of mathematics to insure a background for

teaching most of the courses offered at the undergraduate

level.

5. It is recommended that programs for the professional

doctorates in mathematics and education be planned jointly

by departments of education and departments of mathematics.

It is further recommended that a candidate be permitted to

do his work under the primary direction of either department,

as determined by the nature of his research interests.

195

6. It is recommended that research be done concerning

holders of the professional doctorates who are actually en-

gaged in teaching of college mathematics to determine (1)

the type of teaching the holders of these degrees are engaged

in, (2) the degree of satisfaction with their doctoral train-

ing as preparation for the work they are doing, and (3) sug-

gestions the holders of these degrees might have for modifi-

cation of programs for the professional doctorates.

APPENDIX

Definition of Degree Titles Used in the Questionnaires

The degrees with which this study is concerned are char-

acterized by the fact that they are designed for the prepara-

tion of teachers of undergraduate mathematics rather than

for. preparing university teachers of mathematics. They em-

body training both in mathematics and in education. The

titles of the degrees may vary. Where such degrees are

referred to in the questionnaires they are designated by the

titles Ph. D., math, ed., and/or Ed. D., math. ed. By these

titles are meant degrees essentially as described below:

Ph. D., mathematics education

The Ph. D., mathematics education is a Ph. D. degree

which comprises broad training in mathematics combined with

special preparation for teaching. Forty per cent or more of

the course work would be in mathematics and the remainder

in education. The dissertation might be a study in the

teaching of mathematics, an historical study, a critical

study, or an expository study. The work in mathematics is

planned so as to give thorough preparation in mathematics

of a somewhat more extensive nature than that required for

196

197

the Ph. D. in mathematics. The course work would be of a

level equal to that required for the Ph. D. in mathematics

and should prepare the graduate to teach almost any of the

courses commonly offered at the undergraduate level. Foreign

languages would probably be required.

Ed. D., mathematics education

The Ed. D., mathematics education would be almost iden-

tical to the Ph. D., math, ed., described above. The differ-

ences xtfould probably be that languages might not be required

and that the dissertation might be concerned with a practical

problem rather than with original research.

Ph. D. in mathematics

Where the title Ph» D. in mathematics occurs,it implies

the traditional research degree requiring a dissertation

which makes an original contribution to mathematical knowledge,

198

SCHOOL OF EDUCATION ~ NORTH TFXAS STATE UNIVERSITY - DENTON, TEXAS

Dear College President, College Dean, or Head of Department of Mathematics:

Your cooperation is needed for a study being made as the basis of a doctoral dissertation at

North Texas. The title of the proposed study is, "Doctoral Programs in Mathematics and Education

as Related to Instructional Needs of Junior Colleges and Four Year Colleges".

Questionnaires are being sent to officials of a sample of junior and senior colleges in the

United States and to officials of all such colleges in Texas with the exception of those colleges

which offer doctoral degrees. All information collected will be held in strict professional

confidence and none of the information will be connected with you as an individual or with your

school.

The purpose of the study Is to analyze doctoral programs in mathematics and education for the

preparation of teachers of undergraduate mathematics and to determine: (1) the need for such

programs, (2) the attitude of college and university officials toward them, (3) the composition

of present offerings, and (U) the future course their development should take.

It is hoped that the data gained in this study will be of considerable value and interest.

Would you complete the questionnaire at your convenience? Tryouts indicate that it should take

only a few minutes of your time. A digest of the results obtained will be mailed to all schools

whose officials return questionnaires.

A postage paid envelope is enclosed for your reply.

Thank you for your cooperation,

William Wingo Hamilton,Student conducting study.

Dr. E. W. Kooker, Professor directing study.

To Whom it May Concern:

The study of doctoral degrees In mathematics and education being conducted by Doctor of

Education candidate W„ W. Hamilton has the endorsement of the School of Education and the Depart-

ment of Mathematics of North Texas State University.

We feel that the results should be of general interest to those concerned with the teaching

of college mathematics. The data should also be helpful to us in appraising our program for the

Ed. D. in college teaching of mathematics.

Your cooperation will be .appreciated,

(^AJ\XX Dr. Witt Blair, Dean of the School of Education.

n

^ ft I Drj John T. Mohat, Director of the Department of Mathematics.

199

SCHOOL OF EDUCATION - NORTH 1EAAS STATE UNIVERSITY - DENTON, TEXAS

Dear Head of Department of Mathematics:

A short time ago a questionnaire was mailed to you requesting certain information needed for

a doctoral study being made at North Texas State University. This study is concerned with doctoral

degrees in mathematics and education designed for the preparation of teachers of undergraduate

mathematics. Because of the importance of having replies from as many heads of departments of

colleges in the sample as possible, it has been decided that a second mailing should be made to

those heads of departments of mathematics who have not yet returned the questionnaire. For this

mailing a shorter questionnaire, identical to that mailed to presidents and deans, is being used.

An important objective of the study is the testing of certain hypotheses concerning differences

in the distribution of responses to question number ten of this questionnaire as answered by

presidents, deans, heads of departments of mathematics, and members of a panel of experts in

mathematics education. It will be greatly appreciated if you can find time in your busy schedule

answer this shorter questionnaire.

A postage paid envelope is enclosed for your reply.

Thank you for your cooperation,

William~Wingo HamTlFon, Student conducting study.

Dr. E. V/. Kooker~Professor directing study.

To Whom it May Concern:

The study of doctoral degrees in mathematics and education being conducted by Doctor of

Education candidate W. W. Hamilton has the endorsement of the School of Education and the Depart-

ment of Mathematics of North Texas State University.

We feel that the results should be of general interest to those concerned with the teaching

of college mathematics. The data should also be helpful to us in appraising our program for the

Ed. D. in college teaching of mathematics.

Your cooperation.will be Appreciated,

p J V t *

Dr. Witt Blair, Dean of the School of Education#

Dr(J~JoHh T. Mohat, Director of the Department of Mathematics.

200

SCHOOL OF EDUCATION - NORTH TEXAS STATE UNIVERSITY - DENTON, TEXAS

Dear College President or College Dean:

A short time ago a questionnaire was mailed to you requesting certain information needed for

a doctoral study being made at North Texas State University, This study is concerned with doctoral

degrees in mathematics and education designed for the preparation of teachers of undergraduate

mathematics. Because of the importance of having replies from a greater percentage of the presidents

and deans of colleges in the sample, it has been decided that a second mailing should be made to

these officials.

An important objective of the study is the testing of certain hypotheses concerning differences

in the distribution of responses to question number ten of the questionnaire as answered by presi-

dents, deans, heads of departments of mathematics, and members of a panel of experts in mathematics

education. It will be greatly appreciated if you can find time in your busy schedule to complete

the enclosed questionnaire. If for any reason you prefer not to answer the entire questionnaire,

would you check question number ten and return with just this one question ansv/ered?

A postage paid envelope is enclosed for your reply,

Thank you for your cooperation,

William Wilii^HamiTto^^udent conducting study.

u) /-f

Dr. E. W. Kooker, Professor directing study.

To Whom it May Concern:

The study of doctoral degrees in mathematics and education being conducted by Doctor of

education candidate W, W. Hamilton has the endorsement of the School of Education and the Depart-

ment of Mathematics of North Texas State University.

We feel that the results should be of general interest to those concerned with the teaching

of college mathematics. The data should also be helpful to us in appraising our program for the

Ed, D. in college teaching of mathematics.

Your cooperation will be appreciated,

O Dr. Witt Blair, Dean of the School of Education.

^ fyyi0-Jirj Dvj John T. Mohat, Director of the Department of Mathematics.

201 Questionnaire Number One

Name Position

Institution _______ Academic Field

Highest Earned Degree: Ph. D. Ed. D. Ph. D. designed for preparation of college

teachers Ed. D. designed for preparation of college teachers _ _ _ _ _ M. A.

M. S. M. Ed. Other Give title of other degree

Check the appropriate response or supply requested information in blanks:

1. Some people believe that in the years ahead the four year colleges and junior colleges will be

able to attract, in competition with the universities and industry, only the less able Ph. D.'s in

mathematics. Is this likely to happen, in your opinion?

Already happening Probably will happen No sign now and little likelihood

No opinion

2. There are some indications that for junior colleges and non-Ph, D. granting senior colleges there

may be almost no Ph. D.'s in mathematics available in the forseeable future. Is this likely to be

true in your opinion?

Already happening _ Probably will happen _ No sign now and little likelihood _

No opinion

3. Do you think it is necessary that a teacher of mathematics at the undergraduate level be a pro-

ductive research mathematician?

Necessary _ _ _ _ _ Desirable Not necessary and not desirable _ _ _ _ No opinion

Do you think that research training at the doctoral level is necessary or desirable for the

teacher of undergraduate mathematics?

Necessary _ _ _ _ _ Desirable Not necess iry and not desirable No opinion

5. Do you think it is necessary or desirable for a prospective teacher of mathematics at the under-

graduate level to have some type of special preparation for teaching in addition to training in his

own subject field?

Necessary Desirable _ Not necessary and not desirable _ _ No opinion

6. If you checked either necessary or desirable in % above, rank the following in order of

desirability:

Formal instruction in methods Relatively unsupervised teaching as a graduate student

Supervised teaching as a graduate student _ _ _ _ _

7. If you had to choose, as part of the preparation of college teachers of undergraduate mathematics,

between instruction in methods of teaching and instruction in the history, philosophy, and problems

of higher education, which would you choose?

Instruction in methods of teaching _ _ _ Instruction in history, philosophy, and problems of

higher education Equally desirable No opinion _ Would prefer to have

neither

202 8. Considering the Ph. D., math. ed. and the Ed. D„, math. ed. as vehicles for training personnel

in mathematics education, check bolow t.h:; ty^oz of positions for which you consider these degrees to

be adequate preparation. Check as many as you wish.

Teacher of mathematics Director of teacher Research in the teach-in four year college _ _ _ _ _ training in mathematics ing of mathematics

Teacher of mathematics Teacher of special courses in in junior college mathematics for teachers _ _ _ _

Chairman, supervisor, or Teacher of methods courses for teacher in public school prospective public school

mathematics teachers

9. Rank the following degrees in order of preference in filling future vacancies in your depart-

ment of mathematics:

Ph. D. in mathematics Ph. D., math. ed. Ed. D., math. ed. _ _ _ _ _ M. A. or M. S.

in mathematics M. A. or M. S. in education M. Ed.

10. Taking into consideration the present situation in mathematics as you see it and considering

the degrees as designed primarily for preparation of teachers of non-university undergraduate

mathematics in junior colleges and four year colleges, do you agree that it is desirable for such

degrees as the Ph. D., math. ed. and the Ed. D., math. ed. to be offered?

Ph. D., math, ed.: Agree strongly Agree _____ No opinion Disagree

Disagree strongly _ _ _ _ _

Ed. D., math, ed.: Agree strongly Agree No opinion Disagree

Disagree strongly

When completed, mail in the enclosed envelope to: W. W. Hamilton Assistant Professor of Mathematics Arlington State College Arlington, Texas

203 Q ue s 11 oft f}£ i: * o Nnmber O'vo

Name Position .

Institution _ _ _ _ _ Academic Field _ _ ;

Highest Earned Degree: Ph. D. Ed. D« _ _ Pru D. designed for preparation of college

teachers _ _ _ _ _ Ed. D. designed for preparation of college teachers M. A. _ _ _ _ _

M. S. . M. Ed. , Other Give title of other degree

Check the appropriate response or supply requested information in blanks:

1. About how many undergraduates are enrolled in your institution during the current semester? _

2. ' About how many undergraduates are enrolled in mathematics classes during the current

semester?

3# What degrees with a major in mathematics are offered by your school?

Bachelor *s Master's Doctor's

k. If the B. A. or B. S. is offered with a major in mathematics, about how many mathematics majors

do you have?

5. Do you consider the preparation of mathematics teachers for secondary schools to be a major

function of your institution? Yes _ _ _ _ _ Moderately important No

6. Do you consider the preparation of elementary teachers to be a major function of' your

school? Yes _ _ _ _ _ Moderately important No _ _ _ _ _

7„ Is there close cooperation between your department of mathematics and your department of educa-

tion in preparing teachers for teaching elementary and secondary mathematics? Very close _ _

Moderately close Very little Antagonism

8. Which department conducts methods courses designed for teachers of mathematics?

Elementary mathematics: Mathematics _ _ _ _ _ Education _ _ _ _ _ Both * Neither '

Secondary mathematics: Mathematics _ _ _ Education _ _ _ Both Neither

9. Which department conducts courses in mathematics designed primarily for teachers?

Elementary mathematics: Mathematics

Secondary mathematics: Mathematics

Education _ _ Both Neither

Education Both Neither

10, About how many regular faculty members are there on your mathematics staff?

11. Give the approximate number of staff members in mathematics holding each of the following

degrees as the highest earned degree: Doctorate, with major in mathematics Doctorate, with

other major _ Master's, with major in mathematics . Master's, with other major

Bachelor's _ _ _ _ _

12. About how many new members have joined your mathematics staff in the past four years?

13. About how many new staff members do you anticipate adding in the next four years? _

l*f. Have you experienced difficulty in getting the desired number of teachers of mathematics

at the doctoral level? Great difficulty _ Moderate difficulty _ _ Little difficulty

204

15. Do you anticipate any such difficulty in the o^xt few years?

Yes _ No No opinion u

16. Ideally, what percentage of staff members in mathematics would you wish to be holders of

the Ph. D„ in mathematics? _

17. Some people believe that in the years ahead the four year colleges and junior colleges will be

able to attract, in competition with the universities and industry, only the less able Ph. D.fs in

mathematics. Is this likely to happen, in your opinion? Already happening _ _ _ Probably will

happen No sign now and little likelihood _ _ _ _ _ No opinion

18. There are some indications that for junior colleges and non-Ph. D. granting senior colleges

there may be almost no Ph. D.*s in mathematics available in the foreseeable future. Is this likely

to happen, in your opinion? Already happening • Probably will happen No sign now and

little likelihood No opinion _ _

19. Have you experienced any difficulty in getting the desired number of properly prepared teachers

of mathematics at the master !s level? Great difficulty _ _ _ Moderate difficulty _ _ _ _ _

Little difficulty _ _ _ _ _

20. Do you anticipate any such difficulty in the next few years?

Yes No _ _ _ _ _ No opinion _ _ _

21. How satisfactory have the teachers of mathematics who have come to you directly from graduate

school been with respect to the following:

A. Knowledge of subject matter: Highly satisfactory _ _ _ Moderately satisfactory

Unsatisfactory Highly unsatisfactory

B. Ability to teach: Highly satisfactory _ _ _ _ _ Moderately satisfactory

Unsatisfactory _ Highly unsatisfactory

22. Do you think it is necessary that a teacher of mathematics at the undergraduate level be a

productive research mathematician? Necessary _ _ _ _ _ Desirable _ _ _ _ _ Not necessary and not

desirable No opinion

23. Do you think research training at the doctoral level is necessary or desirable for the teacher

of undergraduate mathematics? Necessary Desirable Not necessary and not

desirable _ _ _ _ _ No opinion

2h. Do you think it is necessary or desirable for a prospective teacher of mathematics at the

undergraduate level to have some type of special preparation for teaching in addition to training

in his own subject field? Necessary _ Desirable Not necessary and not

desirable No opinion

25. If you checked either necessary or desirable in 2 ^ above, rank the following in order of

desirability: Formal instruction in methods Relatively unsupervised teaching as a

graduate student Supervised teaching as a graduate student „

205 26, If you had to chooso, as part of the preparation of college teachers of undergraduate mathe-

matics, between instruction in methods of teacMf.f, arri instruction in the history, philosophy, and

problems of higher education,- which would you choose?

Instruction in methods of teaching . Instruction in history, philosophy and problems of higher

education ______ Equally desirable No opinion Would prefer to have neither _ _ _ _ _

27. Considering the Ph. D., math^. ed. and the Ed. D., math. ed. as vehicles for training personnel

in mathematics education, check below the types of positions for which you consider these degrees

to be adequate preparation. Cheek as many as you wish.

Teacher of mathematics Director of teacher Research in the teach-in four year college _ _ training In mathematics ing of mathematics

Teacher of mathematics Teacher of special courses in in junior college mathematics for teachers _

Chairman, supervisor, or Teacher of methods courses for teacher in public school _ prospective public school

teachers

28. Do you at present have on your mathematics staff a member v/ith a doctorate similar to the

Ph. D., math. ed. or the Ed. D., math, ed., described in the enclosure?

Yes No _ _ _

29. If the answer to 28, above, was yes, how many such staff members do you have?

30. In your opinion, would it be desirable for a mathematics staff to have one or more members

trained both in mathematics and in education?

Highly desirable _ _ _ Desirable _ _ _ _ No opinion _ _ _ Undesirable _ _ _

31. Rank the following degrees In order of preference in filling future vacancies in your

department of mathematics:

Ph. D. in mathematics _ _ _ _ _ Ph. D., math. ed. Ed. D., math. ed. _

M. A. or M. S. in mathematics M. A. or M. S. in education M. Ed. 32. Taking into consideration the present situation in mathematics as you see it and considering

the degrees as designed primarily for preparation of teachers of non-university undergraduate

mathematics in junior colleges and four year colleges, do you agree that it is desirable for such

degrees as the Ph. D., math. ed. and the Ed. D., math. ed. to be offered?

Ph. D., math, ed.: Agree strongly _ Agree ______ No opinion _ Disagree

Disagree strongly

Ed. D., math, ed.: Agree strongly Agree _ _ _ _ _ No opinion Disagree

Disagree strongly _ _ _ _ _

When completed, mail in the enclosed envelope to: W. W. Hamilton Asst. Professor of Mathematics Arlington State College Arlington, Texas

SCHOOL OP EDUCATION - NORTH TEXAS STATE UNIVERSITY - DENTON, TEXAS 206

Dear Sir:

Your cooperation is needed for a study being made as the basis of a '

doctoral dissertation at North Texas, The title of the proposed study is

"Doctoral Programs in Mathematics and Education as Related to Instructional

Needs of Junior Colleges and Four Year Colleges".

Data is being collected from presidents, deans, and heads of departments

of mathematics of a sample of colleges vhich should yield information as to

the need for such programs and the attitude of colleges and university

officials toward them.

Date is also being collected from colleges vhich offer such degrees

as to the composition of, present offerings.

With the approval of the committee supervising the study, a list of

experts has been compiled from three sources: (l) members and former members

of CUPM, (2) officials of the National. Council of Teachers of Mathematics,

and (3) a list of people known to be interested in mathematics education

who are prominent in research in this field. It has been agreed that these

from the above list who return the enclosed questionnaire shall constitute

an acceptable panel of experts.

It is hoped that the data gained in the study will be of considerable

value and interest. It will be greatly appreciated if - you can find time in

your busy schedule to complete the enclosed questionnaire. All information

will be held in strict professional confidence and none of the information

will be connected with you as an individual, A digest of the results will

be mailed to all who return questionnaires.

A postage paid envelope is enclosed for your reply.

Thank you for your cooperation,

i/J

W.W. Hamilton, Student conducting study.

Dr. E. W. Kooker™ Professor directing" study.

207

SCHOOL OF EDUCATION - NORTH TEXAS STATE UNIVERSITY - DENTON, TEXAS

To Whom it May Concern;

The study of doctoral degrees in mathematics and

education being conducted by Doctor of Education can-

didate W. W. Hamilton has the endorsement of the School

of Education and the Department of Mathematics of North

Texas State University.

We feel that the results should be of general in-

terest to those concerned with the teaching of college

mathematics. The data should also be helpful to us in

appraising our program for the Ed.D. in college teaching

of mathematics.

Your cooperation will be appreciated,

Dr. Witt Blair ~ Dean of the School of Education

J T -

•. John T. Mohat .rector of the Department of Mathematics

208 Questionnaire Number Three

Name _ ______ Position

Institution Academic Field

Highest Earned Degree: Ph. D. _ _ _ Ed. D. „ Ph. D« designed for preparation of college

teachers Ed, D. designed for preparation of college teachers M. A.

M. S. _ M. Ed. Other Give title of other degree

It is realized that course requirements for doctoral degrees are often not listed precisely in semester hours. However, the questions below have been phrased in terms of semester hours in order to provide a convenient way to indicate approximately the desirable content.

Check the appropriate response or supply requested information in blanks:

1. Assuming that degrees similar to the Ph. D., math. ed. and the Ed. D., math, ed., described in the enclosure, will continue to be offered, at least*by the schools now offering them, check below the statement which seems most desirable as a minimum requirement in undergraduate mathematics for entrance to such a program.

Twelve semester hours beyond elementary calculus

Eighteen semester hours beyond elementary calculus

Eighteen semester hours beyond elementary calculus including advanced calculus and abstract algebra

Twenty-four semester hours beyond elementary calculus ..

Twenty-four semester hours beyond elementary calculus including advanced calculus and abstract algebra

Thirty semester hours beyond elementary calculus

Thirty semester hours beyond elementary calculus including advanced calculus and abstract algebra

2. Check below the division of work between mathematics and education which seems to you to be desirable for such degrees. All requirements are stated in semester hours and a dissertation carrying twelve semester hours credit is assumed.

Mathematics Education Dissertation 30 *+8 12 36 k2 12 k2 36 12 k8 30 12 $¥ 2b 12 60 18 12 66 12 12 z _ r ~

3. Select fields which you consider should be included in the mathematics requirements for such degrees as adequate preparation for the teaching of undergraduate mathematics. Enter semester hours in each field and/or elective to total the number of hours checked in 2, above.

Semester Hrs. Semester Hrs. Real Analysis Linear Algebra Other: Specify Semester Hrs

Complex Analysis _ _ _ Topology _ _ _ _ _ _

Geometry: Specify Probability and Statistics

Abstract Algebra

Number Theory

History of Mathematics Elective

209 k. Select fields in education which you think should he included in the requirements for these degrees. Give the number of semester hours for each to correspond to 2, above.

Bern. Brs. Sen:, Rrs> Serru Krs. Statistics • Adolescent Psychology Other: Specify

Educational Psychology Improvement•of College — — _ — — Teaching ~ ~

Personality Theory ~ — — — Organization ana Admin-

Human Growth and istration of Higher Development Education

Elective _ _ _ _ _

Other: Specify

Curriculum and Method Elective in Higher Education ..

Learning Theory

5». Do you think the work in mathematics for these degrees should include some training in methods of mathematical research through seminars or courses providing for independent mathematical work?

Yes _ _ _ _ _ No . No opinion _ _

6. Do you think languages should be required for these degrees?

One _ Two None No opinion _ _ _ _ _

7. Considering the Ph. D., math, ed. and the Ed. D., math. ed. as vehicles for training personnel in mathematics"education, check below the types of positions for which you consider these degrees to be adequate preparation. Check as many as you wish.

Teacher of mathematics Director of teacher Research in the teach-in four year college _ training in mathematics ing of mathematics t

Teacher of mathematics Teacher of special courses in in junior college _ _ _ mathematics for teachers _

Chairman, supervisor, or Teacher of methods courses for teacher in public school _ _ _ _ prospective public school _ _ _

mathematics teachers

8. Taking into consideration the present situation in mathematics as you see it and considering the degrees as designed primarily for the preparation of teachers of non-university undergraduate mathematics in junior colleges and four year colleges, do you agree that it is desirable for such degrees as the Ph. D., math. ed. and the Ed. D., math. ed. to be offered?

Ph. D., math, ed.: Agree strongly _ _ _ _ _ Agree _ No opinion _ _ _ _ Disagree _ _

Disagree strongly

Ed. D., math, ed.: Agree strongly _ Agree _ _ No opinion _ _ _ Disagree _ _ _

Disagree Strongly _

When completed, mail in the enclosed envelope to: V, W. Hamilton Assistant Professor of Mathematics Arlington State College Arlington, Texas

210 SCHOOL OF EDUCATION ~ NORTH TEXAS STATE UNIVERSITY - DENTON, TEXAS

Dear Graduate Dean or Head of Department of Mathematics;

Your cooperation is needed for a study being made as the basis of a doctoral dissertation at

North Texas. The title of the proposed study is, "Doctoral Programs in Mathematics and Education

as Related to Instructional Needs of Junior Colleges and Four Year Colleges"•

Data is being collected from officials of a sample of junior and senior colleges which should

yield information as to the need for such programs and the attitude of college officials toward

them. Data is also being obtained from a panel of experts in mathematics education concerning the

optimum content of such degree programs.

It is necessary to know definitely what graduate schools offer doctoral degrees in mathematics

and education designed for the preparation of college teachers and to know something of the attitude

of officials of graduate schools toward these degrees.

It is hoped that the data gained in this study will be of considerable value and interest.

Would you complete the questionnaire at your convenience? Tryouts indicate that it should take

only a few minutes of your time. A digest of the results obtained will" be mailed to all schools

whose officials return questionnaires.

If your school confers any such degree it will be included in a listing of institutions

offering degrees of this type. Otherwise, all information collected will be held in strict pro-

fessional confidence.

A postage paid envelope is enclosed for your reply.

Thank you for your cooperation,

William Wingo Hamilton, Student conducting study.

^ lJL* La)

Dr. E. W. Kooker, Professor directing study.

To Whom it May Concern:

The study of doctoral degrees in mathematics and education being conducted by Doctor of

Education candidate W. W. Hamilton has the endorsement of the School of Education and the Depart-

ment of Mathematics of North Texas State University.

We feel that the results should be of general interest to those concerned with the teaching

of college mathematics. The data should also be helpful to us in appraising our program for the

Ed. D. in college teaching of mathematics.

Your cooperation will be appreciated, b^K.Kj

Dr. Witt Blair, Dean of the School of Education.

Drj/JoKn T. Moh&t, Director of the Department of Mathematics.

211 Questionnaire Number Four

Name _ _ _ .. Position _______

Institution _ Academic Field

Highest Earned Degree: Ph, D. Ed. D. Ph. D. designed for preparation of college

teachers Ed. D. designed for preparation of college teachers M. A.

M. S. M. Ed. Other _ _ Give title of other degree

Check the appropriate response or supply requested information in blanks:

1. Does your school offer the Ph. D. in mathematics? Yes _ _ No

2* Do you offer any other doctoral degree primarily in mathematics but with a dissertation require-

ment differing from that of the research Ph. D. in mathematics?

Yes _ _ _ _ _ No If answer is yes, give title of the degree

3. Do you offer a doctoral degree similar to the Ph. D., math. ed. and the Ed. D., math. ed.

described in the enclosure or any other doctoral degree in mathematics and education designed for

preparing teachers of undergraduate mathematics?

Yes No If answer is- yes, indicate the degrees offered: Ph. D., math. ed.

Ed. D., math. ed. _ _ _ _ Other(Give title of degree)

b. If the answer to 3, above, was yes, approximately how many graduates have you had in the past

ten years for each degree offered?

Ph. D., math. ed. _ _ _ _ _ Ed. D., math. ed. Other . _ _ _

5. If graduates were enumerated in *f, above, what percentage of the total of such graduates do

you estimate to be engaged in college teaching of mathematics? __

6. If you do not now offer doctoral degrees such as those in item 3> above, do you anticipate any

such offerings in the future?

Yes No No opinion

7. If you have no present plans for such degrees as those in 3> above, would you consider such

offerings if a demand for them should develop on the part of junior colleges or four year colleges?

Yes No No opinion _ _ _ _

8. Which statement best describes your feeling as to the status of doctoral degrees in mathematics

designed primarily for preparation of teachers of undergraduate mathematics?

The research Ph. D. should be the sole terminal degree for preparing college teachers.

The current situation in undergraduate mathematics instruction makes it desirable to offer degrees similar to those listed in 3, above.

The offering of degrees such as those in 3, above, is justified by the need for more people prepared for teaching as well as prepared in subject matter.

9. If such degrees are to continue to be offered, rank the following in order of preference:

Ph.D., math. ed. _ _ _ Ed. D. , math, ed

212

10, In your opinion, would teachers holding doctoral degrees such as the Ph. D., math. ed. and

the Ed. D., math. ed. be suitable for some positions on the staff of a university which confers

the Ph. D. in mathematics?

Yes No No opinion _ _ _ _ _

11. If the answer to item 10, above, was yes, check the positions below which you think might

be satisfactorily filled by such teachers:

Teacher of undergraduate mathematics _

Teacher of special mathematics courses designed for teachers of elementary and secondary mathematics

Teacher of special mathematics or methods courses offered in the school of education for elementary and secondary teachers _

Teacher of methods courses offered within a math-matics department for elementary and secondary teachers

Graduate instruction in the teaching of mathematics _ _

Direction of research in the teaching of mathematics

Director of teacher preparation of elementary and secondary mathematics teachers _ _ _ _ _

12. Do you, at present, have on your staff a member with a doctorate similar to the Ph. D.,

math. ed. or the Ed. D,, math, ed.?

Yes No

When completed, mail in the enclosed envelope to: W. W. Hamilton Asst. Professor of Mathematics Arlington State College Arlington, Texas

213 SCHOOL OF EDUCATION - NORTH TEXAS STATE UNIVERSITY - DENTON, TEXAS'

Dear Graduate Dean, Dean of School of Education, or Head of Department of Mathematics:

Your cooperation is needed for a study being made as the basis of a doctoral dissertation

at North Texas, The title of the proposed study is, "Doctoral Programs in Mathematics and Education

as Related to Instructional Needs of Junior Colleges and Four Year Colleges".

Data has been collected from officials of a sample of junior and senior colleges concerning

the need for such degrees and the opinion of such officials toward these degrees. Also, a panel of

experts in mathematics education has supplied information as to the opinion of these experts con-

cerning the optimum content of such degree programs, From a questionnaire mailed to graduate schools

it was determined that your school is one of a number which offer one or more such degrees. It is

necessary to know the content of degree programs of this type which are now available.

It Is hoped that the data gained in this study will be of considerable value and interest. If

your school is known to offer more than one degree designed for preparation of teachers, a ques-

tionnaire is enclosed for each degree. Would you complete a questionnaire for each degree offered

at your convenience? A digest of the results obtained will be mailed to all schools whose officials

return questionnaires.

Your school will be included in a listing of institutions offering degrees of this type. The

requirements for each degree will be listed by schools. Otherwise, all information will be held

in strict professional confidence.

A postage paid envelope is enclosed for your reply.

Thank you for your cooperation,

William. Wingo Hamilton, Student conducting study.

£* tsJL Dr. E. W. Kooker, Professor directing study.

To Whom it May Concern:

The study of doctoral degrees in mathematics and education being conducted by Doctor of

Education candidate W. W. Hamilton has the endorsement of the School of Education and the Depart-

ment of Mathematics of North Texas State University.

We feel that the results should be of general interest to those concerned with the teaching

of college mathematics. The data should also be helpful to us in appraising our program for the

Ed. D. in college teaching of mathematics.

Your cooperation will be appreciated,

(XJXKX Dr. Witt Blair, Dean of the School of Education.

John T. Mohat, Director of the Department of Mathematics.

214

Que st i cnna Ir e Numbor FX vc.

Name - Position _ „

Institution _

Requirements for the _ degree in mathematics and education:

If you have available a summary of the program for this degree which covers the information requested, feel free to send a copy of it in lieu of answering the questionaire. If not, and if a question is covered completely in a catalog or bulletin issued by your school, feel free to indicate the bulletin by number or title instead of answering that question.

If additional space is needed for question *+, 5\ or 7, complete on the reverse side.

1. Is the preparation of teachers of undergraduate mathematics one of the purposes of the program

for this degree? Yes No

2. Prerequisites for entrance to the program in addition to a bachelor's degree. Summarize in

terms of semester hours or in terms of major cr minor.

Mathematics Education Other

3. Total requirements for the degree in semester hours:

Mathematics Education Elective _ _ _ Dissertation Total

List required mathematics courses and give semester hours for each:

5. List required education courses and give semester hours for each:

6. Check any of the following types of dissertation which are accepted for the degree:

Research in mathematics Historical _

Research in the teaching Critical or of mathematics _ _ _ Expository

Statistical _ _ _ _ _ 0t> er (specify) _ _ _

7. Check examinations required and indicate briefly the nature of each:

Entrance examination ,

Qualifying examination _ ,

Final examination

8. Is a reading knowledge of foreign languages required? No One Two

9. Is evidence of any other special knowledge or skill required? Statistics

Methods of educational research Other (specify)

10. Is a practicuum or internship required? Yes ______ No

II. Is the candidate required to have experience in teaching prior to the conferring of the

degree? Yes _ _ _ _ _ No

2.15

TABLE LXXXVIII

NATIONAL SAMPLE OF SENIOR COLLEGES 3 GROUPED ACCORDING TO STATES, AND WITH RESPONDENTS CLASSIFIED

AS TO POSITION*

Institution Pres. Dean Head

Alabama: Huntingdon College, Huntingdon r r Samford University, Birmingham r r r. Arkansas: Arkansas A & M College, College Heights r Arkansas Polytechnic College, Russelville r r Southern State College, Magnolia r r r California: Long Beach State College, Long Beach r r Orange State College, Fullerton r Pasadena College, Pasadena r St. MaryTs College of California,

St. Mary's College r r University of Redlands, Redlands r r r Colorado: Regis College, Denver r r r Colorado WomanTs College, Denver r r Connecticut: Annhurst College, Woodstock r Central Connecticut State College

New Britain r r Fairfield University, Fairfield r r District of Columbia: Trinity College, Washington r Georgia: Atlanta University, Atlanta r Idaho: Boise College, Boise r r r Illinois: Eastern Illinois University, Charleston r Elmhurst College, Elmhurst r r George Williams College, Chicago r Illinois College, Jacksonville r r r MacMurray College, Jacksonville r r Indiana: DePauw University, Greencastle r Valparaiso University, Valparaiso r r

TABLE LXXXV111--Cont inued

216

Institution Pres. Dean Head

Kansas: Friends University, Wichita McPherson College, McPherson Kentucky: Brescia College., Owensboro Campbellsville College, Campbellsville Transylvania College, Lexington Ursuline College, Louisville Western Kentucky State College,

Bowling Green Louisiana: Southeastern Louisiana College, Hammond University of Southwestern Louisiana,

Lafayette Maryland: Columbia union College, Tacoma Park Maryland State College, Princess Anne Massachusetts: American International College,

Springfield New Bedford Institute of Technology,

New Bedford Southeastern Massachusetts Technological

Institute, Boston Wheaton College, Norton Michigan: Albion College, Albion Eastern Michigan University, Ypsilanti Hope College, Holland Minnesota: Augsburg College, Minneapolis College of St. Teresa, Winona Mississippi: Delta State College, Cleveland Missouri: Lindenwood College, St. Charles Missouri Valley College, Marshall Notre Dame College, St. Louis Nebraska: Concordia Teachers College, Seward Doane College, Crete

r r

r

r

r r

r r

r r

r r

r

r

r r

r

r

r r r

r r

r r

r r r r

r

r

r

r r

r

r

r r

r r r

r r

r r r

r r

TABLE LXXXVIII--Continued

217

Institution Pres. Dean Head

New Jersey: Bloomfield College, Bloomfield r r Fairleigh Dickinson University,

Rutherford r r New Mexico: Eastern New Mexico University, Portales r r r New York: College of New Rocheile, New Rochelle r r Hobart College, Geneva r Nazareth College of Rochester, Rochester r r Niagara University, Niagara r r St. Bernardine of Siena College,

Loudonville r r State University of New York at Brockport,

Brockport r r State University of New York at Buffalo,

Buffalo r r State University of New York at Genesco,

Genesco r r r State University College, Oeonta r r r North Carolina: Bennett College, Greensboro r Elizabeth City State College,

Elizabeth City r Elon College, Elon College r High Point College, High Point r r r Saint Augustine?s College, Raleigh r r Wake Forrest College, Winston-Salem r Winston-Salem College, Winston-Salem r North Dakota: Jamestown College, Jamestown r r r Ohio: Ashland College, Ashland r r Heidelberg College, Tiffin r Mount Union College, Alliance r r Ohio Northern University, Ada r r Western College for Women, Oxford r r Oklahoma: Phillips University, Enid r r Pennsylvania: Alliance College, Cambridge Springs r r California State College, California r r

TABLE LXXXV111--Cont i nue d

218

Institution Pres. Dean Head Edinboro State College, Edinboro Gannon College, Erie Grove City College, Grove City Kutztown State College, Kutztown St. Francis College, Loretto Villa Maria College, Erie Wilkes College, Wilkes-Barre South Carolina: College of Charleston, Charleston South Dakota: Sioux Falls College, Sioux Falls Augustana College, Sioux Falls Tennessee: East Tennessee State College, Johnson City King College, Bristol Memphis State University, Memphis Utah: Westminster College, Salt Lake City Virginia: Randolph Macon Women's College, Lynchburg Washington and Lee University, Lexington Vermont: Trinity College, Burlington Wisconsin: Dominican College, Racine Wisconsin State College, Eau Claire

r

r

r

r

r r

r

r

r r

r r r

r

r

r

r r r

r

r

r r

r r

r r

r r r

r

r

r r

*The letter r appearing opposite the name of a college in the column under President, Dean, or Head, indicates a re-sponse was received from that official of the college.

219

TABLE LXXXIX

NATIONAL SAMPLE OF JUNIOR COLLEGES, GROUPED ACCORDING TO STATES, AND WITH RESPONDENTS CLASSIFIED

AS TO POSITION*

Institution Pres. Dean Head

Alaska: Anchorage Community College, Anchorage r Arkansas: Southern Baptist College, Walnut Ridge r r Arizona: Eastern Arizona Community College,

Thatcher r r r Phoenix College, Phoenix r r r California: Barstow College> Barstow r r Cabrillo College, Aptos r r College of the Siskiyous, Weed r r College of Marin, Kentfield r r r Compton College, Compton r r Contra Costa College, San Pablo r r r Gavilan College, Gilroy r r Los Angeles Valley College, Van Nuys r Pacific College, Fresno r Pasadena City College, Pasadena r r r San Bernardino Valley College,

San Bernardino r r San Diego City College, San Diego r r r San Benito College, Holister Sacremento City College, Sacremento r r r Vallejo Junior College, Vallejo r r Ventura College, Ventura r Colorado: Trinidad State Junior College, Trinidad r r Connecticut: Mitchell College, New London r r r Delaware: Wesley Junior College, Dover r r Florida: Brevard Junior College, Cocoa r r Central Florida Junior College, Ocala r Indian River Junior College, Fort Pierce r r r Manatee Junior College, Bradenton r r Miami-Dade Junior College, Miami r r • r

TABLE LXXXIX —Continued

220

Institution Pres. Dean Head

North Florida Junior College, Madison r r Georgia: Abraham Baldwin Agricultural College,

Tifton r r Southern Technical Institute, Marietta r r r Illinois: Black Hawk College, Moline r Joliet Junior College r r Kendall College, Evanston r r Morton Junior College, Cicero r r Springfield Junior College, Springfield r r Idaho: Ricks College, Rexford r r Iowa: Burlington Community College, Burlington r r Eagle Grove Junior College, Eagle Grove r Fort Dodge Community College, Fort Dodge r r Mason City Junior College, Mason City r Kansas: Butler Junior College, Eldorado r r Coffeyville College, Coffeyville r r Kentucky: Cumberland College, Williamsburg Midway Junior College, Midway r r Paducah Junior College, Paducah r Maryland: Essex Community College, Essex r r Massachusetts: Berkshire Community College, Pittsfield r Holyoke Junior College, Holyoke r r Mount Ida Junior College, Newton Center r Newton Junior College, Newtonville r r Michigan: Flint Community Junior College, Flint r r r Grand Rapids Junior College,

Grand Rapids r r r Jackson Junior College, Jackson r Port Huron Junior College, Port Huron r Suoird College, Hancock r Minnesota: Austin Junior College, Austin

TABLE LXXXIX--Continued

221

Institution Pres. Dean Head Mississippi: Copiah-Lincoln Junior College, Wesson r Jones County Junior College, Ellisville r r r Meridian Municipal Junior College,

Meridian r r Pearl River Junior College, Poplarville r r r Perkinston College, Perkinston r r Missouri: Christian College, Columbia r Junior College of Kansas City,

Kansas City r r St# Joseph Junior College, St. Joseph r r r Montana: Dawson County Junior College, Glendive r r Nebraska: Fairbury Junior College, Fairbury r McCook College, McCook r r Scottsbluff College, Scottsbluff r r North Carolina: Louisburg College, Louisburg r Mount Olive Junior College, Mount Olive r r r New Jersey: Union Junior College, Cranford r New York: Adirondack Community College, Hudson Falls r r r Dutchess Community College, Poughkeepsie r r Mohawk Valley Community College, Utica r Monroe Community College, Rochester r Nassau Community College, Garden City r Rockland Community College, Suffern r Westchester Community College, Valhalla r Oklahoma: Cameron State Agricultural College,

Lawton r r r El Reno Junior College, El Reno Pennsylvania: Robert Morris Junior College, Pittsburg r York Junior College, York r r r Rhode Island: Roger Williams Junior College, Providence South Carolina: Anderson College, Anderson r r

TABLE LXXXIX—Continued

222

Institution Pres. Dean Head

» Madisonville Pulaski

Tennessee: Howasee College. Martin College, Utah: Dixie Junior College, St. George Weber State College, Ogden Virginia: Ferrum Junior College, Ferrum Shenandoah College, Winchester Vermont: Champlain College, Burlington Vermont College, Montpelier Washington: Columbia Basin Community College, Pasco Everett Junior College, Everett Highline College, Seattle Olympic College, Bremerton Skagit Valley College, Mt. Vernon Wenatchee Valley College, Wenatchee Yakima Valley College, Yakima

r r

r r r

r r

r r

r r

r r

*The letter r appearing opposite the name of a college in the column under President, Dean, or Head, indicates a response was received from that official of the college.

TABLE XC

TEXAS SAMPLE OF SENIOR COLLEGES WITH RESPONDENTS CLASSIFIED AS TO POSITION*

223

Institution Pres Dean Head

Abilene Christian College, Abilene Angelo State College, San Angelo Austin College, Sherman Bishop College, Dallas East Texas Baptist College, Marshall Hardin-Simmons University, Abilene Howard Payne College, Brownwood Huston-Tillotson College, Austin Incarnate Word College, San Antonio Jarvis Christian College, Hawkins Lamar State College, Beaumont Le Tourneau College, Longview McMurry College, Abilene Mary Hardin-Baylor College, Belton Midwestern University, Wichita Falls Our Lady of the Lake College, San Antonio Pan American College, Edinburg Prairie View A & M College, Prairie View Sacred Heart Dominican College, Houston St. Edward's University, Austin St. Mary's University, San Antonio Sam Houston State College, Iluntsville Southwest Texas State College, San Marcos Southwestern University, Georgetown Stephen F. Austin State College,

Nacogdoches Sul Ross State College, Alpine Texas College of Arts and Industries

Kingsville Texas Lutheran College, Seguin Texas College, Tyler Texas Southern University, Houston Texas Wesleyan College, Ft. Worth Texas Western College, El Paso Trinity University, San Antonio University of Corpus Christ!,

Corpus Christi University of Dallas, Dallas University of St. Thomas, Houston

r r

r

r

r

r

r r

r r

r r

r r

r

r

r r r

r r r r r r

r r r r r r r

r r r r r

r r

r r r

224

TABLE XC—Continued

Institution Pres. Dean Head

Wayland Baptist College, Plainview West Texas State University, Canyon Wiley College, Marshall

r r

r *The letter r appearing opposite the name of a college

in the column under President, Dean, or Head, indicates a response was received from that official of the college.

TABLE XCI

TEXAS SAMPLE OF JUNIOR COLLEGES WITH RESPONDENTS CLASSIFIED AS TO POSITION*

225

Institution Pres. Dean Head Allen Academy, Bryan Alvin Junior College, Alvin Amarillo College, Amarillo Blinn College, Brenham Cisco Junior College, Cisco Clarendon Junior College, Clarendon Cooke County Junior College, Gainesville Dallas Baptist College, Dallas Decatur Baptist College, Decatur Del Mar College, Corpus Christi Frank Phillips College, Borger Henderson County Junior College, Athens Hill County Junior College, Hillsboro Howard County Junior College, Big Spring Jacksonville College, Jacksonville Kilgore College, Kilgore Laredo Junior College, Laredo Lee College, Baytown Lon Morris College, Jacksonville Lubbock Christian College, Lubbock Concordia College, Austin Navarro Junior College, Corsicana Odessa College-, Odessa Panola College, Panola Paris Junior College, Paris Ranger Junior College, Ranger San Jacinto Junior College, San Antonio St. Phillips College, San Antonio San Antonio College, San Antonio Schreiner Institute, Kerrville South Plains College, Levelland South Texas Junior College, Houston Southwest Texas Junior College, Uvalde Southwestern Assemblies of God College,

Waxahachie Southwestern Union College, Keene Temple Junior College, Temple Texarkana College, Texarkana

r r r

r r

r r

r r

r r r r

r r

r r r r

r r

r r

r r

r r r r

r r

r r

r r

r r

r r r r r r r

TABLE XCT--Continued

226

Institution

Texas Southmost College, Brownsville Tyler Junior College, Tyler Victoria College, Victoria Weatherford College, Weatherford Wharton County Junior College, Wharton

Pres.

r r

Dean Head

r r r

r r

r r

*The letter r appearing opposite the name of a college in the column under President, Dean, or Head, indicates a response was received from that official of the college.

227

TABLE XCII

LIST OF GRADUATE SCHOOLS WITH RESPONDENTS CLASSIFIED AS TO POSITION*

Institution Dean Head Adelphi College, Garden City, N. Y. University of Alabama, Birmingham, Ala. University of Alaska, Fairbanks, Alaska Alfred University, Alfred, N. Y. American University, Washington, D. C. University of Arizona, Tucson, Arizona Arizona State University, Tempe, Arizona Auborn University, Auburn, Alabama Ball State Teachers College, Muncie, Ind. Boston University, Boston, Mass. Brandeis University, Waltham, Mass. Brigham Young University, Provo, Utah Polytechnic Institute of Brooklyn,

Brooklyn, N. Y. Brown University, Providence, R. I. Bryn Mawr College, Bryn Mawr, Pa. Catholic University of America,

Washington, D. C. University of California, Los Angeles, Calif. University of California, Berkeley, Calif. University of California, Davis, Calif. California Institute of Technology,

Pasadena, Calif. Carnegie Institute of Tech., Pittsburgh, Pa. Case Institute of Technology, Cleveland, Ohio University of Chicago, Chicago, 111. University of Cincinnati, Cincinnati, Ohio Colorado State College, Greeley, Colorado Colorado State University, Fort Collins, Col. University of Colorado, Boulder, Colorado Columbia University, New York, N. Y. Teachers College, Columbia University,

New York, N. Y. University of Connecticut, Storrs, Conn. Cornell University, Ithca, N. Y. Dartmouth College, Hanover, N. H. University of Delaware, Newark, Delaware University of Denver, Denver, Colorado

r r r r

r

r

r r

r r

r r r

r r

r r

TABLE XCII--Continued

228

Institution Dean Head

Duke University, Durham, N. C. Emory University, Atlanta, Georgia University of Florida, Gainesville, Fla. r Florida State University, Tallahassee, Fla. • r Fordham University, New York, N. Y. George Peabody College for Teachers,

Nashville, Tenn. George Washington University, Washington,

D. C. Georgetown University, Washington, D. C. University of Georgia, Athens, Georgia Harvard University, Cambridge, Mass. r r University of Hawaii, Honolulu, Hawaii r University of Houston, Houston, Texas r r University of Idaho, Moscow, Idaho r Illinois Institute of Technology, Chicago,

Illinois University of Illinois, Urbana, 111. r Indiana Teachers College, Terre Haute, Ind. r Indiana University, Bloomington, Ind. Iowa State University of Science and

Technology, Ames, Iowa r r State University of Iowa, Iowa City, Iowa r Johns Hopkins University, Baltimore, Md. r University of Kansas City, Kansas City, Mo. Kansas State University, Manhatten Kansas University of Kansas, Lawrence, Kansas University of Kentucky, Lexington, Ky, r Lehigh University, Bethlehem, Pa. r r Louisiana State University, Baton Rouge, La. r Loyola University, Chicago, 111. r Marquette University, Milwaukee, Wis. r r University of Maryland, Baltimore, Md. University of Massachusetts, Amherst, Mass. Massachusetts Institute of Technology,

Cambi'idge, Mass. r University of Miami, Miami, Florida r Michigan State University, East Lansing,

Michigan r University of Michigan, Ann Arbor, Michigan r University of Minnesota, Minneapolis,

Minnesota

TABLE XCII--Continued

229

Institution Dean Head

Mississippi Southern College, Hattiesburg, Miss.

Mississippi State University, State College, Miss.

University of Mississippi, University, Miss.

University of Missouri, Columbia, Mo. Montana State University, Missoula, Mont. Montana State College, Bozeman , Mont. University of Nebraska, Lincoln, Neb. University of New Mexico, Albuquerque,

New Mexico New Mexico State University,

University Park, New Mexico State University of New York at Buffalo,

Buffalo, N. Y. New York University, New York, N. Y. State University of New York at Albany,

Albany, N. Y. Notre Dame University, South Bend, Ind. University of North Carolina, Chapel Hill,

North Carolina University of North Dakota, Grand Forks,

North Dakota North Dakota State University, Fargo, N. D. Northwestern University, Evanston, 111, Ohio State University, Columbus, Ohio Ohio University, Athens, Ohio University of Oklahoma, Norman, Okla. Oklahoma State University, Stillwater, Okla. University of Oregon, Eugene, Oregon Oregon State University, Corvallis, Oregon University of the Pacific, Stockton, Calif. Pennsylvania State Univ., Univ. Park, Pa. University of Pennsylvania, Philadelphia, Pa. University of Pittsburg, Pittsburgh, Pa. Princeton University, Princeton, N. J. Purdue University, Lafayette, Ind. Rensselaer Polytechnic Institute, Troy, N.Y. University of Rhode Island, Kingston, R. I. Rice University, Houston, Texas

r

r

r

r r

r r

r r

r r

r r

r

r

r r

r r

r r r r r r

r r

r r

TABLE XCII--Continued

230

Institution Dean Head University of Rochester, Rochester, N. Y. Rutgers University, New Brunswick, N. J. University of Southern Illinois,

Carbondale, Illinois University of Southern Calif., Los Angeles,

Calif. University of South Carolina, Columbia, S.C. University of South Dakota, Vermillion, S.D. Stanford University, Palo Alto, Calif. Stevens Institute of Technology,

Hoboken, N. J. St. Bonaventure University, St. Bonaventura,

New York St. Johns University, Jamaica, N. Y. St. Louis University, St. Louis, Mo. Syracuse University, Syracuse, N. Y. Temple University, Philadelphia, Pa. University of Tennessee, Knoxville, Tenn. Texas A & M University, College Station, Tex, Texas Christian University, Ft. Worth, Tex. University of Texas, Austin, Texas Texas Woman's Univ., Denton, Texas University of Toledo, Toledo, Ohio Tulane University, New Orleans, La. University of Tulsa, Tulsa, Okla. Tufts University, Medford, Mass. Utah State University, Logan, Utah University of Utah, Salt Lake City, Utah Vanderbilt University, Nashville, Tenn. Virginia Polytechnic Institute, Blacksburg,

Virginia University of Virginia, Charlottesville, Va. University of Washington, Seattle, Wash. Washington State University, Pullman, Wash. Washington University, St. Louis, Mo. Wayne State University, Cleveland, Ohio Western Reserve University, Cleveland, Ohio West Virginia University, Morgantown, W. Va. University of Wisconsin, Madison, Wis. Univex'sity of Wyoming, Laramie, Wyoming

r r r

r r

r r r r

r r r

r r

r

r

r r r r

r r r

r r r

r r r r r

231

TABLE XCII--Continued

Institution Dean Head Yale University, New Haven, Conn. Yeshiva University, New York, N. Y.

r

*The letter r appearing opposite the name of a graduate school in the column under Dean or Head, indicates a response was received from that official of the graduate school.

232

TABLE XCIII

LIST OF SPECIALISTS IN MATHEMATICS EDUCATION

Name Response Received

Allendoerfer, C. B Yes University of Washington Seattle, Washington

Anderson, R. D. . Yes Louisiana State University Baton Rouge, La.

Begle, Edward No Stanford University Stanford, Calif.

Bezuszka, Stanley T Yes Boston College Chesnut Hill, Mass.

Brune, Irvin H Yes Bowling Green State University Bowling Green, Ohio

Buck, R. Creighton Yes University of Wisconsin Madison, Wisconsin

Cohen, Leon W No University of Maryland College Park, Md.

Dubisch, Roy . . . . . . . . . Yes University of Washington Seattle, Washington

Edmondson, Don E Yes University of Texas Austin, Texas

Eves, Howard No University of Maine Orono, Maine

233

TABLE XC111—Continued

Name Response Received

Fehr, Howard Yes Teachers College, Columbia Univ. New York, N. Y.

Guy, W. T. . . No University of Texas Austin, Texas

Henderson, Kenneth B Yes University of Illinois Urbana, 111.

Jones, Phillip S Yes University of Michigan Ann Arbor, Mich.

Jones, Burton W Yes University of Colorado Boulder, Colorado

Johnson, Donavan A. Yes University of Minnesota . Minneapolis, Minn.

Karnes, Houston T. Yes Louisiana State University Baton Rouge, La.

Kelley, J. L No University of California Berkeley, Calif.

Kemeny, John G. . Yes Dartmouth College Hanover, New Hampshire

Lenore, John No University of Chicago Chicago, 111.

234

TABLE XCIII--Continued

Name Response Received

Lloyd, Daniel B No District of Columbia Teachers College Washington, D. C.

Loflin, Z. L. ... . No University of Southwestern Louisiana Lafayette, La.

Meserve, Bruce E. . . . . . . . Yes University of Vermont Burlington, Vermont

Moise.., E. E No Harvard University Cambridge, Mass.

Moore, John C No Princeton University Princeton, N. J.

Mosteller, Frederick No Harvard University Cambridge, Mass.

Nichols, Eugene No Florida State University Tallahassee, Fla.

Olmsted, J. M. H. Yes Southern Illinois University Carbondale, 111.

Payne, Joseph Yes University of Michigan Ann Arbor, Mich.

Peak, Phillip Yes Indiana University Bloomington, Ind.

235

TABLE XCIII--Continued

Name Response Received

Pingry, Robert E. . . Yes University of Illinois Urbana, 111.

Rannucci, Ernest Yes State Teachers College Unior, N. J.

Schaaf, William L Yes Brooklyn College Brooklyn, N. Y.

Smith, Eugene P. . . . . . No Wayne State University Detroit, Mich.

Stephens, Rothwell . . . . . Yes Knox College Galesburg, 111.

Suppes, Patrick Yes Stanford University Stanford, Calif.

Tinnappel, Harold Yes Bowling Green State University Bowling Green, Ohio

Trimble, Harold C. . . . . Yes Ohio State University Columbus, Ohio

Tucker, A. W No Princeton University Princeton, N. J.

Van Engen, Henry . . . . . . . . . . . . . . . . . . Yes University of Wisconsin Madison, Wisconsin

236

TABLE XCIII--Continued

Name Response Received

Walker, R. J . Yes Cornell University Itnaca, N. Y,

Whitmore, Edward H Yes Central Michigan University Mt. Pleasant, Mich.

Young, G. S Yes Tulane University New Orleans, La.

237

TABLE XCIV

COLLEGES, IN THE NATIONAL SAMPLE OF SENIOR COLLEGES, WHICH STRESSED TEACHER EDUCATION*

Institution Secondary Elementary

Augsburg College, Minneapolis, Minn. # # Augustana College, Sioux Falls, S. D. # # American International College,

Springfield, Mass. # # Annhurst College, Woodstock, Conn. # Arkansas A & M, College Heights, Ark. # # Ashland College, Ashland, Ohio # # Atlanta University, Atlanta, Ga. # # Bennett College, Greensboro, N. C. # # Boise College, Boise, Idaho # # Brescia College, Owensboro, Ky. # California State College, California,

Pa. # Central Connecticut State College,

New Boston, Conn. # # College of Saint Teresa, Winona, Minn. # # Concordia Teachers College, Seward,

Neb. # Dominican College, Racine, Wis. "# # Eastern Michigan University,

Ypsilanti, Michigan # # Edinboro State College, Edinboro, Pa. # # Elmhurst College, Elmhurst, 111. # # Friends University, Wichita, Kansas # # High Point College, High Point, N. C. # Kutztown State College, Kutztown, Pa. # # Lindenwood College, St. Charles, Mo. # McPherson College, McPherson, Kan. # # Missouri Valley College, Marshall, Mo. # # Nazareth College of Rochester,

Rochester, N. Y. # # Notre Dame College, St. Louis, Mo. # # Phillips University, Enid, Okla. # # Samford University, Birmingham, Ala. # Southeastern Louisiana College,

Hammond, La. # # Southern State College, Magnolia, Ark. # # State College at Boston, Boston, Mass. # #

238

TABLE XCIV--Continued

Institution Secondary Elementary

State Univ. of New York at Genesco, Genesco, N. Y. # #

Ursuline College, Louisville, Ky. # Villa Maria College, Erie, Pa.' # Westminster College, Salt Lake City,

Utah # # Winona State College, Winona, Minn. # Wisconsin State Univ., Eau Claire, Wis. # #

*The symbol "#" opposite the name of a college in the column under Secondary or Elementary indicates that prepa-ration of teachers of mathematics for that type of school was stressed.

239

TABLE XCV

GRADUATE SCHOOLS IDENTIFIED AS OFFERING PROFESSIONAL DOCTORATES IN MATHEMATICS AND EDUCATION

Graduate School. Degrees Offered

Auburn University . . . . . Ed. D. Auburn, Alabama

Boston University . . . . . Ed. D. Boston, Mass.

Colorado State College Ed. D., Math.; Greeley, Colorado Ed. D., Math.Ed,

Teachers College, Columbia . . Ed. D.; Ph. D. ; New York, N. Y. Ed. D., College

Teaching

University of Florida Ed. D. Gainesville, Florida

Florida State University Ed. D.; Ph. D. Tallahassee, Florida

University of Iowa Ph. D. Iowa City, Iowa

University of Kansas Ph. D. Lawrence, Kansas

Louisiana State University Ed. D. ; Ph. D, Baton Rouge, Louisiana

University of Michigan Ed. D., Teach-Ann Arbor, Michigan ing of Math.;

Ph. D., Teach-ing of Math.; D. Ed., Math.

Michigan State University Ed. D. ; Ph. D. East Lansing, Michigan

New York University Ed. D.; Ph. D. New York, N. Y.

240

TABLE XCV--Continued

Graduate School Degrees Offered

North Texas State University Ed.D., Col-Denton, Texas lege Teaching

Northwestern University . . Ph. D. Evanston, Illinois

Ohio State University Ph. D. Columbus, Ohio

University of Oklahoma Ed. D.; Ph. D. Norman, Oklahoma

Oklahoma State University Ed. D. Stillwater, Oklahoma

George Peabody College Ph. D. Nashville, Tennessee

Pennsylvania State University D. Ed. University Park, Pa.

Purdue University . . . . . Ph. D. Lafayette, Indiana

University of Rochester Ed. D. Rochester, N. Y.

Syracuse University . . . . . Ph. D. Syracuse, N. Y.

University of Tennessee Ed. D. Knoxville, Tennessee

Texas A & M University Ph. D. College Station, Texas

University of Toledo Ed. D.; Ph. D. Toledo, Ohio

University of Wisconsin Ph. D. Madison, Wisconsin

Yeshiva University Ph D New York, N. Y.

BIBLIOGRAPHY

Books

American Council on Education, American Junior Colleges, 6th edition, Washington, D. C., 1963.

American Council on Education, American Universities and Colleges, 9th edition, Washington, D. C., 1964.

Berelson, Bernard, Graduate Education in the United States, New York, McGraw-Hill, 1960.

Guilford, J. B., Fundamental Statistics in Psychology and Education, New York, McGraw-Hill, 1956.

Kenney, J. F. and E. S. Keeping, Mathematics of Statistics, Part II, New York, D. Van Nostrand, 1951.

Long, Luman H., The World Almanac, New York, New York World-Telegram Corp., 1966.

Lovejoy, Clarence E., Love joy? s College Guide, New York, Simon and Schuster, 1962.

Articles

Axelrod, Joseph, "Depth Versus Breadth in the Preparation of College Teachers," Journal of Teacher Education, XIII (September, 1962), 262-267.

Carmichael, Oliver C., "Improving the Quality of Graduate Education for Prospective Teachers," Journal of Teacher Education, XIII (September, 1962), 253-257.

Coon, L. H., "The Doctor of Education in Higher Education-Mathematics at Oklahoma State University," American Mathematical Monthly, LXXII (March, 1965), 306-310.

Hunt, Erling M., "An Ed. D. for College Teachers," Journa 1 of Teacher Education, XIII (September, 1962), 279-283.

241

242

Lindquist, Clarence B., "Mathematics and Statistics Degrees During the Decade of the Fifties," American Mathematical Monthly, LXVIII (August-September, 1961), 661-666.

McGrath, Earl J., "The Preparation of College Teachers: Some Basic Considerations," Journal of Teacher Education, XIII (September, 1962), 247-252.

Millett, John D., "Graduate Education: A Reappraisal," Journal of Teacher Education, XIII (September, 1962), 258-261.

Pfnister, Allan 0., "Historical Perspective and Current Issues in the Preparation of College Teachers," Journal of Teacher Education, XIII (September, 1962), 237-246.

Rees, Mina, "Support of Higher Education by the Federal Government," American Mathematical Monthly, LXVIII(April, 1961), 371-378.

Young, G. S., "The Ph. D. Class of 1951," American Mathemati-cal Monthly, LXXI (August-September, 1.964), 787-790.

Reports

Committee on the Undergraduate Program in Mathematics, The Production of Mathematics Ph. D.'s in the United States, Berkeley, Calif., Mathematical Association of America, 1961.

Conference Board of the Mathematical Sciences, Manpower Prob-lems in the Training of Mathematicians, Washington, D.C., 1963. " ~

Lindquist, Clarence B., Mathematics in Colleges and Univer-sities, Washington, D. C., U. S. Government Printing Office, 1965.

Mathematical Association of America, Official Reports and Communications, American Mathematical Monthly, LXVIII (April, 1961), 402.

Mathematical Association of America, Official Reports and Communications, American Mathematical Monthly, LXX (April, 1963), 473.

243

Mathematical Association of America, Official Reports and Communications, American Mathematical Monthly, LXVIII (June-July, 1961), 589.

Unpublished Materials

Zant, James H., Doctoral Programs in Mathematics and Higher Education, mimeographed bulletin, Department of Mathe-matics and Statistics, Oklahoma State University, Stillwater, Oklahoma, 1966.