71-7437
EBERLE, Betty Jobes, 1938- MATHEMATICS PROGRAM FOR GIFTED HIGH SCHOOL STUDENTS. A PARTICIPANT FOLLOW UP, SUMMERS 1964 THROUGH 1969 AT THE OHIO STATE UNIVERSITY.
The Ohio State University, Ph.D., 1970 Education, general
University Microfilms, A XEROXCompany , Ann Arbor, Michigan
Copyright by
Betty Jobes Eberle
1971
THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED MATHEMATICS PROGRAM FOR GIFTED HIGH SCHOOL STUDENTS
A PARTICIPANT FOLLOW UP
Summers 3.964 through 1969 at The Ohio State University
DISSERTATION •
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University
By
Betty Jobes Eberle, B.S.Ed., M.Ed,
* -X- X X X X
The Ohio State University 1970
Aporoved by
C /
Adviser College of Education PLEASE NOTE:
Some pages have indistinct print. Filmed as received.
UNIVERSITY MICROFILMS. ACKNOWLEDGMENTS
I wish to express my thanks to my advisor, Dr. Harold
Trimble. Without his assistance and confidence in me,
completion of this dissertation would have been impossible.
Special thanks are due to Dr. Harold Brown who not only
served as a member of my reading committee, but also made
available to me the records of the SSTP program from which I
obtained much of my data.
I am grateful to Dr. Herbert Coon v/ho served as a member
of my reading committee. He also was my advisor for my studies
in the area of Teacher Education.
I wish to recognize Dr. Arnold Ross, who lectures so ably to the SSTP participants, for his help with my study.
I am grateful to Dr. Arthur White v;ho kindly helped, me with the computer analysis of my data.
I give very personal thanks to Dr. Leslie Miller. His confidence in me has greatly aided me in my years of under graduate and graduate study. He also served as my advisor for my studies in the area of Mathematics.
I wish to thank my husband. Art, for his oatience during my college study and during the comploti.on of this dissertation.
Finally, I am grateful to my daughter, Linda, who watched her mother's progress all through this study.
11 VITA
September 8, 1938 .... Born, Bartlett, Ohio i960 ...... B.S.Ed., The Ohio State University, Columbus, Ohio
1963-1966 ...... Teacher of Mathematics West High School, Columbus, Ohio
1964 ...... M.Ed., The Ohio State University, Columbus, Ohio
1966-196 7 ...... Academic Year Institute at The Ohio State University, Sponsored by The National Science Foundation
1967-1966 ...... Teacher of Mathematics West High School, Columbus, Ohio
I96S-I97O ...... Teaching Associate, Department of Mathematics, The Ohio State University, Columbus, Ohio
FIELDS OF STUDY
Major Field; Mathematics Education
Studies in Mathematics Education. Professor Harold C. Trimble
Studies in Mathematics. Professor Leslie H. Miller
Studies in Teacher Education. Professor Herbert L. Coon
] 11 TABLE OF CONTENTS
ACKNOWLEDGMENTS ...... il
VITA ...... ill
LIST OF T A B L E S ...... vi
Chapter
I. INTRODUCTION ...... 1
Background for the Problem Purpose of the Study Specific Objectives of the Study Scope of the Study Organization of the Dissertation
II. REVIEW OF RESEARCH...... 7
Special Needs of Mathematically Gifted Students The Student Science Training Program
III. DESIGN OF STUDY ...... 17
Development of the Questionnaire The Sampling Procedures Student Records Record of Data
IV. RESULTS FROM OBJECTIVE D A T A ...... 23
Description of Participants in Sample Comparison of Sample with Total SSTP Population at The Ohio State University Present Status of the Participants Recruitment Evaluation of the Program Expectations versus Exneriences Success at End of Summer An Examnl.e of a Regression Analysis
V. RESULTS FROM SUBJECTIVE D A T A ...... 66
An Introduction Student Views of the Goals of the Program Faculty Views of the Goals of the Program Parents' Vi'"vs of the Goals of 'Jie Program i V The Per.t Thnn% about the Program The Worst Thin% about the Program Suggestions for Changes in the Program Commuters Further Comments
VI. SUMMARY AND CONCLUSIONS......
Summary and Conclusions Recommendations for Further Study
APPENDIX
A ...... è 9
B ...... 97
C ...... 99
D ...... 106
E ...... log
F ...... 115
G ...... 122
H ...... 126 1 130
J ...... 134
K ...... 147
BIBLIOGRAPHY ...... 156
V LIST OF TABLES
Table I. Grade Conpletod in Hiph School ...... ?!\
2. Type of High S c h o o l ...... 24
3. Size of High S c h o o l ...... 25
h. Geographical Distribution of the Students .... 26
5. Participation in Special Summer Programs .... 27
6. Participation in Mathematical Competitions . . . 2?
7. Participation in Science Fairs ...... 28
8. Mathematical Reading ...... 30
9. Knowledge of How Mathematics is U s e d ...... 31
10. Sex of the Participants...... 33
11. Geographical Location of High School ...... 33
12. College Majors of Participants ...... 35
13. Amount of Education Completed ...... 36
14. Acquaintance with Previous Participant ...... 37
15. Reason for Choosing Program at Ohio State University...... 38
16. Person Most Influential in Decision to Apply . . 39
17. Student Ratings of Importance of Aspects of P rogram ...... 41
18. Item of Greatest Importance and Greatest Hindrance...... 42
19. Student Evaluation of the P r o g r a m ...... 44
20. Evaluation of Counselors...... /j5
21. Usefulness of Program for Making You Use Your Full Potential ...... 46
22. Agreement - Disagreement Statements ...... 47
23. "I Found Wo Time for S l e e p " ...... 52 vi LIST OF TABLES (CONTINUED)
Tnblo Paco ?J\-. "I Alv/ays Felt R u s h e d " ...... 53
25. "The Counselors Were a Real H e i n ...... 5A
26. Exnectations and Experiences , ...... $6
27. Correlation Between Rank and Three Statements . . 60
2B. 02R Stepwise Repression with Rank on Test Scores for Dependent Variable ...... 63
29. 02R Stepwise Regression with Student Rating of Imnortance of Intellectual Challenge as Denendent Variable ...... 64
Vll CHAPTER I
INTRODUCTION
Background for the Problem
The Summer Science Training Program for High-Ability
Secondary Students, SSTP, sponsored by the National Science
Foundation, began in the summer of 1959. This program was intended "to provide the superior high school student with educational experience in science and mathematics beyond that normally available in high school courses". In 1969 there were 112 such programs at various educational insti tutions in the United States.
In 195#, Dr. Arnold Ross initiated an SSTP program at
Notre Dame University as an experiment. He offered inten sive mathematical experience to talented young prople. The following year, 1959, the program was no longer experimental but was well established. It lasted at Notre Dame University under the direction of Dr. Ross from 1959 through 1963. Then
Dr. Ross established the program at The Ohio State University where it has been in operation since 1964.
During the summer of 1969, this researcher became interested in the program. She asked who these young people were, what the program was trying to do, what happened to the participants after their summer in college, what was the
1 2
impact of the program on the participants.
The general feeling of the people involved in the
program at The Ohio State University was that it was "useful".
They were sure it made an "impact on the lives of the young
people involved". No study had been made at this university.
Yet each year high school students make about I6OO inquiries.
Of these, 250 to 300 complete application forms. Of these,
60 participants are selected. These students are given
scholarships by the National Science Foundation so that they
can afford the experience. Very competent professirs spend many hours making this program work.
Purpose of the Study
The purpose of this study was to carry out a partial evaluation of the Summer Science Training Program, SSTP, which is directed by Dr. Arnold Ross and Dr. Harold Brown at The Ohio State University.
This study examined the students who have participated in the summer program at this university to see what tyne of student attended the program.
It attemnted to determine the goals of the program at this institution. Here the researcher was interested in the stated goals of the urogram as expressed by the directors and as expressed in the literature. The researcher was also interested in learning the goals as expressed by the unrtici- uants. This study examined the successes or failures of the 3 participants in terms of these goals. This involved personal and academic success or failure.
The study examined the present status of the past participants in an attempt to determine any long-range effects of the program.
Finally, the study looked at the recruitment of the participants.
Specific Objectives of the Study
Specifically, the study was an assessment of the
Summer Science Training Program for High-Ability Secondary
Students which was conducted at The Ohio State University from 1964 through 1969 under the direction of Dr. Arnold
Ross and Dr. Harold Brown, in terms of the goals stated by its directors and in terms of the goals the participants hoped to achieve when they were chosen as participants.
This study looked at the following areas;
1. Goals of the Program.
The study sought to determine the goals from three points of view. First it determined the goals as expressed by the faculty involved. Second, it determined the goals expressed in the recruiting material issued by The Ohio State
University and by the National Science Foundation. Third, it attempted to determine the goals of the participants when they applied for the program.
2. Recruitment of the Participants. h
The study examined the recruiting procedure. It
examined how the students learned about the program and how
the participants were chosen. It described some of the
personal and academic characteristics of the participants.
3. The Successes and Failures of the Participants.
The study attempted to discover if the participants
succeeded or failed to achieve their goals.
4. The Present Status of the Participants.
The study attempted to discover what the people who
participated in the program have done since they participated
in the program in order to determine the long-range effects
of the program.
Scope of the Study
This study dealt with the program at The Ohio State
University from 1964 through 1969.
Information was drawn from four sources;
1. Information included with the application forms.
2. Information gathered through questionnaires.
3. Information included in parents’ letters.
4. Information obtained from interviews with faculty members.
Because tv;o of the four sources consisted of information
in files, some information was not available on all partici pants. For example, each year the parents were invited to write a letter and comment on the program if they wished to do so. Many parents did not write a letter. Also, when the 5 students applied for the program, their high schools sent official transcripts of their grades. Since many of the participants were tenth grade students, their transcripts did not yet include scores from the Preliminary Scholastic
Aptitude Test (PSAT) of the College Entrance Examination
Board.
Data was collected in two forms— objective and sub jective. The objective data such as test scores, size of high school, and objective answers on questionnaire items were treated statistically. The subjective data such as comments from parents, comments from students, and comments from instructors were treated in a subjective manner in a separate chapter.
In this study, questionnaires were sent to 120 of the
429 students who took part in the program over the six year period.
Organization of the Dissertation
This first chapter has provided an introduction to the study by describing the background of the problem and the objectives of the study. Chapter II will review selected research that has been done in the area of education for gifted students. Chapter III will be concerned with the design of the study. Chapters IV and V will give results obtained in the study. Chapter IV will give results obtained from ob jective data while Chapter V will give results from data 6 that was subjective in nature. Chapter VI will give a summary and list any conclusions obtained from the study. Suggestions for further study will also be given in Chapter VI. CHAPTER II
REVIEW OF RESEARCH
This chapter contains a review of selected research concerning the education of superior students. It concentrates on research in two major areas; (1) special needs of mathe matically gifted students and (2) previous studies made of the Student Science Training Program.
Special Needs of Mathematically Gifted Students
In Research on the Academically Talented Student,
Anuerson points out that "an academically talented group is not by definition a homogeneous group. Tremendous differences may exist between the highest and lowest members of such a group". (1, p. 23) Bray notes that "at one time the gifted individual was expected to be a versatile performer. Today, however, he may be viewed as especially- gifted only in a particular respect". (2, p. 17) These two statements illus trate the difficulty involved in identifying the pupil who is highly talented and, in particular, who is highly talented in one field.
Much study has gone into the characteristics of the superior student. He has been described in terms of his personal characteristics, his reading ability, his interests,
7 Ills school cclii cvrsriopt, his scores on IQ tests, his person ality traits, his types of play, his behavior, and his adjustment problems. These topics are discussed in The choloyy of ICxcentional Children by Garrison and Force. (C, p. 154-179)
If the reader wishes to delve more deeply into the tonic of the gifted child he may consult the bibliography on pages #1-92 in (l) or the bibliography on pages 349-164 in
(l6). In this study we are specifically interested in the education of mathematically superior students.
In Mathematics for the Academically Talented Student,
Hlavaty states that pupils with potential for mathematics will fall into at least four different groups:
Group A consists of students readily identifiable because of high general intelligence, outstanding accomplishment in all courses throughout their chool. careers, and deep interest in and satisfaction derived from the study of mathematics. Students in this category are usually highly motivated to continue with all the mathematics available to them at the secondary level. Group B consists of students with high measurable ability, but whose performance in mathematics has not been commensurate with their ability. Possible reasons for their underachievement are: inadequate mot i vat i.on, a negative attitude— sometimes due to poor instructional procedures; lack of insight into the areas of learning for which mathematics is required. Group C consists of students from i.ov? socio-economic areas in which environmental inf]nonces in the community, in the homo and even in the school have served to denri.ve studenl,s of onportunities to develon innate ability to tlie extent that it can be measured accurately by our present evaluation instruments. More it should be reco/yiised t.hat intelligence tests reveal to a large degree only "developed ability", not innate intelligence. I''inal ly, there is Groun D, student:;! of Iri.^di general intcll :i.genco, whoso general aclri evement. :in tlioir liigli school course is mediocre, but who, because of motivation and special talents, have achieved outstandingly in mathematics. It is clear, from these considerations, that if only those students in Group A were selected for intensive work in mathematics, we would exclude many who with proper motivation and skiliiul guidance, might later prove to be our most promising college- bound students. (10, p. 10-11)
This report by Hlavaty (10) and also the report edited by
Anderson (1) deal with methods of identifying academically talented and specifically mathematically talented students.
After identifying the mathematically gifted student, special provision must be made for his needs. Next we consider what some of these needs are.
Pearson (14) speaks of a special need. He was consider ing that few students take college mathematics. Fewer still major in mathematics in college. He observes "The aesthetic appeal of mathematics is glimpsed by fewer still. Although high school students do meet one elegant branch of mathematics
(Euclidean geometry), any potential interest is usually snuffed out by teachers who employ either the rote approach or the meat-cleaver method. Introductory mathematics courses at university level also tend to be low on intellectual appeal. Thus, in practice, only those who specialize in math ematics in their university careers are able to enter the realm of aesthetic appreciation". This "aesthetic appreciation" is a need of the superior student.
Hlavaty mentions more special needs.
Bright students are particularly stimulated by working with others of like ability. In such a 10
situation they cannot achieve well without working near capacity; too frequently, near-capacity effort is not required when they find themselves in un differentiated groups. In being with other talented students, bright students also gain in worthy attitudes, such as greater humility. Too often a student who constantly achieves well in a group where he is outstanding but is not challenged to his best efforts will have an inflated notion of his abilities. (10, p. 16)
In this same work the author states
The academically able have a need for, and derive great profit and stimulation from, contact with other young people of like interest and drives and with adults whose professions involve day-by-day uses of mathematics, such as mathematicians, physicists, scientists in general and others. (10, p. 33)
Some people have noiced the opinion that separating
the superior students from the average and below-average
students, and treating them in special ways will cause them
to develop "superiority complexes". According to Garrison
and Gray
Where the child is educated in an environment of his peers, he is far less likely to develop into an intellectual snob than when he is plugged into a situation where, coming to realize that he is by far the mental superior of most of his classmates, he begins also to feel that he is being "held back" in his ovm educational progress by what he cannot help to regard as their "stupidity". {-J, p. 468-69)
These authors go on to say
The superior child should understand his capabilities and should be guided in setting goals in harmony with his abilities. Failure to do this leads to personal maladjustments and a waste of human resourses. (9, p. 468-69)
Writing in 1957, DeHaan and Havighurst (4, p. Iv) also
expressed the need for the gifted child to realize his potential. They stated that under present conditions less 11 than half the gifted children in our schools "will realize their potentialities and become distinguished persons, contributing in an outstanding way to the welfare of their society and gaining for themselves the satisfaction of excellent performance".
Terman also asserted the need to stimulate the gifted child. He said "no method or combination of methods for the gifted well succeed that does not awaken their intellectual ambition". (13, p. 18)
This idea of challenge was also expressed by the committee preparing Education of the Gifted. They said
Sometimes curriculum offerings are restricted in scope; sometimes the quality of instruction is poor; or of poor quality; but probably the most frequent type of educational inadequacy is the failure to challenge the gifted students to achieve up to capacity. (7, p. 29)
Not only does the gifted child need to be challenged, but he must not be hampered by repetition. Hlavaty states
Many students of creative potentialities for mathe matics have been given a distaste for the subject by being forced to submit to routine repetitions and boring details and computations in standard courses which are geared to the pace of average or below- average students. (10, p. l6)
A final need of the gifted child which was stated by many authors was the need for a special type of teacher.
Hlavaty states
The key consideration in any educational program is the teacher. The teachers of talented students must understand the capacities and talents of their students, as well as of all students; they must be able to give the students the stimulus and guidance 12
necessary for effective and enriched learning. (10, p. 21)
Later in that same work he says
Of course, the crucial element in providing a program for the talented is the teacher. In general, it is not true that bright students can and will learn in spite of the teacher. Especially with the talented it is important to lead them to rediscover or re create some of the mathematics they are learning. It is through such rediscovery or re-creation that boys and girls first experience the delight in research that will lead some of them to find a satisfying life in a career in mathematics. (10, p. 39)
Nicholas Hobbs also states the need for a good teacher.
He says
The ability to teach superior students effectively is a personal skill which some teachers possess and some do not. Intellectual achievement cannot be stimulated by teachers who have not themselves experienced intellectual achievement. (11, p. 266)
In summary, the different writers have expressed several needs of mathematically superior students. These are;
(1) Need
(2) Need
(3) Need
(4) Need
(5) Need
(6) Need
(7) Need
(6) Need
(9) Need 13
The Student Science Training Program
The Student Science Training Program is described in the Guide to Programs issued by the National Science Found ation this way:
The National Science Foundation awards grants that provide advanced educational opportunities for superior secondary school students. These activities, usually conducted at the grantee institution, en courage student participation in either scientific research or special course work....Course-oriented projects present subject matter at a level more advanced than can be expected in high school. (12, p. 43)
This brief description of the national program in general does not focus on the Ohio State University pro gram in particular. A paper issued by the current director.
Dr. Harold Brown, describes that program this way:
As in the past we used Number Theory as the basic vehicle for the development of the student’s capacity for observation, invention, the use of language, and of all those traits of character which we refer to as intel lectual discipline. (3)
This paper goes on to describe the objectives of the number theory course:
It is our aim to develop attitudes as well as skills, to introduce the students to in intelligent use of algorithms as well as to the mastery of the underlying theory, and to make use of number theory not only as an important stepping stone to the study of both analysis and algebra, but also as an environ ment in which we can exhibit a whole gamut of vital dilemmas which confront any scientist in any field at one time or another. From the very beginning the student is given the opportunity to develop his powers of observation, to experiment, and to discover significant relation ships between the objects of his experimentation. The student learns to use the devices of counter example to destroy the untenable conjectures, and as 14
hic experience grows he learns the meaning of providing the security of a proof for the surviving conjectures. As is natural in all fields of human activity the word labels follow recognition of phenomena, and the incentive for the precise and concise use of language comes from the desire and the need to share one's experience with others. (3)
This researcher does not think the program at The Ohio
State University has been adequately described until the
teaching method of Dr. Ross has been considered. His
method might be called the "Language Method" because as
Dr. Ross describes in his paper The Shape of Our Tomorrows
(13), "We borrowed from our linguistic friends the technique
of introducing language through usage". In this paper he was describing his techniques in a program called New Careers, but it is the same technique used in the SSTP program.
Dr. Ross states in this same paper, "It is necessary from the very beginning to make the student conscious of the prob
lem of developing a means of sharing the newly gained
experience through the building of adequate resources of of vocabulary and idiom".
In order to discover any previous research done on the
Ohio State University SSTP program or on any similar program at another institution, the researcher wrote a letter of
inquiry to the National Science Foundation. The National
Director stated that there was only one known study of an
SSTP program in the field of mathematics. It was a study of the program at the University of Texas which operated until
1,'6S under the direction of Dr. Hyman J. Ettlinger. This 15 program has not operated since his retirement in 1968. No
study had been made of the program at The Ohio State Univer
sity.
Two studies were made under National Science Foundation contracts. These were done by Harold A. Edgerton.
Impacts (5) "is a study of the impact 147 Summer Science
Programs supported by the National Science Foundation made upon the participants and their schools". Data were collected before, during, and after participation from a sample of 18 of the programs diversified as to program type and geographic location. Both students and high school teachers completed questionnaires before and after the program and experienced observers visited and reported on the program as they observed it in progress. This study, as already stated, did not examine the program at one school in depth. Also, within the sample of l8 programs, many were science programs rather than math ematics programs.
Three Years After SSTP (6) is an attempt to answer "To what extent is the Summer Science Training Program for High
Ability Secondary Students attaining its purposes?" It summarizes a follow-up study of the participants in the I960
SSTP programs. The data was collected from questionnaires which were mailed to the participants in 19'63— three years after their participation. 7028 questionnaires were mailed.
As in the previous study, the participants represented programs at many different colleges and programs which were either 1 6 science or mathematics or a combination of both.
With this brief survey of the literature as background,
Chapter II proceeds to the design of the study. It will describe the development of the questionnaire, the sampling procedures, and the collection of the data. CHAPTER III
DESIGN OF STUDY
This chapter includes the development of the question
naire and the sampling procedures.
Development of the Questionnaire
Major steps in the development of the questionnaire
consisted of observation of SSTP classes, interviews with
participants, counselors, and faculty, determination of
major areas of interest, and the construction of the
questionnaire items.
Before developing a questionnaire the researcher
attempted to become very familiar with the program. She
attempted to learn what the students experienced during the summer program. She attempted to learn what caused the students problems and what the students considered
important. This was necessary before she could determine
in what major areas of the program she wished to concen trate her study.
For three weeks during the summer of 1969 the researcher observed the Number Theory lectures delivered by Dr. Ross.
She sat in the back of the lecture room and observed the classroom proceedures, watched the facial expressions, listened 17 lô
to student comments, and solved some of the homework problems.
Next the researcher interviewed 2? of the participants.
With the approval of Dr. Ross, she gathered groups of eight to
ten students and talked with them in informal sessions in the
lounge of the dormitory. Because the researcher was attempt
ing to learn what was important to the students, she did not try to structure the discussions. The students expressed their
feelings, reacted to each other’s comments, and talked about the things that were causing them difficulty. Faculty and
counselors were not included in these discussions.
After listening to the participants, the researcher interviewed another group of participants who were attending the program for a second or third year. These were students whose experiences had been satisfactory enough the first year that they applied to return for another summer. They could look back at the previous year’s experience as a completed course and express the things about the program that they still considered important after a year at home.
This time the researcher did interject some questions into the discussion. She had the second and third year partici- react to some of the ideas expressed by the first year par ticipants.
Next the researcher talked with nine of the counselors who gathered as a group in the dormitory lounge. Since the counselors live in the dormitories with the students and help them with their personal and academic problems, the 19
researcher asked them to explain just what a counselor does.
She asked them what, in their view, were the problems of the
students. She asked them to explain what they thought the
program was attempting to accomplish.
Finally, the researcher talked with a group of faculty
members. This group included Dr. Ross and the recitation
instructors. She listened while they expressed what they
considered to be the important gains the students would make during the summer. They expressed the difficulties the
students were experiencing. They expressed their views on what the program was trying to accomplish.
The researcher then began to design a questionnaire which would answer these questions;
1. What is the present status of the participants?
2. How did the participants learn about the program?
3. Why did the participants choose the program at
The Ohio State University?
if. Did the participants consider the program a
success or a failure?
5. How would the participants evaluate the different
aspects of the program?
6. Before the students attended the pro grain, what
did they expect would take place?
7. How correct wore the participants’ expectations
of what would occur?
A first draft of the questionnaire was written. It 20 was read by Dr. Harold Trimble, Dr. Harold Brown, Dr. Herbert
Coon, and several graduate students in the College of
Education. Their comments and criticisms were considered and the questionnaire was revised.
The Sampling Procedures
It was decided to send questionnaires to 120 participants.
20 participants were selected from each of the years from
1964 through 1969. Within each year the selection was random.
Since some of the participants each year were attending for their second or third summer, care was taken to choose only from the first year participants. The 120 participants represented approximately 28^ of the total of 429 who had attended as first year students during the 6 year period.
Addresses were obtained from the SSTP records. A cover letter was composed which explained the purpose of the questionnaire. The questionnaire, the cover letter, and a stamped return envelope were enclosed in a packet and mailed to each of the 120 members of the sample. S6 completed questionnaires were returned. This represented a return of approximately 1 2 i o of the questionnaires.
Student Records
When each participant initially applied for the program, a file was begun. Into this file were put his application form which contained personal information and a test of his mathematical ability, letters of recommendation, and a copy 21 of his high schoo]. transcript. From these records, the re searcher recorded the following items of information for each of the 120 participants in the sample :
1. Score on mathematics test 2. Sex
3. Birth date (month and year)
h . Type of high school he attended
5. Grade completed before attending the program
6. Size of high school
7. Geographic area of residence
Ô. Amount of previous experience in special summer
programs
9. Amount of previous experience in mathematical
competitions
10. Amount of previous exnerience in mathematics clubs,
science fairs, etc.
11. Student’s choice of future college major (if he had
made a choice)
12. A judgment about how much mathematical reading the
student had done. This judgment was based on Question
IS of the application form. (See Appendix A for a
sample application form.)
13. A judgment about the student's mathematical experience.
This judgment was based on Question 1/ of the appli
cation form. (See Appendix A for a sample applica
tion form.) 22
14. The student’s IQ score
15. The student's scores on the PSAT test
16. The faculty evaluation of the student's work
during the summer.
In addition to this information, one further piece of
information was available for some of the students.
Following the summer a letter was sent to the parents of the
students asking that they write and comment on the influence
the program had on their son or daughter. Not all of the
parents responded, but some letters were available.
Record of Data
The answers to open-ended questions on the question naire were listed in sentence form. The information taken
from the parents' letters was listed in this way also.
This was used as subjective data.
The items of objective information from the question naire as well as from the student records were converted to punch card data and analyzed by computer methods.
With the completion of the description of the Design of the Study, Chapter IV is now devoted to presenting the objective data collected. Then, in Chapter V, the subjective data is summarized. CHAPTER IV
RESULTS FROM OBJECTIVE DATA
In this chapter, results are presented which were obtained
from data that was objective in nature. The information was
punched on data cards and computer methods were used to
analyze it. Later, in Chapter V, the results from the more
subjective data is presented.
Description of Participants in Sample
During the six years from 1964 through 1969, there were
429 first year participants in the program. Several of the participants returned for a second or third year, and some of them became counselors later. For this study, twenty people were chosen at random from the first-year participants in each of the six years to make a total sample of 120 people.
When the questionnaires were returned, three of the participants indicated that they did not complete the entire program. For this reason they were eliminated from the
sample, and the sample was reduced to 117 people.
The sample was composed of 99 boys and IC girls. Most of them had just completed the tenth or eleventh grade of high school at the time of participation in the program.
Table 1 shows their educational level just prior to the program.
23 24
TABLE 1
GRADE COMPLETED IN HIGH SCHOOL
Year Year of Attendance 8 9 10 11 12
1964 1 8 9 2
1965 1 3 14 2
1966 9 7 4 1967 1 8 10 11
1968 1 9 9 1
1969 6 6 5
Total 1 3 43 55 15
The members of the sample were enrolled in tree types of high schools as shovm in Table 2.
TABLE 2
TYPE OF HIGH SCHOOL
Type of High School Year of Attendance Public Parochial Private (Non- Denominational)
1964 14 k 2
196$ 13 4 3
1966 16 4 0
lv67 17 2 1
1968 15 1 4
1969 1/, 2 1
Total 89 17 11 25
They came from high schools of many different sises
as shown in Table 3. The mean size was in the range of
1000-14V9 pupils.
TABLE 3
SIZE OF HIGH SCHOOL
Number of Pupils Enrolled in the High School Year of 0- 100-- 500- 1000- 1500- 2000- 2500- 3OOO& Attendance 99 499 999 1499 1999 2499 2999 over
1964 1 7 8 1 1
1965 3 3 8 5 1
1966 4 5 5 2 4
1967 2 3 8 2 2 3
1968 4 4 3 4 2 3
1969 1 1 2 3 4 3 2 1
Total 1 11 23 35 21 11 2 11
They came from many different states of the United
States and also from Canada. The states were grouped accord ing to the regional accrediting agencies into seven groups.
(See Appendix D for the states within each jurisdiction.)
Table 4 shows the geographical locations from which the students came. 26
TABLE 4
GEOGRAPHICAL DISTRIBUTION OF THE STUDENTS
Regional Year of Attendance nccx'euxuj-ug - Agency lv&4 196$ 19 6 6 1967 1968 1969 Total
Middle States 3 4 9 5 7 6 34
New England 1 1 2 1 5
North Central 17 1$ 9 15 7 6 67
Northwest
Southern 1 1 3 2 7
Western 1 1
Canada 1 1 1 3
For most of the students, this was their first experience in a special summer program in any discipline. Eighty-three of the students had not participated in any special programs previously and 2S had participated in one other special program. Table 5 shows the previous experiences of the participants in special summer programs.
The participants had more experience in mathematical competitions and science fairs in their home schools and states than in special summer programs. Table 6 shows the number of times the students had participated in mathematical competitions. Table 7 shows the number of times the partici pants liad entered projects in science fairs. 27
TABLE 5
PARTICIPATION IN SPECIAL SUMMER PROGRAMS (NSF or Other)
Number of programs participated in previously 1 ÜC11 U1 Attendance 0 1 2 3
1964 14 5 1
1965 16 4
1966 15 3 1 1
1967 14 4 2
1968 13 6 1
1969 11 6
Total 83 28 5 1
TABLE 6
PARTICIPATION IN MATHEMATICAL COMPETITIONS
Number of Times Year of Attendance 0 1 2 3 4 5 6 More
1964 10 5 1 2 1 1
lv65 7 5 4 3 1
lv66 4 8 5 1 1 1
1967 9 5 4 1
l;68 4 10 5 1 1
1969 h 4 4 2 1 1
Total 38 37 23 y h 1 3 1 28
TABLE 7
PARTICIPATION IN SCIENCE FAIRS
Number of Times Year of Attendance 0 1 2 3 4
1964 14 5 1 1
1965 12 4 3 1
1966 4 11 1 1
1967 11 7 2
1968 11 8 1
1969 9 4 1 2
Total 61 39 11 4 1
The next three items of information came from the appli cation form. A sample application form for 1969 is given in
Appendix A. The reader should realize that the application form varied from year to year. This form was essentially divided into two parts. The first part, which dealt with personal information about the participant, was, except for a few minor changes, constant from year to year. In some years there was a variation in the order of the questions from the previous year. The second part of the application form, which was a set of problems for the student to solve, was changed each year.
Question I? (of the I;69 application form) asked, "Where does mathematics fit into your overall interests? Tell in 29
your own words about your plans and ambitions." In response
to this question, 54 students indicated they planned to major
in mathematics in college. Nineteen indicated they planned to major in a physical science or engineering field. Forty-
one did not predict a college major. Two students predicted
careers in social science and education.
In the application form, Question 1Ô asked, "Is there a mathematical question or a mathematical problem which you found particularly interesting or challenging? Tell of this
in your own words." This researcher used the answers to this question as an indication of how much mathematical reading the student had done. She read the responses and rated them on a scale of 0, 1, 2. If the student said "No", left the question blank, or alluded to a mathematical question which admited an obvious answer, he was given a rating of 0. If the student mentioned a question which would arise in the context of a high school course, he was given a rating of 1.
If the student indicated that he had done some significant work on a problem outside of his regular school program, he was assigned a rating of 2. Table 8 shows the ratings of the students in the sample. The mean of the ratings was .78.
This researcher wishes to point out that two important things enter into the results shown in Table 8. (1) If the student didn't answer the question or said "No" because he might not have considered his mathematical investigations
"important", his response v/as rated as 0. Hence, perhaps 30
the G response tends to be heavy. (2) It was the researcher's
hypothesis that this question on the application form is a
measure of how much mathematical reading the student had
done. Perhaps this is not a good question to use for
measuring reading breadth.
TABLE è
MATHEMTICAL READING
Rating X Uili U X *" Attendance 0 1 2
1964 12 4 4
196$ 7 9 4 1966 6 6 8
1967 12 6 2
1968 13 4 3
1969 4 4 8
Total 54 33 29
Question 19 (of the 1969 application form) asked, "Do you think you need a first class mathematical education to master the theory of physics, chemistry, biology, economics?
Would you mention, if you can, some mathematical ideas which you consider important for these fields." This researcher considered the answers to this question to be an indication of the students’ experience with subjects that use mathematics.
Entering into their responses to this question would be tlie 31
quality of the high schools from which they came. Some
schools don’t offer economics. Some schools offer chemistry
and physics, but only at a very elementary level. Other
schools give quite rigorous courses in all these subjects.
A second factor which would enter into their responses is
the grade levels of the students.
This researcher read the responses to Question 19 and
rated them on a scale of 0, 1, 2. If the student showed
little knowledge of how mathematics is used or did not answer
the question, he was assigned a rating of 0. If he gave a
response which indicated a knowledge a high school student
would show if he had taken high school courses in these
subjects, he was assigned a rating of 1. A rating of 2
indicated the student was quite knowledgable about the uses of
mathematics. Table 9 shows the ratings of the students in
the sample. The mean of the ratings was .84.
TABLE 9 KNOWLEDGE OF HOW MATHEMATICS IS USED
Rating Year of Attendance 0 1 2
1964 6 10 4 1/6$ 6 12 2 1966 5 10 5 lj67 10 6 3 1>^8 10 6 4 1969 6 4 7 Total 43 48 2$ 32
The students in the sample were superior students intellectually. Intelligence Quotient (IQ) scores were included in the records of 65 of the students. These scores had been obtained by using a variety of different intelligence tests. As they were listed, they ranged from 109 to 162 with a mean IQ of 13$. Forty-two of the students had taken the Preliminary Scholastic Aptitude Test (PSAT) and their scores were included in their records. On the verbal part of the PSAT test the scores ranged from 39 to 77 out of a possible maximum of SO. The mean score of 62 would put them in the >'Sth percentile of all juniors and seniors in the country. On the non-verbal part of the PSAT test the students had scores ranging from $0 to SO out of a possible maximum of So. Here the mean score was 71. This would place them in the 99+ percentile of all high school juniors and seniors in the country.
Comparison of Sample with Total SSTP Population at The Ohio State University
An attempt was made to learn how representative the sample was. The names had been chosen at random within each year in order to get a representative sample. As an in dication of how the sample compared to the total population of SSTP participants at The Ohio STate University, the researcher compared the sex and geographical areas of the sample and the total population. Table 10 shows a comparison of the two groups in terms of sex. Table 11 compares the geographical locations of their high schools. 33
TABLE 10
SEX OF THE PARTICIPANTS
Sex Sample Total SSTP Population at The Ohio State Univ.
Female 1 Û (15.4/0 87 (20.3/)
Male 99 (84.6/) 342 (79.7/)
Total 117 429
TABLE 11
GEOGRAPHICAL LOCATION OF HIGH SCHOOL
Accrediting Agency Sample Total SSTP Population at The Ohio State Univ.
Middle States 34 (29.1/) 103 (24.0/)
New England 5 ( 4.3/) 9 ( 2.1/)
North Central 67 (57.3/) 264 (61.5/)
Northwest 0 4 ( 0.9/)
Southern 7 ( 6.0/) 35 ( 8.2/)
Western 1 ( 0.9/) 2 ( 0.5/)
Canada 3 ( 2.6/) 12 ( 2.8/)
Total 117 429
These tables show that the sample population and the total population do compare closely. Table 10 shows that in the total SSTP population at The Ohio State University,
'T:.l'/o of the participants are boys. Table 11 shows that the majority of the participants at The Ohio State University 3/4 came from two areas of the country— those states whose schools are accredited by the Middle States Association of
Colleges and Secondary Schools and those states whose schools are accredited by the North Central Association of
Colleges and Secondary Schools. (Refer to Appendix D to learn which states are in these jurisdictions.)
Present Status of the Participants
Most of the participants are still in school. Of the
è k people who returned questionnaires, 75 indicated that their chief present activity was going to school. The other
9 were gainfully employed. Table 12 indicates their college majors if they have a major. (See Appendix E for a list of the colleges they are attending).
Table 12 indicates that each year a smaller number are choosing mathematics for a college major. Sixteen participants were still attending high school or had just finished.
On page 36, Table 13 shows the amount of education com pleted by the participants. This table reflects the amount of time that has elapsed since the students participated in the program. 35
TABLE 12
COLLEGE l'IAJORS OF PARTICIPANTS
Year of Attendance Major 1964 1365 1966 1^67 1/68 196; Total
Mathematics Computer Science 12 S s 6 3 0 37
Physical Science Engineering Chemistry 2 3 3 3 2 0 13
Biological Science Pre-Medicine 1 0 0 3 0 1 4
Social Science Anthropology 0 0 1 0 0 1 2
Medicine 1 0 0 0 0 0 1
Languages Humanities 0 1 2 0 2 0 5
Administrative Science Accounting 1 0 0 1 0 0 2
Home Economics Food Technology 1 0 0 0 0 0 1
High School 0 0 0 0 6 10 16 36
TABLE 13
AMOUNT OF EDUCATION COMPLETED
Education Completed Year of Attendance 1964 1965 1966 1967 1968 1969 Total
Still in High School 6 è 14
High School Graduate 2 2
1 Year of College 1 7 9 2 19
2 Years of College 1 1 7 7 16
3 Years of College 1 3 3 7
4 Years of College 3 5 2 10
Bachelors Degree S 3 11
Masters Degree 3 1 h
Recruitment
The students were asked, "How did you first hear about the Summer Science Training Program in mathematics?" Most of them heard about it in one of three ways. Forty-three learned about the program from a teacher. Nineteen learned from another student. Thirteen learned from another source such as a pamphlet. Only 7 were told about it by a guidance counselor. Tv:o students saw a notice on a bulletin board or in a newspaper.
In order to learn how much the previous participants were promot;ing the program, the students were asked if they 37
knew a person who had participated in the program before
they applied. Table 14 summarizes their replies.
TABLE 14
ACQUAINTANCE WITH PREVIOUS PARTICIPANT
Response Year of Attendance No Yes
1964 16 1
1965 10 3
1966 10 3
1967 9 5
196Ü 7 10
1969 7 3
Total 59 25
This table shows that as the program was in operation longer, more of the students had talked with previous participants before applying.
The next question considered was, "Why did you apply for the program at The Ohio State University?" The responses are recorded in Table 15. TABLE 15
REASON FOR CHOOSING PROGRAM AT OHIO STATE UNIVERSITY
Year of Attendance Reason 1964 1,65 1/66 I /67 lv68 196v Total
Interest in courses offered 17 7 10 8 12 7 56
Reputation of the University 1 4 0 0 4 1 10
Near Home 6 5 2 0 3 0 16
Chance to get away from home 2 5 3 1 4 3 18
Suggested by previous participant 0 1 2 4 5 1 13
Good chance of acceptance 1 0 2 1 1 1 6
Only one the teacher/ counselor had information about 1 0 0 0 1 0 2
Other 1 3 3 5 1 4 17
This table shows that many of the 84 students listed more than one reason. The two most popular reasons were
"interest in the courses offered" (6?^) and geographical location— "near home" or "chance to get away from home" (40^).
Finally, the students were asked, "Who was most influ ential in your decision to apply for the SSTP program at
The Ohio State University?" Here, most students said they decided for themselves. In no case did a school counselor have any influence. Table 16 summarizes the responses. 39
TABLE 1 6
PERSON MOST INFLUENTIAL IN DECISION TO APPLY
Year o f Attendance Person 1964 196$ 1966 1967 196B 1969 Total
Me, myself B 10 9 9 10 9 55
Mathematics teacher 6 2 0 0 1 1 10
Other teacher, principal,or superint endant 0 1 0 1 0 0 2
Parents 2 0 1 2 1 0 6
No one person 0 0 1 0 1 0 2
Another student 0 0 1 1 2 0 4
Counselor 0 0 0 0 0 0 0
Other 1 0 1 1 2 0 5
Evaluation of the Program
Before actually asking the students to evaluate the program, the researcher tried to learn what the students considered important. In other words she wanted them to evaluate the program in terms of their own goals. Their directions were as follows:
"Some aspects of the program were important in making it successful for you as a person. Other aspects probably hindered the success of the program so far as you were concerned. Indicate the importance of each Item below using the following code:
VI - Very important to success of program I - Important to success of nrogram N - Neutral (neither a help nor a hindrance) H - Hindered the success of the program GH - Was a great hindrance to success-" 40
The students' ratings are given in Table 17. Later the
researcher assigned a numerical value to the ratings so
that a mean value could be computed. The numerical values
are given in parentheses above each code. The mean values
are listed in the last column of the table.
According to the student responses, none of the items
had a mean response that indicated the item was a hindrance.
The faculty was rated very important to success (VI) most
often. The intellectual challenge was rated very important next most often.
The researcher looked further to see if the students rated these items differently as the program progressed through the six year period. Using the 5^ level for
significance for the correlation coefficient, there was no
significant correlation between the year the student participated and the way he rated these items as contributing to his success. Table 17 is given on page 41.
Next the researcher asked the students to look again over the list of 15 items they had just rated in importance and pick out the one that was most important and the one that was the greatest hindrance to his personal success.
These responses are given in Table 18 on page 42. This table shows that the item most often chosen as the one most important was "the intellectual challenge". The one item of greatest hindrance was "the living arrangements". 43-
table 17
STUDENT RATINGS OF IMPORTANCE OF ASPECTS OF PROGRAM
Rating (4) Item (1) (2) (3) (5) GH H N I VI Mean
The faculty 0 1 1 33 44 4.5
The social and recrea tional activities 1 è 47 25 3 3.3
Getting away from home 1 1 3Ô 34 •J 3.6
The amount of homework assigned 3 11 15 40 15 3.6
Working in a college environment 0 1 21 31 31 A . 1
The subject matter 1 1 12 42 28 4.1
Contact with stimulating personalities 0 1 16 25 41 4.3
The amount of material covered 0 13 25 37 9 3.5
The living arrangements— Dormitory,food; etc. 1 15 46 16 5 3.1
The individual attention 2 S 14 26 34 4.0
The lectures 0 5 17 52 10 3.8
The intellectual challenge 0 2 g 2g 46 4.4
Living and working with other young people of similar interests 1 0 11 35 37 4.3
The textbooks, reference books, library 2 13 37 2g 4 3.2
The teaching methods used 0 S 23 33 ly 3.6 42
TABLE IB
ITEM OF GREATEST IMPORTANCE AND GREATEST HINDRANCE
Item Most Important One of Greatest Item Hindrance
The faculty 5 0
The social and recrea tional activities 0 6
Getting away from home 0 3
The amount of homework assigned 1 15
Working in a college environment B 0
The subject matter 1 6
Contact with stimulating personalities 13 1
The amount of material covered 1 13
The living arrangements— Dormitory, food, etc. 2 17
The individual attention B 5
The lectures 1 2
The intellectual challenge 21 1
Living and working with other young people of similar interests 19 2
Tlv:; textbooks, reference books, library 1 13
The teaching methods used 3 1 43
Then the students evaluated the program. The students were asked to judge objectively the quality of the items.
Their instructions were as follows:
’’Evaluate each item below using the scale:
VP - very poor P - poor A - average G - good VG - very good”
The items and the student evaluations are summarized in
Table 19. Again a numerical value was assigned to each
evaluation so that a mean could be computed. The numerical values are shown in the table. The last column in the table gives the mean for each item.
Overall, the students rated the "lecturers" highest with a mean of 4.4 and the "usefulness of the program for making you use your full potential" as second highest with a mean of 4.3. The lowest evaluation was given to the
"social and recreational activities". Here the mean was
2.9 - between poor and average. A4
TABLE 19
STUDENT EVALUATION OF THE PROGRAM
Evaluation (1) (2) (3) (4) (5) Item VP P A G VG Mean
Lectures 2 3 11 45 23 4.0
Lecturers 0 1 g 30 45 4 «4
Recitation sessions 3 12 28 34 4 3.3
Recitation instructors 4 9 16 46 6 3.5
Counselors 2 4 11 31 33 4.1
The materials— text book, equipment, etc. 2 12 33 28 8 3.3
The living arrangements— dormitory room, food, etc. 3 11 34 24 5 3.2
The usefulness of the subject matter in terms of your studies follow ing the program 5 21 12 27 19 3.4
The social and recrea tional activities 4 25 31 18 4 2.9
The usefulness of the program for making you use your full potential 2 2 12 24 44 4.3
In two instances, there has been a shift in the way the
students would evaluate the items as the program progressed through the six year period. There was a positive correla tion of .42 between the evaluation of the counselors and the year of attendance. That is, students in later years rated 45
the counselors as better. Table 20 shows a frequency
distribution by year.
TABLE 20
EVALUATION OF COUNSELORS
Response X UÜ.I UX " " ' Attendance VP P A G VG
1964 2 2 5 4 2
1965 1 è 4
1966 1 2 5 4
1967 1 2 3 6 196a 1 6 10 1969 5 5
Total 2 4 11 31 33
In the second case, there was a shift in the way the students evaluated the usefulness of the program for "making you use your full potential". There was a correlation coefficient of .37 between this item and the year of attendance. Students in later years rated this item higher. Table 21 shows this frequency distribution by year. /i6
TABLE 21
USEFULNESS OF PROGRAM FOR MAKING
YOU USE YOUR FULL POTENTIAL
Response Year of Attendance VP P A G VG
1964 2 1 5 4 5
1965 2 4 7
1966 2 6 5
1967 1 2 3 8
1968 6 11
1969 1 1 8
Total 2 2 12 24 44
The next series of questions dealt with personal success or failure of the students. The students were asked to agree or disagree with a series of statements which were positive or negative. The positive and negative items were mixed. Table 22 lists the statements and the student responses. Later, numerical values were assigned to the responses so that the means could be computed. These means are listed in the last coDumn. (Here SD means strongly disagree, MD means mildly disagree, N means neutral, MA means mildly agree, and SA means strongly agree.) TABLE 22
AGREEMENT - DISAGREEMENT STATEMENTS
Response (-2) (-1) (0) (1) (2) Statement SD m N m SA Mean
1. I felt that I understood the lectures most of the time. 8 19 7 36 14 .35
2. I feel there was too much homework. 9 20 17 24 14 .17
3. I found no time for sleep. 23 15 18 21 7 -.31
4. I learned a lot of mathematics that summer, but I have forgotten most of it since. 17 31 8 22 6 -.37
5. I met some great people my ovm age. 2 4 11 22 45 1.24
6. I wish the summer could have been longer. 7 16 17 24 20 .40
7. I found myself getting farther and farther behind as the summer progressed. 15 14 15 32 8 .05
8. The summer taught me a lot about my capabilities as a student. 2 4 6 31 41 1.25
9. The work was much harder than I expected when I came. 4 10 18 25 27 .73
LO. The summer was good for me because it really challenged me. It helped me know myself. 3 3 6 24 48 1.32 TABLE 22 (CONTINUED)
Response (-2) (-1) (0) (1) (2) Statement SD MD N HA SA Mean
11. I found the counselors a real help because they were available when needed. 7 13 18 23 22 .48
12. The first two weeks were really hard, then things got easier. 17 29 12 20 5 -.40
13. The amount of homework assigned was just about right. 12 26 14 26 4 -.20
11. 1 still "keep in touch" with at least one person 1 met for the first time at the summer program. 31 7 5 14 27 -.01
1$. The program was easier than 1 expected when 1 applied. 41 25 15 1 1 -1.25 l6. The program was not at all what 1 expected when 1 applied. 9 23 29 10 12 -.08
17. 1 found the counselors were often "too busy" doing something when 1 needed them. 24 21 21 14 2 -.62 l8. 1 always felt rushed. 4 21 15 28 16 .37
19. The lectures were good but I found I couldn't seen to apply them when 1 needed solutions to homework problems. 13 22 17 23 -.11
CO. TABLE 22 (CONTINUED)
Response (-2) (-1) (0) (1) (2) Statement SD MD N HA SA Mean
20. When I returned to high school I found mathematics boring because it was not as much of a challenge. 12 14 ë 26 17 .27
21. When 1 returned to high school 1 had a deeper ingerest in my mathematics course in my senior year. S 14 14 22 iS .37
22. When 1 returned to high school my mathematics teachers considered me a threat. They felt insecure. 33 S IS 13 4 -.70
23. The summer program had a positive influence in my decision to make mathematics or a mathematics-related area my college major. IS 1 12 21 31 .55
24. The summer program helped me decide not to make mathematics or a mathematics-related area my college major. 55 4 6 3 13 -1.05
25. 1 can't remember many of the facts 1 learned, but 1 learned a method of study that has been valuable to me since. 11 10 I6 23 23 .45
26. The summer was good "mental exercise" but 1 can't see where it has especially helped me since. 36 26 5 11 4 -.96 TABLE 22 (CONTINUED)
Response (-2) (-1) (0) (1) (2) Statement SD I-ID N m SA Kean
27. I "grevr up" a lot that summer. It had a maturing influence on me. 4 1 21 26 32 .92
28. Alter the program I demanded more of myself in terms of precise expression of a problem, pursuing a problem longer, etc. 4 5 12 36 27 .v2
29. The program had a bad effect on me because it was too difficult and really an unpleasant summer. 58 14 5 6 1 -1.45
30 . The summer would have been more successful overall if the uace had been slower so that I could have had more time to really learn things. 17 19 12 25 11 -.07
O 51
From this table some statements can be made which
statistically describe the students. They understood most
of the lectures, could work a lot of the problems, and
learned a good method of study. There was too much homework,
the program was harder than expected and didn’t get easier
as the summer progressed, they got farther and farther
behind, they always felt rushed, but they did find some
time for sleep and they even said the pace v;as not too fast.
The counselors were a real help and readily available. The
students learned a lot about their capabilities as students,
they were challenged, they "grew up" a lot and demanded
more of themselves. For many of them the program helped them
decide to make mathematics their career choice. They met
some great people their own age but did not keep in touch with
many of them after the summer. They wished the summer could
have been longer. Upon their return to high school they
found they had a deeper interest in mathematics but found
high school mathematics classes boring. However, they did not think their high school teachers were intimidated by
having them in their classes.
The above description of the students would be good
if they were all identical with a "mean student". Certainly this is not true of any one particular student.
In a few instances the attitudes of the participants
changed as they were away from their experience longer.
One case was on the item, "I found no time for sleen". The 52
The most recent participants expressed this view more often,
As the years passed and the students were a longer time
away from the program, their feelings about loss of sleep
seemed to mellov/. This is shown in Table 23.
TABLE 23
"I FOUND NO TIME FOR SLEEP"
Response Year of Attendance SD MD N MA SA
1964 9 4 3 1
1965 6 3 3 1
1966 3 2 2 6
1967 2 4 3 3 2
1968 3 1 4 6 3
1969 1 3 4 2
Total 23 15 18 21 7
This same feeling of fatigue showed in the responses to the item "I always felt rushed" as shovm in Table 24 on page 53. 53
TABLE 24
"I ALWAYS FELT RUSHED"
Response Year of Attendance SD lœ N m SA
1964 1 s 1 5 2
1965 2 3 3 4 1
1966 1 3 2 5 2
1967 1 5 4 4
196# 4 4 5 4
1969 2 5 3
Total 4 21 15 28 16
The item "I found the counselors a real help because they were available when needed" also showed a change in attitude as the program progressed through the years. Here, there is no evidence to indicate whether the attitude of the participants changed as they were away from the program longer or whether the counselors were better in later years, but the most recent participants regarded the counselors more highly. This is shovm in Table 25. Here the reader should recall that earlier in this study it was shovm that the most recent particinants also evaluated the counselors higher in performance than the earlier participants did. 5 h TABLE 25
"THE COUNSELORS WERE A REAL HELP"
Response Year of Attendance SD r€) N m SA
1964 5 2 6 3
1965 1 4 4 4
1966 2 4 5 2
1967 5 1 3 5
1968 5 1 8 3
1969 2 3 5
Total 7 13 18 23 22
Expectations versus Experiences
In this part of the study the researcher tried to learn
what the participants expected to happen during their summer
at The Ohio State University before they came. Also, she wished to learn hov; many of these expectations were realised
and if there was any correlation between expectation and
reality.
The students were given a list of items with the follow
ing instructions;
"When you were selected for the program (before you
attended the urogram) what did you expect to bo part
or results of the summer experience? To the left of 55
the item, put a 'B' in the correct column to indicate
your degree of expectation.
'Lot' means you expected a lot of it.
'Some' means you expected perhaps some of it.
'None' means you expected none of it."
After they did this they were given further instructions;
"Looking back, what things were a part or result of
the program? Go back to Question VI and to the left
of each item check with an 'A' the degree to which
each item was a part or result of the program."
Later, the researcher assigned numerical values to the responses as follows: "Lot" was given a value of 2, "Some" was given a value of 1, and "None" was given a value of 0.
Then a mean value was computed for each item. Finally the correlation coefficients were computed between the "before" and "after" responses on each item. These responses and results are recorded in Table 26. TABLE 26
EXPECTATIONS AND EXPERIENCES
Before After Correlation Item Lot Some None Mean Lot Some None Mean Coefficient
1. Lectures by outstanding Mathematicians 11 65 7 1.05 13 55 10 1.04 0.09
2 . Lectures by faculty members at the college 58 24 1 1.69 46 30 3 1.54 0.25
3. Tests on the material being studied 8 61 14 0.93 14 64 1 1.16 0.24
4. Conferences with college faculty members 4 44 35 0.63 2 24 53 0.35 -0.00
5. Independent research work 13 38 32 0.77 5 22 52 0.41 0.42
6 . Homework 33 49 1 1.39 63 16 0 1.80 -0.04
7. To meet people; make friends 38 40 5 1.40 31 46 3 1.35 0.41
6. To make it easier for me to get into college 13 44 26 0.84 12 39 28 0.80 0.48
V. To learn more about the history of mathematics 1 30 52 0.39 2 41 37 0.56 0.20 o TABLE 26 (CONTINUED)
Before After Correlation Item Lot Some None Mean Lot Some None Mean Coeffici
10. To help me decide what field to major in in college 16 45 22 0.93 22 38 20 1.03 0.52
11. To participate in many non-academic campus activities 7 39 37 0.64 1 30 49 0.40 0.16
12. To write a research report 0 69 0.17 1 14 65 0.20 0.20 i 13. To teach me to study better 15 49 19 0.95 19 41 20 0.99 0.36
11. To help me decide what college to go to 4 35 44 0.52 9 21 50 0.49 0.45
15. To find out what a mathematician does 34 39 10 1.29 22 41 17 1.06 0.40
16. To have round-table discussions with other students 22 46 14 1.10 18 38 23 0.94 0.37
17. To increase my know ledge of mathematics 6B 15 0 1.82 53 26 1 1.65 0.46
18. To help make me a better student when 1 get back to my high school 29 36 16 1.16 19 36 20 0.99 0.66
- o TABLE 26 (CONTINUED)
Before After Correlation Item Lot Some None Mean Lot Some None Mean Coefficient
19. Student dances 0 22 60 0.27 0 22 56 0.2S 0.24
20. To get to know some outstanding mathe maticians 10 42 31 0.75 7 39 34 0.66 0.41
21. To take field trios 2 14 67 0.22 0 3 77 0.04 0.05
22. To teach me something about college 32 46 5 1.33 31 39 10 1.26 0.47
23. To increase my interest in mathematics k-h- 35 4 1 .4a 39 24 16 1.29 0.31
Critical value of correlation coefficient at 5^ level of significance = .21?
CTL 59
This table shows that the students did know what to
expect durins; the summer program. For l6 of the items, there was a correlation between expectation and experience that was
significant at the 5i ° level.
Success at End of Summer
During the summer program the students were given
examinations over the material covered. For each year except
1964, these test scores were on file. The researcher took
each student’s test scores and added them together to give him a total number of test points. Then within each year the students were ranked in order of these test-score totals.
Thus, the top student had a rank of 1 and the bottom student had a rank of 20 (1? in 1969). This rank in the class at the end of the summer was used as an indication of one kind of success during the summer.
This study showed a high correlation between the rank of the student at the end of the summer and three of the agreement-disagreement statements considered earlier. These correlation coefficients are summarized in Table 27. When interpreting the table, remember that a lower rank number corresponds to a more successful student. The information recorded in Table 27 would indicate that the "best" students had no difficulty keeping up with the work. 60
TABLE 27
CORRELATION BETWEEN RANK AND THREE STATEMENTS
Correlation Statement Coefficient
I found myself getting farther and farther behind as the summer progressed. .40
The amount of homework assigned was just about right. — . 40
The summer would have been more successful overall if the pace had been slower so that I could have had more time to really learn things. .46
One would expect there would be a high correlation between rank at the end of the summer and the score the
student was given on the problems he solved on the application
form. Here, the student was asked to solve several difficult problems, and if he could not solve them he was to submit his partial solutions. He was given a score from 0 to 6 according to his performance on these problems. This score was not meant to be a percentage but was supposed to indicate, among other things, how strong a mathematics student he was. This
study showed there was little correlation between this
"application test score" and the student's rank at the end of the summer. The correlation coefficient was -.26. Again the reader should recall that this negative correlation coefficient was to be expected due to the inversion of the rank scale. 6 1
This study did show a high correlation between the student's rank at the end of the summer and his PSAT non verbal score. Here the correlation coefficient was -.51.
If the reader recalls that a low numerical value indicates a high rank, this -.51 shows that a high-ranking student tends to be one who has a high PSAT score.
An Example of a Regression Analysis
At this point the researcher wondered if there was a combination of factors which would predict rank on test scores at the end of the summer. Since the data was already punched on data cards, she decided to run an 02R Stepwise Regression
Analysis. This was more of an example of something that could be done than a main part of this study. The results of the analysis were greatly influenced by several factors.
In order for this analysis to be performed, the data on each participant had to be complete. For this reason, if an item of information was missing on a large number of participants, this item could not be used as an independent variable in the analysis. As already stated, IQ scores and
PSAT scores were missing for many of the participants. Hence these variables, which would be expected to play an important role, were eliminated. Also, several participants were eliminated from the analysis because their records had several pieces of missing information. Hence, the sample used in the regression analysis was reduced to 54 neople. 62
For those very important reasons, this regression analysis should be viewed as an example of what could be done rather than as an important part of this study.
Table 2 8 , on page 63, summarizes the results of the 02R
Stepwise Regression Analysis using rank on test scores at the end of the summer for the dependent variable.
Using the first two variables, which were significant at the \ i a level, this researcher would interpret the informa tion in Table 2 8 as indicating the following;
Those who ranked high on test scores at the end of the summer were those students who disagreed with the statement
"The summer would have been more successful overall if the pace had been slower so that I could have had more time to really learn things" and whose scores on the application form problems were high.
This same 02R Stepwise Regression Analysis was performed using as the dependent variable the student rating of how important for his own personal success he considered the intellectual challenge of the program. Again the analysis was performed on a reduced sample of 54 people and with the important variables of IQ scores and PSAT scores omitted.
Table 2y, on page 64, summarizes the results of this analysis. TABLE 2è
02R STEPWISE REGRESSION V7ITH RANK ON TEST SCORES FOR DEPENDENT VARIABLE
Step Increase F value to Variable Entered or Removed Multiple Nuir.be r in enter or RSQ removeRRSQ
1 Agreement with "The summer would have been better if the pace had been slower" 0.5333 0.2845 0.2845 20.6725
2 Application test score 0.64^5 0.4218 0.1374 12.1191
3 Amount of expectation of independent research work 0.6806 0.4632 0.0413 3.8479
L Importance of working in a college environment 0.7170 0.5141 0.0510 5.1386
5 Importance of living and working with other young people of similar interests 0.7503 0.5629 0.0488 4.9759
Critical value of F at 1^ level = 5*06 TABLE 29
02R STEPWISE REGRESSION WITH STUDENT RATING OF IMPORTANCE
OF INTELLECTUAL CHALLENGE AS DEPENDENT VARIABLE
Step Variable Entered or Removed Multiule Increase F value to Number in enter or R RSQ RSQ remove
1 Agreement with "The summer was good for me because it really challenged me" 0.4493 0.2019 0.2019 13.1508 2 Evaluation of Counselors 0.5572 0.3104 0.1086 8.0311
3 Amount of expectation of tests on the material being studied 0.6458 0.4171 0.1066 9.1456
L Agreement with "I feel there was too much homework" 0.7031 0.4944 0.0773 7.4941
Critical value fo F at I f o level = 3-68 65
Using the first four variables, which wore significant at the level, this researcher would interpret the infor mation summarized in Table 2 J as indicating the following:
Those who considered the intellectual challenge of the program highly important in making the summer a success for them were those who (l) agreed with "The summer was good for me because it really challenged me", (2) evaluated the counselors high, (3) did not expect tests over the material, and (4) did not feel there was too much homework.
This chapter on results from objective data ends with these two examples of the type of study which could be done to predict success in the program. Chapter V presents results obtained from data that was more subjective. CHAPTER V
RESULTS FROM SUBJECTIVE DATA
An Introduction
The data presented in this chapter is more subjective than that presented in Chapter IV. It was collected in the form of replies to open-ended items in the student question naire, discussions with faculty members, and letters written by parents. ■
The purpose of this chapter is to bring together the personal feelings of the people involved in the program.
This researcher thought this was necessary because she considered it an important measure of the success or failure of the program.
As reported in Chapter IV, all except nine of the par ticipants are still attending school. Hence it is too soon to measure the long-range effects of the program as it influences careers.
In Chapter IV the students were ranked within each year according to their total number of points on tests. This is an immediate and easily accessible indication of their ability to perform well on the tests during their surmner of attendance. But the reader must not forget that these studedts were unusually intelligent. Hence the achievement of the student of lowest rank (the poorest student relative to test 66 67 scores during the summer) may well have been high when compared to what a student of average intelligence would have achieved. Hence, relatively low achievement is by no means equivalent to failure.
For the reasons just mentioned, possibly the best indication of what the program is achieving is the feelings of the people involved.
Throughout this chapter the reader will be referred to the Appendices to read the students’ statements or the parents' statements in their own words. This researcher feels that in this study the Appendices are an integral part of the study and cannot be skipped without losing much of the value of the study.
Student Views of the Goals of the Program
The questionnaire contained some open-ended questions.
One of them was, "What do you think is the one important thing the program is trying to accomplish?"
In response to this question, ?6 participants wrote replies. The replies could be divided into nine categories.
1. Teach mathematics— to give insight, broaden background, teach what mathematics is, teach problem solving, teach to think logically, teach mathematical intuition.
Thirty-five of the reulies (46.1'/^) fit into this cate gory. The following are some of the replies which express this as the central goal of the program:
"To get students to think logically and originally— to ^'ain an understanding for the logic and structure 6ü of mathematics and proofs."
"To teach us hov; to think, and to develop some sort of mathematical sense or intuition."
"I would say approaching math from an experimental discovery angle."
2. Teach a person his capabilities.
Thirteen of the students (17.2^) expressed this as the main goal of the program. The following are some student replies expressing this thought:
"At least for those who were successful, it showed them not only how much they didn't know, but also how much they could learn."
"Find out how much v;e were capable of."
"Challenge you to a tremendous degree to bring out your full potential and let you become aware of it and your limitations."
3. Intellectually stimulate arid challenge.
Eight of the students (10.5'/) considered this to be the chief goal of the program. Here are some expressions of their views:
"Challenge and stimulate high-potential and high- achievement high school students; with thoughts of the future."
"Intellectual stimulation and exposure to a really academic environment."
4. Teach what a mathematician does.
Six students (7.;/) thought the most important goal of the program was to teach the students what a mathematician docs. Some of their replies follow:
"The teaching of the life and ways of a mathematician."
"To convey, perhaps in a somewhat exaggerated manner, the life and discipline of a mathematician." 69
5. Teach to think creatively.
Six students (7.9/0 expressed this as the main real.
Some of their replies follow:
"To get students to think creatively and originally."
"Stimulation of participants to do original thinking in mathematics (as opposed to knowing Cayley's Theorem)."
6. Teach interest in and enjoyment of mathematics.
This goal was expressed by four students (5.3‘/^). One such response was, "It was trying to teach us to enjoy math."
The four remaining students listed one or more of the following as the main goal of the program:
7. Haye the student experience total dedication.
S. Teach the student self-reliance.
9. Recruit people into a mathematics career.
This list summarizes the items the students considered to be the central goals of the program. A complete listing of the responses, separated by year, is given in Appendix F.
Faculty Views of the Goals of the Program
Several of the faculty members expressed their ovm views of the goals of the program. These were not "official" goals. Their list could be summarized as follows:
1. Make academic good citizens.
It is the aim of the program to develop attitudes as well as skills. The method of making academic good citizens is by example. The students are exposed to productive, prominent mathomaticd.ans who show a deep concern for their 70 studentG and for the academic community.
2. Learn to know what mathematicians do— really feel it, experience it.
The student is put into an environment in which he can experience a whole gamut of vital dilemas which confront a scientist in an}'’ field at one time or another.
3• Have a^ intellectual experience .
The faculty member speaking here expressed the view that the particular subject matter being taught was not the most important thing. It v;as a vehicle. Mathematics was being used to challenge students who had perhaps not worked to capacity before.
4. Develop techniques and attitudes for attacking scientific problems.
This view was expressed by several of the faculty members.
Parents' Views of the Goals of the Program
One indication of the immediate effects of the program is found in letters from parents. Each year after the program the parents were invited to write a letter expressing their thoughts about the program. Thirty-four parents of students in the sample wrote letters.
The researcher first checked to see if a special group of parents wrote letters. She checked to see if there W'as a significant correlation between a student's rank at the end of the summer and whether or not his parents wrote a 71
letter. There v/as no significant correlation. This indicated
that the parent’ letters were not just from the most
successful students, but rather were from a representative
sample of the parents.
A complete list of the parents’ letters is found in
Appendix K. The researcher would summarize the important
achievements of the program as expressed by the parents in the following list:
1. Contact with other stimulating students, instructors, and counselors.
2. Development of confidence and increased skills in meeting and dealing with new people and situations.
3. Solidification of an already strong interest in mathematics.
4. Gain of confidence in ability to perform well in mathematics.
5. Challenge by other students.
6. Realization of the significance of achievement.
7. Maturation.
S. Estimation of his potential in mathematics.
Excerpts from some of the more revealing letters of the parents follow:
•'He found the work hard, difficult but not impossible; a challenge that could be met. His fellow students impressed him not only with their high degree of intelligence but also with their wide range of knowledge on many subjects and thought. Quite different from the average student here. He gained confidence in his ability to perform well in mathematics."
"You asked how we think the summer Math program has influenced Raluh. It has made him more sure of himself. He has always been a very shy person, very rarely joining in even a family discussion. Now, he 72
does not hesitate to add his well worded ideas, that usually leave little room for argument. He is also more at ease when meeting people."
"For the first time in her life, she was in the company of children of her ovm intellectual ability and with interests similar to hers. She also had her first test of herself against people of this caliber. I feel that it opened windows for her into the broader world of the intellect, that she received her first taste of the joy of scholarship and also her first taste of really working to achieve. She v;as enchanted by the library, by the type of classes, by the companionship and really interested in the subject matter she v/as taught."
"Preparing the apnlication itself was the first occasion on which he had ever perceived the significance of a record of achievement, or even of achievement itself beyond the minimal. We think that the depth and intensity of the course, and the contact with many outstanding students and instructors, continued to reinforce that new perception. It is certain that he worked harder than ever before, and thus knows that he can."
"At the start, when he saw the caliber of the students enrolled, he had a fev/ misgivings as to his ability to participate in such a program. As the course progressed, his confidence increased as he realized that dedicated study and perserverence would enable him to keep up with his class. His counselors were also a source of inspiration. It is our opinion that the program has helped him early in life to aim for a goal in mathematics and also helped him to estimate his potential in this field."
Very few parents made critical comments. Here is one such comment:
"Unfortunately Douglas did not enjoy his weeks spent at O.S.U. as much as wo had hoped. He found recreation very limited, not because the facilities wore not there, but because so many of the students he came in contact with were students only and did not care to oarticipate in any of the sports, or even attend church or movies. This we thought was the only v/eak point in the nrogram." 73
The Best Thing about the Program
Another open-ended question in the questionnaire was,
"What is the one thing you would list as the best thing about the program. The researcher grouped the students' replies into categories. They are listed below. After each category is the percentage of the replies which fell into that category.
1. The People (20.6^)
2. The Intellectual Challenge (23.4^)
3. The College Environment (l$.6^)
4. The Teaching Methods (10.4/^)
5. The Subject Matter (7.6^)
6. The Faculty (6.5^)
7. The Counselors ($.2^)
S. Other (2.6^)
These are categories which list the topics the students mentioned. Within each topic the students' replies ranged widely. In Appendix G the students' answers are recorded in their ovm words. The replies arelisted by year of attendance.
The Worst Thing about the Program
Next the students wore asked, "What is the £nn thing you would list as the worst thing about the program?" Their renlies are given in their ovm words in Appendix H. The researcher grouped the students' reulies to this question into categories. They are listed below in order of frequency. 74
After each category is the percentage of the replies which
fell into that category.
1. Pace and Work Load { 2 ^ , 0 / o )
2 . Living Conditions (22.2>0
3. Teaching Methods (18.1^)
4. Organization of the Program (12.5/0
5. Adjustment { 9 - 7 ' / ° )
6. Social and Recreational Activities (5.6^)
7. Other (6.9^)
The above list gives the topics the students mentioned.
Within each topic the students’ replies again ranged v/idely.
Suggestions for Changes in the Program
Finally the students were asked, "How would you change the program if you had the opportunity?" The student replies could be grouped into nine major categories as listed below. After each category is the percentage of replies that fell within that category.
1. Organization of the Course (35.4^)
2. Pace and Work Load (17.1^)
3. Living Arrangements (14.6^)
4. Subject Matter (8.5/^)
5. Recruitment (7•3/0
6. Recreation and Social Activities (6.1';0
7. Counselling (4.9;0
4. Grades, Comnetition (3-7/0
9. Other (2./;>0 15 Their comments within each category represented a
full spectrum of ideas. For example, in the category of
Organization of the Course, one student would eliminate
the tests while another student would have more tests.
The reader should refer to Appendix I and read their replies
to really understand hov; the students felt.
Commuters
The replies to two of the open-ended questions indicated
that the students who did not live in the dormitories were
dissatisfied with the living arrangements. Several of the
commuters stated that not living on campus was the worst thing about the program. They said that they did not get
enough personal attention and that they felt isolated. Later, when the students were asked how they would change the program if they had the opportunity, the commuters again said that they would have all students live in the dormitories.
Further Comments
The participants were invited to write further comments on the last page of the questionnaire. Sixty-four of them did so. The students seemed quite free in expressing their views— both positive and negative. These comments are listed in full in Appendix J. The things they emnhasized wore quite varied so that they could not be grouped into mcaninr'ful categories. The most frequent comments dealt with nraiso for the program. Second in frequency was nraise 76 for Dr. Rons and hio methods. Some illustrative remarks follow;
"I found the program most valuable both in my intellectual and personal development. I learned mtich about mathematics, but even more about the scope of my mind and how to best attempt to utilize it. I learned much about people by being in close contact with a diverse group of young people. I also was shown a preview of college and feel that my summer at O.S.U. was responsible for making my transition into college so easy. While I am not majoring in math, O.S.U. did not turn me aw^ay from it, but rather strengthened my interest in mathematics."
"During the program, I wanted very much to do more than I actually did. I thought that some of the problems were very hard and that there v r a s a lot of pressure present. Although at the time I complained about the amount of homework, I don't think I would change it at all. I pushed myself and did more vrark than I would have if there was less homework. For as long as I didn't understand the material, I was displeased with the testbooks. Once the material sank in, the proofs appeared remarkably clear and simple."
"I felt that the SSTP math program at O.S.U. was a very fine program. Its value came from a realization (presumably on the part of Dr. Ross) that the 6-week experience could be most beneficial not as a stepning stone to higher mathematics but as a perch from which to look at various "simple" mathematical systems. Dr. Ross tried to show some of the interrelationships in mathematics, and I think he was successful."
"The entire program could have been more meaningful if there had been some reinforcement at high school. On the contrary, I felt the students and decidedly the faculty used this as a starting point in hating me, actually discouraging me from returning the second year, and using every means to prevent me from continuing a vital interest in mathematics. As a result, I began very much to feel superior to the people at home, and yet inferior (especially the second summer) to those at OSU, so that a social problem got started I am still struggling v/ith. Also I became glib and sententious with my new-found vocabulary upon returning home, and I found iiiyse.lf professing knowledge about things I didn't understand at ail. Although I did set a vital spark that su .'timer, I don't think I've yet been able to adjust to the fact that normal people in a normal place, 77
and even ne in another place, can't possibly have thj.s intensity or singleness in purpose. Perhaps I was just too young and emotionally/intellectually too immature for this program, but it was really an overwhelming experience, almost too much for me to handle at the time."
"The summer was my first subjection to such a mental torture. I reacted with a proper amount of activity— but it was a piecemeal self-preservation of doing homework problems. A great deal of the continuity of succession of topics was lost to me. It was possible to do this since I had a minimal amount of contact with floor counsel, discussion group leader, or the faculty. Most of the benefits of the summer came by reviewing the experience and using the discipline and "acuter perception, intuition" I got, after the program was over."
"I'm being married in June t o ______whom I met at the summer program."
"The program could probably use more publicity. Not very many high school students hear about the NSF courses. As far as I know no one from my high school other than myself has attended anything of this nature."
"Looking back on it (and it is almost 5 years now), I feel the infectious enthusiasm generated by Dr. Ross for mathematics was the most significant aspect of the program. The program was certainly extremely challenging and I feel rewarding. Far more than a set of mathemat ical facts was being taught. The students were forced to prove theorems and develop the theory themselves in many cases. The very art of mathematics was really the topic (or subject) being taught."
These examples of the students' remarks illustrate the range of ideas expressed by the students. They certainly do not give the whole picture. The reader is referred to
Appendix J for a complete list of their remarks.
In Chapter VI, an effort is made to summarize and to identify any unanswered questions that have come to light as a result of this study. CHAPTER VI
SUM'IARY AND CONCLUSIONS
Summary and Conclusions
The objective of this study was an assessment of the
SSTP program at The Ohio State University in terms of
1. The goals of the program
2. The recruitment of the participants
3. The successes and failures of the participants
4. The present status of the participants.
The study was conducted by using information from four sources:
1. Information included with the application forms
2. Information obtained from questionnaires
3. Information included in parents' letters
4. Information obtained from interviews.
The goals of the program
The goals of the program were expressed by The National
Science Foundation, the faculty involved in the program at
The Ohio State University, the students who participated in the program, and the parents of the students.
The National Science Foundation expressed the official goal of the program as "to provide the superior high school student with cducationaJ experience in science and mathe-
li' 79 inatics beyond that normally available in high school courses".
Some members of the faculty involved with the program at
The Ohio State University expressed one or more of the following objectives of the program:
1. Make academic good citizens.
2. Learn to know what mathematicians ^ — really feel
it, experience it.
3. Have an intellectual experience.
/i-. Develop techniques and attitudes for attacking
scientific problems.
The students, upon looking back at the experience they had completed, expressed the following as what they considered to be objectives: (After each item is the percentage of students who expressed this view.)
1. Teach the students to do mathematics. (16.1/0
2. Teach a person his capabilities. (17.2^)
3. Intellectually stimulate and challenge the students. (10.5#)
h . Teach what a mathematician does. ( 7
5. Teach the student to think creatively. (7.9/^)
6. Teach interest in and enjoyment of mathematics.
(5.3#)
7. Have the student experience total dedication. (2.6#)
6. Teach the student self-reliance. (1.3#)
9. Recruit pconlo into a mathematics career. (1.3#)
Some of the parents wrote letters expressing what they ÜO
considered to be accomplishments of the program. These
might be summarized as follows; (These are listed in order
of frequency mentioned.)
1. Contact with other stimulating students, instructors,
and counselors.
2. Gain of confidence in ability to perform well
in mathematics.
3. Challenge by other students.
4. Solidification of an already strong interest in
mathematics.
5. Estimation of his potential in mathematics.
6. Maturation.
7. Development of confidence and increased skills in
meeting and dealing with new people and situations.
S. Realization of the significance of achievement.
As one looks at the goals expressed by the different people involved in the program an important question is how they compare. The following comparisons could be made:
1) One of the goals expressed by the faculty members at The Ohio State University was to develop techniques and attitudes for attacking scientific problems. In the list of goals expressed by the students, 46.1/^ said the program was trying to teach students to do mathematics.
2) A second goal listed by the faculty members was to let the students have an intellectual exnerience. Among the goals listed by tlic students, 17.2/) of the students lasted 21 that a prime Roal war to teach a person his capabilities while 10.5'/> stated intellectual stimulation and challenge as the goal of the program.
3) A third goal listed by the faculty members was to teach what a mathematician does. Among the students, 7.9^ listed this as the main goal of the program.
These results indicate that the goals expressed by the faculty members at The Ohio State University were being achieved, as evidenced by the fact that over è O f o of the students in the sample stated the same goals as the faculty did. This would indicate that the program was successful in terms of its expressed goals.
Other Possible Goals
One question is left open. Are there other worthwhile goals the program might achieve? While conducting this study, the researcher found two concerns that were not being met.
First, many of the students commented that they felt a need for more planned social and recreational experiences.
As an illustration of this feeling, one student described in detail a summer program she attended the following summer in
Arizona during which the participants were taken on field trios to the Grand Canyon and the Painted Desert. Most suggestions wore not, however, for activities of this magnitude. Most of the suggestions indicated the partici pants wanted more organised activities. 82
A second concern, which v/as expressed by the faculty at
The Ohio State University, was the lack of cultural activities.
The students, in their answers to open-ended questions, also indicated this v/as a concern. One faculty member illustrated his thoughts by suggesting the students could be taken to a summer theater production of a play. Following this produc tion, the students could meet with a well qualified faculty member from the English Department to discuss the play. One participant suggested that the organizers of the SSTP program should "arrange some cultural and intellectual activities not related to mathematics".
As already stated, these two possible goals of the program— organized social experiences and cultural experiences— are not presently goals of the program. Before they could be instituted some important details would have to be considered,
(l) Competent personnel would have to be found to conduct the social activities and arrange for participation in cultural events. (2) High quality faculty members in departments outside the Department of Mathematics would have to be involved in the project. (3) These additional features of the program would have to be funded.
Of course the overriding concern in regard to instituting any changes in the program is whether or not the gains made would outv/elgh accomnanying losses. The program is eight weeks long. During this eight weeks the students experience an intensive mathematics program which "pushes them to capacity" and "lets them find out what they arc capable of".
Any changes in the program in terms of adding features might
produce a loss in what the program is now achieving. Hence,
such changes would have to be made with caution.
Recruitment of the participants.
The students first learned of the program from two
major sources— from a teacher, from another student. In
very few instances did a student learn about the program
from a school guidance counselor.
The three most often stated reasons for applying for
the program at The Ohio State University were:
1. Interest in the courses offered
2. The geographic location— either because it was
near home or because it was a chance to get away
from home.
3. Suggested by a previous participant.
After learning of the program, most students said that the
decision to attend was their own.
The successes and failures of the participants
The students were first asked to evaluate the different
parts of the program in terms of their importance to their
own personal success or failure during the summer.
The students indicated that all of the items listed
had a positive influence in the success of the program for them personally. The four items the students listed as Ü/, greatest, in Importance were:
1. The faculty
2. The intellectual challenge
3. Contact with stimulating personalities
4. Living and working with other young people of
similar interests.
The four items the students listed as least in importance to their personal success were:
1. The living arrangements
2. The textbooks, reference books, library
3. The social and recreational activities
4. The amount of material covered.
The students then evaluated the different parts of the program. The three items judged best were:
1. The lecturers
2. The usefulness of the program for making you use
your full potential
3. The counselors.
One item was judged as less than average— the social and recreational activities.
These results led the investigator to the following conclusions:
1. The students considered the faculty to be the big gest factor in making the T)rogram successful for them personally and in this program they judged the lecturers to be excellent. 2. The students considered the intellectual challenge to be an important factor in the success of the program and they judged this program successful in making them work to realize their own potential.
This study sought to learn what the students expected to happen during their summer and whether or not these expectations were realized. They were given 23 items about which they were to indicate their degree of expectation before they began the program. Later they indicated the degree to which they experienced these same 23 items during the summer.
In l6 instances, there was a correlation significant at the 5 per cent level between expectation and realization.
This evidence supports the conclusion that there was a good correlation between what the students expected to happen and what they actually experienced.
Commuters
An important finding of this study was that the students who commuted to class rather than lived on campus did not consider the program successful. When the students were asked to list the worst thing about the program, the com muters, almost without exception, listed the fact that they did not live in a dormitory was the worst thing. They were quite specific about their reasons for this statement. They said they did not get enough nersonal attention, tliey could not oarticipate in all the activities, they felt isolated, B6 and they did not have the advantage of counselors close at hand.
This researcher should note that by the time this study took place, a change had been made in the program at
The Ohio State University so that all of the students do live in dormitories.
Present status of the uarticioants
This study showed that most of the participants were still attending school. Sixteen of them were still in high school or had just completed high school. Fifty-eight of the participants were attending college at some level. Nine were gainfully employed. Of the fifty-eight attending college, 37 (63.6^) were majoring in mathematics or computer science. Thirteen (I5.7i^) were enrolled in the mathematically related fields of physical science, engineering, or chemistry.
Recommendations for Further Study
1. In order to measure the long-range effects of the program when the students are finished with school and are in career positions, another study would be needed after five to ten years have passed.
2. The items rated lowest by the students were the social, recreational activities and the living arrangements. Whether or not changes should bo made in these regards could become the focus of a further study.
3 . An example of the type of regression study which could be Ü7
used to predict a student's success in the propram was performed in this study. However this study was not designed specifically to ascertain the factors in a student's back ground which would lead to secccss in the program. To achieve this purpose a regression study would be needed. Such a study would require at least the following things in its design: (1) a decision about what would be considered as success, (2) a conscious effort to secure complete data on a sufficiently large random sample of the partaicpants.
4. From their letters the parents of the participants appear to this researcher to be well educated people. There may be interest in a study designed to discover whether only chileren of well-educated parents or children of parents with high incomes are taking advantage of the program.
5. In this study there was no attempt to compare the participants with a control group consisting of students who did not take part in the program. A study which does use a control group might enable one better to assess the impacts of the program and also to evaluate the process by which participants are selected for the program.
6. This study was an in-depth study of the SSTP program at
The Ohio State University. In-depth studies have not been made of any other SSTP programs. An in-denth study of one or more of the other programs might be of interest. Perhaps a comparison of the SSTP programs at two different institutions 88 would prove enlightening in providing contrasts.
7 . In this study, information was gathered from students, faculty members, and parents. The high schools and high school teachers involved were not used as sources of infor mation. A controlled study which works closely with the high schools and delves into the effects of the program upon the students' high school studies could be performed.
8. This study looked only at the eight week long SSTP ' program at The Ohio State University. A study which compares and contrasts different types of special summer programs might cast light upon the most effective and economical way of providing special enrichment study for high-ability students. APPENDIX A
APPLICATION FORM
89 THE OHIO STA'IE UNIVERSITY 90 DEPARTMENT OF MATHEMATICS S’TUDENT SCIENCE TRAINING PROGRAM FOR HIGH-ABILITY SECONDARY SCHOOL STUDENTS June 16 - August 8 , I969
TO BE FILLED OUT BY THE APPLICANT (Each application should be accompanied by the official transcript of credit.)
1. Name;______Male____Female
2. Social Security Number: ______
3. Permanent Address (including ZIP code):
U. Telephone Number:______Area Code:_
5 . Date of Birth (not 19$9) :______
6 . Names of Parents or Guardian:
7 . Name of your High School:____
Public ____ Parochial Private (non-denominational)
6 . Address of High School:______
9. Name (in full) of Principal of High School:_
10. Name of your Sponsoring Teacher:_ (The letter or recommendation should be sent by the sponsoring teacher directly to Dr. Harold D. Brown, Director SSTP, Department of Mathematics, The Ohio State University.)
11. What grade will you complete by June I969?______
12. How many pupils attend your high school?______
13. Number of miles from your home to The Ohio State University (one way): 91 Use additional space if needed to answer questions_ 1 4 21.
1^. Have you ever participated in a special summer program before this year?
Yes ____ No
If yes, briefly identify and describe the program(s).
15 . Did you participate in any school, regional, or national mathematics competitions? Please describe the kind of competition you took part in and your standing in it.
16 . Did you undertake a special mathematics project for your mathematics club, a science fair, etc.? If so, please describe the project (or projects).
17 . Where does mathematics fit into your overall interests? Tell in your own words about your plans and ambitions. This statement should be handwritten. 92 l8. Is there a mathematical question or a mathematical problem which you found particularly interesting or challenging? Tell of this in your own words.
19 . Do you think you need a first class mathematical education to master the theory of physics, chemistry, biology, economics? Would you men tion, if you can, some mathematical ideas which you consider important for these fields. 93 20. Each applicant should attempt a solution of the following problems. For each complete or partial solution the applicant should prepare a readable presentation. Ihe applicant should write down and send us his observa tions regarding even the problems which he could not solve.
Observation; Discovery, Testing (a possible counterexample). Justification
I. If r is any positive real number and n is a positive integer, show that among the n - 1 real numbers a, 2a, 3a, ... , (n - l)a there is at least one which differs from an integer by at most .
II. Let Zg, z , be four complex numbers on the unit circle.
(See Fig. 1.)
Show that if
then these four complex
numbers form the vertices
of a rectangle.
Fig. 1
III. If P is a convex polygon contained in a square of side length 1
(e.g. Fig. 2), show that
the sum of the squares of
the lengths of the sides
of P does not exceed .
Fig. 2
IV. Let a^, Ug, , Eg be eight integers such that
0 < a^ < Eg < ... < Eg < l6 .
Show that there is an integer c , 0 < c < l6 , such that a. - a. - c ^ 0 for at least three distinct pairs i ,j . 94 V. Let B be a plane rectangle. By a decomposition of R we mean a proper subdivision of R into smaller rectangles (e.g. Fig.3), and by a primitive decomposition we mean a decomposition from which we can remove no lines and still have a decomposition. For example^ in Fig. 3(a), line A can be
removed and thus
3(a) is not pri
mitive . However,
3(b) is primitive.
Show that except (a) (h) for n = 3 ,^ or 6
we can always find a Fig. 3 primitive decomposition
of R into n smaller rectangles.
VI. Let k be a positive integer. Show that the total number of digits in the integers 1 ,2 ,3 , ... , 10^ is equal to the total number of 0 digits in the integers 1,2,3, ••• , 1 0 ^ ’*'^ . (Here all integers are written to base 10 .)
VII. Show that it is possible to partition the square into eight acute triangles. Can you partition the square into seven acute triangles?
VIII. Let S be a non-empty set. a) For any subset X of S (i.e. X C S), we associate a subset T of 8 such that the rule
(*) (A U bJ O Â U B U B
is satisfied for every two subsets A and B of S . Give a convincing argument that for any subsets A and B of S
i) Â A .
ii) A = A .
iii) If A C B , then A C B . VIII. (cont'd) __ 9!) b) Show that if we have an association X to Y of subsets of S such that (i),(ii),(iii) are valid for all subsets A and B of S , then (*) is also valid.
IX. Let n be a positive integer which is divisible by neither 2 nor by 5 . Show that there is a positive integer k which when written to base 10 has all of its digits equal to 9 =Lnd which is divisible by n .
X. Let T bs an m x n billiard table (m,n integers) with no pockets and perfect rebound. If a billiard ball B lying at the center of T is hit at a 4$° angle relative to a side of T , how many rebounds will it make before it returns to where it started? (Here we count a corner rebound as two rebounds.)
21. Is there anything which you would like to say in regard to your interest in joining us next summer?
22. The cost of instruction in this program is paid by the National Science Foundation; the student is expected to pay his own expenses for room, board, and travel. The Foundation has provided very limited funds to help meet the costs for participants who would otherwise be unable to attend. Admission is based upon the student's qualifica- tions without regard to financial need. Expenses for students amount to approximately $238.00 for boys and $235.00 for girls for a dormitory room and twenty meals per week for the duration of the Program. You should also consider laundry, books (about $20 .00) and other incidental expenses.
Would you be able to come without financial a i d ? Y e s No (in case you are able to waive your request for financial aid, you still would receive a full tuition scholarship.) If no, please answer question 23. 23. 96 I. Would you be able to come if given a full tuition scholarship and $lii0.00 (which is approximately one-half of the subsistence)? Y e s No If no, please indicate the amount which in your opinion would enable you to come. $______
II. Could you do with less than $l40.00? Y e s No If yes, please indicate the amount which you would consider as adequate. $______
III. Provision shall be made upon request for one round trip from home to the Program at a rate of 4 cents per mile, with a maximum of $120.00. Do you request this travel allowance? Yes No APPENDIX B
COVER LETTER FOR QUESTIONNAIRE
V7 THE OHIO STATE UNIVERSITY 98 COLLEGE OF EDUCATION I94J NOKTHHIOH STREET COLUMBUS, OHIO 43210
FACUtrr or S c i i n c i a h p MATHtUATICI £»VCATI0N April 9 ) 1970 (614) 2934121
Dear SSTP Participant:
You are one of many who have been involved in the Summer Science Training Program conducted by Dr. Ross at The Ohio State University. But you are a special one. Working with Dr. Harold Brown, I selected a representative group of participants from 1964 through I969. I need answers from each and every one for an accurate picture.
To Improve the program for 1970 and future years-- to report student reactions to the National Science Foundation so that they can convince Congress of the need to continue the program--to conduct an analysis that will form the basis for a Ph.D. dissertation for me-- we (I) need your help.
I have tried to design an enjoyable questionnaire. Your answers will be tabulated along with the answers of other participants to provide guidelines for a more effective program. Your individual answers and comments will be kept quite confidential.
I urge you to take the time to respond. To make your responses useful I need them by May 1, 1970-
Thanks for your help.
Sincerely,
Betty Eberle APPENDIX C
QUESTIONNAIRE
99 Questionnaire 100
I. Identification
1. Na me ______
2 . Year you participated in the Summer* Science Training Program (SSÏP) in mathematics at The Ohio State Univoi*slty,
II, Present Status
1. What is your highest level of educational attainment?
Still in high school High school graduate 1 year of college 2 years of college 3 years of college _4 years of college _Bachelors degree _Masters degree
What is your chief present activity?
Attending high school Attending college--undergraduate Attending school other than college--technical school., etc, Attending college--graduate or professional school [other (Please specify)
3. If you attended college, what was (is) your major?
4. If you are gainfully employed, what is the nature of your work? ______
5. If you attended (or are attending) college, what college did you attend? (If more than one, list them all.) College______Location______College______Location______
III. Selection
1. How did you first hear about the Summer Science Training Program in mathematics?
Teacher Counselor Principal or superintendant Another student _Non-speclfic school source— bulletin board, etc Newspaper _Other (Please specify) ______101 p . Before rpplylur; J'or the prof;rum, cJld you know a por-oon who had participated In the program? ______
3 . Why did you apply for the program at Ohio State UnJvei'oity?
Interest in the courses offered Reputation of the University Near Home Chance to get away from home ^Suggested to me by a previous participant [Good chance of acceptance [Only one the teacher/counselor had information about 'other (Please specify) ______
Who was most influential in your decision to apply foi' the SSTP program at The Ohio State University?
Me, myself Mathematics teacher Other teacher, principal, superintendant [Parents [No one person [Another student ^Counselor 'other (Please specify) ______
I V . Student Evaluation of the Program
1. Some aspects of the program were important in making it successful for you as a_ person. Other aspects probably hindered the success of the program so far as you were concerned. Indicate the importance of each item below using the following code:
VI - Very important to success of program I - Important to success of program N - Neutral (neither a help nor a hindrance) H - Hindered the success of the program GH - Was a great hindrance to success
1. The faculty
2. The social and recreational activities
3. Getting away from home
4. The amount of homework assigned
5* Working in a college environment
6 . The subject matter
y. Contact with stimulating personalities
8 . The amount of material covei-cd
9. The living arrangoments--Dormitory room, food, etc. 102 10. The Individual attention
11. The lectures
12. The intellectual challenf^e
13. Living and working with other young people of similar interests
_l4. The textbooks, reference books, library facilities.
15. The teaching methods
2. From the I5 items in the previous list, write the number of the one that was the most important to you. ______
3 . From the I5 items in the previous list, write the number of the one that was the greatest hindrance to you. ______
4. Evaluate each item below using the scale:
VP - very poor P - poor A - average G - good VG - very good
Lectures Lecturers _Recitation sessions 'Recitation instructors "Counselors "The materials--textbook, classroom equipment, etc. The living arrangements--dormitory room, food, etc, The usefulness of the subject matter in terms of your studies following the program The social and recreational activities The usefulness of the program for making you use your full potential
5 . How would you change the program if you had the opportunity'
6. What is the one thing you would list as the best thing about the program?______
7 . What is the one thing you would list as the worst thing about the program?______
8. Now that you can look back at your summer experience, vdiat do you think is the one most important thing the program was trying to accomplish? 1 0 3 V. A:; you uocaJl your ouiiimor cxpori.oiioo In tho Î'ISTP pi'op,r;mu xndlcaLo your ap;rooinonlor dii'.;j/';i‘CCMrionl vjith lhr':;o :d.al.oinouiLi:. IJno the 1‘ollovri.n/'; code:
3D - 31,ronpdy dinaf/^roe MD - Mildly dlnap.reo N - Neutral MA “ Mildly ap.rec 3A - Strongly a/^ree
1. I felt that I understood the lectures most of the time,
2. I feel there was too much homework.
3. I found no time for sleep.
_4. I learned a lot of mathematics that summer, but I have forgotten most of it since.
_5. I met some great people my own age;.
_6. I wish the summer could have Ijoen longer.
J. I found myself getting farther and farther behind as the summer progressed.
8. The summer taught me a lot about my capabilities as a student.
9. The work was much harder than I expected when I came.
10. The summer was good for me because it really challenged me. It helped me know myself.
11. I found the counselors a real help because they were available when needed.
12. The first two weeks were really hard; then things got easier.
13. The amount of homework assigned was. jus.t about i-ighl,.
14. I still "keep in touch" with at least one pei-son I met for the first time at the summer prop;ram.
19. The program was easier than I expected when I applied.
16. The program was not at all what I expected when I applied.
17. I found the counselors were often "too busy" doing something when I needed them.
18. I always felt rushed.
19. The lectui'os wo so good but I found I couldn't s.eem to apply thorn wlion I needed solut.ions, to homowoj'U problems. 10/, 00, V/lieii I reLurncd to high) :joIiou'J I j'uund inaIheiiiet,Ic:; borin['; because :I.L war; nob a a mi^ch ol‘ a clia ;i leni_';o.
21. V.'licn I returned to high cchool I had a deeper interest in my mathematics course my senior year.
22, When I returned to high school my mathematics teachers considered me a threat. They i’elt insecui-o.
23. The summer program had a positive inriuence J.n my decision to make mathematics or a mathematics- related area my college major.
2/|. The summer program helped me décide; not to ma Ire mathematics or a mathematics-related area my col lop;, ' major.
25. I can't remember many of the facts I learned, but I learned a method of study that has been valuable to me since.
26. The summer v;as good "mental exercise" but I can't see where it has especially helped me since.
27. I "grew up" a lot that summer. It had a maturing influence on me.
28. After the program I demanded more of myself in terms of precise expression of a problem, pursuing a problem longer, etc.
29. The program had a bad effect on me because ;11 was too difficult and really an unpleasant suitimer-.
30. The summer would have been more success.ful overal] if the pace had been slower so that I could have had more time to really learn things.
VI. When you were selected for the program (before you attended the program) what did you expect to be part orresults of the summer experience? To the left of the item, put a "B" in the correct column to indicate your degree of expectation.
"Lot" means you expected a lot of it. "Some" means you expected perhaps some of it. "None" means you expected none of it. iLoi. I Some ' None i' ..j- : 1 . Lectures by outstanding mathematicians 1 • 2. Lectures by faculty members at the college
3 . Tests on tho material being s1;udied
/|. Conference:'' witli college I'acul l,y iiirinhci-r.
9 . Indeiiendeih. r<;search worlc
i i 1 6 . Homework I J jO i. .A) me; None 105 Y. To
8. To
9. To
10, To
11. To
12. To
13. To
14. To
19. To 16. To
17. To
18. To my
19. Sti
20. To
21. To
22. To
23-23. To Increase my Interest In mathematics
VII. Looking back, what things were a part or result of the (jrugramY Go back to Question VI and to the left of each item check v;lth an "A" the degree to v/hlch each item was a part or result, oj" the program.
VIII. Use the space below to add further comment APPENDIX
REGIONAL ACCREDITING AGENCIES
1 0 6 107
REGIONAL ACCREDITING AGENCIES AND STATES WITHIN THEIR
JURISDICTIONS
Source: Accredited Institutions of Higher Education, February, I>67, Published for the Federation of Regional Accrediting Commissions of Higher Education by the American Council on Education.
Middle States Association of Colleges and Secondary Schools Delaware Pennsylvania Districtof Columbia Canal Zone Maryland Puerto Rico New Jersey Virgin Islands New York
New England Association of Colleges and Secondary Schools, Inc, Connecticut New Hampshire Maine Rhode Island Massachusetts Vermont
North Central Association of Colleges and Secondary Schools Arizona Iowa Nebraska South Dakota Arkansas Kansas New Mexico West Virginia Colorado Michigan North Dakota Wisconsin Illinois Minnesota Ohio Wyoming Indiana Missouri Oklahoma
Northwest Association of Secondary and Higher Schools Alaska Oregon Idaho Utah Montana Washington Nevada
Southern Association of Colleges and Schools Alabama Kentucky North Carolina Texas Florida Louisiana South Carolina Virginia Georgia Mississippi Tennessee Mexico
Western Association of Schools and Colleges California Hawaii Guam
Canada APPENDIX E
COLLEGE AND MAJOR
10Ü 109 COLLEGE AND MAJOR
1964
Computer Science M.I.T. Mathematics
Information Science Cal Tech
Food Technology OSU
Computer Science OSU
Physics Carnegie-Millon Univ.
Accounting Ohio Northern Univ.
Computer Science M.I.T.
Mathematics OSU
Mathematics (B.A.) University of Cincinnati Actuarial Math (M.A.) University of Michigan
Mathematics Ohio Wesleyan Univ. Universitat München (Germany)
Mathematics Denison Univ. Univ. of North Carolina (Grad.)
Chemistry OSU Ohio Dominican College
Mathematics Yale
CIS OSU University of Maryland (Germany)
Mathematics University of Toledo
Biology University of Pennsylvania Medicine
Computer Science Brown University 110
1v65
Chemical Engineering Case
French OSU
Mathematics University of Michigan
Mathematics Barnard (Columbia Univ.)
OSU Ohio Tech College
Mathematics Northwestern Univ. Univ. of Chicago (Grad.)
Mathematics Michigan State Univ.
Mathematics Harvard
Electrical Engineering Case Western Reserve
Mathematics OSU
Combined Science Yale (Computer Science applied to the Fine Arts)
Mathematics Youngstown State Univ. (Member of the Sisters Ursuline College of the Humility of Cleveland State Univ. Mary)
Electrical Engineering Univ. of Cincinnati Ill iy66
Mathematics Delta College (Michigan) Physics Univ. of Michigan
Mathematics Yale
History, the Arts and Letters Yale
Mathematics Columbia
Philosophy Haverford College (Pa.)
Mathematics M.I.T.
Computer Science University of Dayton
Mathematics Harvard
Physics Ohio Wesleyan
Mathematics Yale
Applied Physics Columbia
Anthropology University of Chicago
Mathematics University of Notre Dame 112 1967
Mathematics Wise. State Univ. Michigan State Univ.
Pre-Med, Biophysics M.I.T.
Mathematics M.I.T.
Physics Michigan State Univ.
Mathematics Johns Hopkins Univ.
Mathematics Garnegie-Mellon
Chemistry Oberlin College
Pre-Med University of Michigan
Mathematics M.I.T.
Architecture Princeton Univ.
(No Major) St. John's College (Maryland)
Administrative Science OSU
Mathematics Vanderbilt Univ.
Biology Univ. of Rochester 113 iv6a
High School
Undecided M.I.T.
Mathematics Michigan State Univ.
Mathematics Carnegie-Mellon Univ.
High School
Computer and University of Michigan Communication Sci.
English Princeton Univ.
Mathematics McGill University (Montreal)
English Colby College (Waterville, Me.)
Nothing
High School
High School
High School
Physics University of Chicago
(No Major) A technical school
High School
Physics Case Institute of Technology 114 1969
High School
High School
High School
Biology M.I.T,
High School
Philosophy Center College (Danville, Ky.)
High School
High School
High School
High School
High School
High School APPENDIX F
THE ONE IMPORTANT THING THE PROGRAM WAS TRYING TO ACCOMPLISH
115 11 6
What do you think is the one most important thing the program was trying to accomplish?
1964
The advance exposure to college-level math study.
No response
The ability to take a problem and logically plan ways to solve it.
To prepare the capable mathematics student with better insight on problems of the subject which are covered in college curriculum. It broadens his background and makes his analytical methods of approach much more mature.
Broadening the experience and perspective of the participating students.
Directing students toward a career in mathematics.
An interest in theoretical math invisible to most qualified students (those who might now elect mathematics as a college major rather than another "science").
No response
To get students to think creatively and originally— to gain an understanding for the logic and structure of mathematics and proofs.
It was trying to teach us to enjoy math.
Challenge and stimulate high-potential and high-achievement high school students; with thoughts to the future.
Find out how much we were capable of.
Introducing the high school student to a very thorough and intensive study of a non-trivial branch of mathematics (or other subject matter). At least for those who were successful, it shoTTod them not only how much they didn't know, but also how much they could learn.
Develoning the mind into imaginative Math.
S)low that there exists a higher form of mathematics than what we wore exposed to in high school.
InteJl ectua]. stimulation and exposure to a really academic environment.
No response 117 196$ Stimulate students.
To incite people to use their full potential especially in math by providing a stimulating and more diffecult program than high school students normally get.
Improve insight into simnle situations. "Great men think deeply of simple things."— Prof. Ross.
The teaching of the life and ways of a mathematician.
It allowed mo to take a course that I enjoyed but was also challenging. To teach us how to think, and to develop some sort of mathe matical sense or intuition.
An immersion in how a mathematician (or scientist in general) lives. Give students a method of approaching and solving problems.
Provide a challenge to meet a student's limits.
To promote a lasting interest in mathematics.
An introduction in depth to higher mathematics which was designed to teach a way of thinking rather than memorize processes (i.e. ^qt calculus). I would say approaching math from an experimental discovery angle. Academic maturity. lie
1966
An honest appreciation for mathematics as an art/science and an intuitive feeling for the variety of topics included under the heading of "Mathematics'*.
Get students accustomed to college level work.
To v/eed out the math geniuses.
Instill enthusiasm for mathematics in its students.
Awaken participants to the complexity of the universe.
I can't answer this.
Provide an opportunity to develops and exercise a habit of constructive curiosity.
Give a taste of mathematics and life of a mathematician.
To help high school students become involved in challenging learning.
To show successful high school students that they're not as brilliant as they think they are.
Establishing an interest in mathematics.
To help the student to think analytically and creatively.
No resnonse. 119
Active, thou,n;htful, concentrated participation in doing mathematics.
Give a feel, or intuition, for how mathematics is done and felt.
Get the students to work and meet the challenge of the work presented. This teaches the students what they can do and probably what they should expect of themselves.
To teach us the basics of a rigorous approach to a mathematical subject.
It really prepared me for college and gave me confidence in myself.
Teaching mathematical rigor.
Stimulation of particinants to do original thinking in mathe matics (as opposed to knowing Cayley's Theorem.)
Challenge you to a tremendous degree to bring out your full potential and let you become aware of it and your study limitations.
Instillment or bringing about of mathematical maturity.
To teach rigorous treatment of mathematical principles.
To teach that mathematics, good mathematics, is creative and as much an aesthetic art as a discinlined science.
An in depth aunroach to studying mathematics.
To tench me to consider math as exciting and to do mathematical thinking.
Give me a chance to experience college life. 120
As Dr. Ross said— "To give the students the opportunity to live the life of a scientist"— Also to stimulate interest in mathematics, and to teach a method of logical thinking, study method and sclf-discipline that the student can take to all his subjects thereafter.
The development of the ability to think intelligently about material different from the normal.
I think it was trying to give the student an insightful under standing of what mathematics and college living are, by challenging him to do mathematics in a college setting.
The program stressed the use of each individual's potential under an intellectual challenge.
Get across the spirit of mathematics— how one thinks!
Giving students a feeling of what math and college are like (leaving high school experiences behind).
Create a stimulating and challenging intellectual and social environment.
Bring together students of similar interests and have them work and study along one direction so as to improve their chances of success.
To get me to be more self-reliant.
An introduction to total dedication— very important and useful.
It was trying to give an experience of intensive involvement in a highly intellectual discipline.
The program was probably trying to create more aware science students, rather it taught us how to do some mathematics.
To influence us to think in a logical, mathematical manner.
A thorough knowledge and understanding of number theory.
To get us to think and discipline ourselves like mathematicians.
Teach the student sound mathematical techniques and enable him to appreciate individuality in approach to mathematical problems.
To give high schooJ. students a chance to learn mathematics they wou]d never have had in high school. 121 lv6)
To convey, perhaps in a somewhat exaggerated manner, the life and discipline of a inethematician.
To teach us to work, to open our minds, get us interested in different aspects of mathematics.
Mo response
Development of heuristic skills.
To have each participant reach his highest possible level of performance.
Test one's perseverance in the face of many difficulties.
To show us how hard we were capable of working, and hov; much we learned from this work.
To demonstrate the beauty of the interrelationships in mathematics.
To enable the student to deal successfully with mathematical problems.
Bringing out all the potential that was previously hidden in the participants.
Develope mathematical maturity.
Teach the students hovr to think logically. APPENDIX G
THE BEST THING ABOUT THE PROGRAM
122 12 O What is the one thing you would list as the best thing about the program?
College Environment l/'ôTf The advance exposure to college-level math study. College environment and availability of educational opportunities. Introduction to math on a college level Presentation on the college level and atmosphere 1965 Opportunity to be in college environment studying an interesting subject. College environment. 1966 Educational environment The living conditions. 1967 The college environment and the hard work. 1968 The atmosphere The continual interplay inside the dorm. Being together in one dorm. 1969 _____
Intellectual Challenge 1964 ~ 1965 The intellectual challenge The intellectual challenge The intellectual challenge 1966 The intellectual challenge in mathematics. Intellectual challenge The intellectual challenge it provided. 1967 The complete enjoyment of working my brain. Stimulating challenge I96S The challenge of the work. The intellectual challenge. The intellectual challenge of the program. 1969 The challenge and hard work. The intellectual challenge. It makes you work to your full potential. Challenging.
Subject Matter \ j G i l Subject matter offered and method taught. The contact with math in an enjoyable setting. The opportunity of seeing what mathematics really is concerned with. 1965 An introduction in depth to higher mathematics which was designed to teach a way of thinking rather than memorize processes. 1966 The opportunity and the encouragement to do math. 1 9 6 7 ______I96S I learned many mathematical "techniques" that I would have never learned in high school. Iv69 1 24 People 1964 Exposure to very intelligent peer group. Contact with other students. Working with other students with similar interests— challenging work. First contact with intellectually stimulating people of my ovm age. 1/65 Students in program. The people I met there. Opportunity of meeting so many interesting people. 1966 For the students, it’s the opportunity of those who have great potential to meet others of similar abilities and interests. Contact with students and counselors. 1/67 Bringing together young people of high caliber with similar interests. The opportunity to study with others my age in an environment conducive toward gaining self- reliance. Contact with so many intelligent people. 1968 The people involved— instructors, counselors, and students. Communicating with young students of similar interests, The students involved. The people— everybody. The concentration of very bright, highly motivated people. The people involved. Contact with stimulating personalities. Counselors and students exchange of ideas. It provides great opportunity for interaction with other high ability students. 9
Faculty 1964 The enthusiasm for mathematics of Dr. Ross. 1965 Dr. Ross The exposure to a very good college faculty. 1966 Faculty. 1967 lv68 1969 The teachers and counselors.
Counselor;
1965 1966 1967 The counselors Counselors lv68 1/69 The idea of counselors for individual help. Counselors. 195 Teaching Methods T % k Individual help and attention from outstanding instructors— interest in development not material covered. The intensity of the program. This was only successful, however, because it was also complete (very few un-tidy ends left hanging). The speed of coverage. 1965 The energy, drive, enthusiasm, and intellectual curiosity that it not only excites in the students but keeps at a constant level. 1966 1967 The way the problem sets illustrated the material. The Harrassment excel. Becoming totally immersed in mathematical thought; even if one couldn't (as was my case) do the work, he caught a vital spirit. Lectures 1968 1969
Other U 64 Cultural enrichment of seeing new things. 1969 Good opportunity to test one's capacity for a full time math career. APPENDIX H
THE WORST THING ABOUT THE PROGRAM
1 2 6 127 What is the one thing you would list as the worst thing about the program?
Pace and Work Load T 754 The pace and work load. Seemed no hope if you got behind on a subject. 1965 Those who didn’t understand got more and more lost, despite the help of the counselors. 1966 Time it took to adapt to work level. The work load was too heavy. The over abundance of homework. I96S The amount of "homework" assigned. The eight week length (should have been shorter). Work— excessive amount. Amount of sleep. Doing number theory 24 hours a day for S weeks. Time It goes too fast. 1969 Too much work for the amount of time available. Lack of time for recreation. Towards the end, I was becoming depressed by my inability to keep up. The work. The load was oppressive. Lack of free time.
Living Conditions 1954 Living at home (But the opportunity of going far outweighed the disadvantage). The students who commuted failed to get enough personal attention. Lack of program for the off campus participants. 1965 The isolation of the commuters. O.S.U. dormitories. 1966 I didn’t get along with my roommates and didn’t make any lasting friendships. The food 1967 Columbus Recreation and food I96Ô The food The living accomodations The strictness of rules in regard to work assignments and living arrangements. The food The campus-city environment 1969 The living condidions Poor choice of roommates 12Ô Organization of the Program iv6'4 Disorganization Lack of flexibility to adapt program to individual needs. 1;65 Rigid course outline lv66 Total emphasis on mathematics as the intellectual pursuit of the summer. If you weren’t doing mathematics you were thought to be wasting your time. 1>67 Lack of use or reference to good textbooks: text books lend coherence and continuity. No follow-up The narrow field of material covered lv68 Lectures not seminars as main source of information iv6y Inhibiting, i.e. regimented as concerns material covered.
Teaching Methods Lectures sometimes get a little long. The tests The lonesome and lost feeling in the classroom Recitation section with an instructor who spoke very poor English The materials used 1765 Recitations
1967 The emphasis on getting grades above the median on tests. Harrassment to excel. Competition among students The competitiveness that was there during (especially) my first year; the importance both students and counselors attached to the tests. 1968 Recitation sessions Sometimes the conferences were dull. The homework was often related to the lectures— the subject drifted. 1969
Adjustment ■ 1964 ' It is easy to get lost in the shuffle. Disinterested counselors The lack of counseling 1965 1966 Lack of communication between participants The counselors lv67 The wide range of abilities between high and super-high. 1 ; 6 8 1 >'6 ; 129 Social and Recreational Activities Î / W ------1965 Lack of social activities 1966 Poor recreation facilities easily available. Confined to SSTP students. Also I was older than most of the other students. The social and recreational activities 1967 1968 ' ~ ' 1969 Lack of recreation
Other 196$ None 1966 I can’t answer this After 8 weeks, it ends. 1968 There is nothing I would call bad. Human weakness in some participants. APPENDIX I
CHANGES THE STUDENTS WOULD MAKE
1)0 131 How would you change the program if you had the opportunity?
Organization of the Course Distribute course notes. Eliminate the tests. Recitation sessions were ineffective— I would like to have more faculty available for questions. Books were hard to follow; had misprints. Let the program run longer. More recitation time. Structure second year program better. Course should run all summer. Course should be arranged so it could be taken several summers. Encourage more people to take algebra as well as number theory. Allowance for individual interests rather than mass instruction. Use Hardy and Wright for number theory. Use Shoonfield, or maybe Mendelshon, for logic. Use different textbooks. Better structured program for 3rd and 4th year students. Change attitude that 2nd year students don't work with more rigorous homework. Move away from the computer. Maybe drop lectures in favor of recitation sections. Have classes everyday. Allow greater personal freedom. Introduce greater freedom for individual to pursue his ovm interests. Change to more independent type of research-study program. Make recitation sessions more pertinent to specific material. Eliminate requirement of number theory and let the student choose either number theory or algebra (or both). Alter recitations or bring them to dorm. Have notes and reference books listed instead of texts. Have more weekend problems such as "Toward the Abstract". Go through number theory faster to permit analytic number theory class. Have more tests. More time should be spent showing students the solutions.
Pace and Work Load Allow for a slower pace for those v;ho need it. Reduce quantity of problems on a homework assignment. Substantially reduce the number of problems. Decrease intense pressure to work. Lighten the weekend load. Keep homework assignments on level of mental gymnastics. 132 PacG and Work Load Somehow vary the course load or number theory class so less capable students wouldn't get so bogged down. Make some adjustments to the course loads. Shorten the program about one week and lesson the work load. Make more demanding. Make it a bit less demanding. Cover slightly less material— at the end. Toward the end, it got much too rushed. I would cover less material in the eight weeks. I felt the pace was too fast.
Subject Matter Little more diversity in offerings to meet the problems arising from different mathematical backgrounds. Make material more relevant to student's courses coming his senior year in high school and freshman year in college. Introduce some "applied mathematics". Discuss topics more relevant to either future courses or the practical world. Add a yearly course in analysis. More time devoted to talks related to occupational opportunities. Make the number theory section of the course more coherent by greater unification of subject matter.
Recruitment Raise the age or education requirement. Be selective concerning backgrounds and more clear about goals of the program. The program is designed for the math genius. I would attempt to attract people with just a normal interest in math. I'd advertise it more. Try, if at all possible, to determine if an applicant is accustomed to concentrating for long periods of time on a particular subject. I would be more highly selective in acceptance of applicants.
Counselling Instruct counselors to show interest in every student. More counselling Personal attention to assure comprehension of materials more. More individual attention. 133 Living Arrangements Not let students commute. There should be help and organization for commuters. More air-conditioning Reduce gap between commuters and resident students. Change living arrangements. Being a commuter I missed a lot of the experience. Better food Living conditions could be improved. I'd make all commuters live in dorms. Single rooms Change four students in a dormitory room to two students. I needed to be cut off totally from home.
Recreation and Social Activities Provide a central recreational area. Arrange some cultural and intellectual activities not related to mathematics. Need for more supervision out of class, programing events, dorm living, etc. Change the ratio of boys to girls from 5:1 to 1:1. Recreation should be encouraged.
Grades, Competition Not emphasize grades as much. Perhaps make it slightly less competitive. The cooperative spirit, if there is any, was not sufficiently emphasized.
Other Follow-up by mail of interesting problems. Maybe initiate a tutorial program so that the SSTP students could help less fortunate people in Columbus while themselves learning mathematics. APPENDIX J
FURTHER COMMENTS
13A 135
Use the space below to add further comments.
1 >64
I had trouble taking notes and still thinking. Course notes would have helped a lot. (This applies to most math courses here at M.I.T., too.)
First of all I want to wish you much success with your project. I hope I ’ve been of some help. I was really looking forward to my summer of '64 with mixed anxieties. I had just turned I6 and finished my sophomore year in high school and had enjoyed algebra I and especially geometry. However I saw practically nothing of geometry and only algebraH, trig, etc. The girls in the dorm and the guys 1 dated were very good about helping me with the things all the others knew but me! 1 did not study as hard as 1 could have, but 1 became dis couraged very quickly and my grades dropped. 1 was glad for the experience 1 had. My roommate and I still keep in touch and visit now and then. 1 wish there had been a few more activities for us "High school" kids. 1 was too shy and too embarrassed at the college activities or to shy to attend the library. The instructors and professors seemed cold to me and 1 felt inferior and "too dumb" to ask for help. So I ’d say 1 have some bitter experiences from my classroom experiences, and very pleasant memories of the rest of the summer. The summer very quickly made me realize that mathematics was more than geometry. 1 gave up my plans for a math career and w^as discouraged and lost. My sophomore year of college 1 began majoring in accounting and received my degree in accounting December, 1969.
1 hope you get a lot of replies. I'm doing my undergrad uate thesis now and I ’m having difficulty with getting people to co-operate.
Looking back on it (and it is almost 5 years now), 1 feel the infectious enthusiasm generated by Dr. Ross for math ematics was the most significant aspect of the program. The program was certainly extremely challenging and 1 feel reward ing. Far more than a set of mathematical facts was being taught. The students were forced to prove theorems and develop the theory themselves in many cases. The very art of mathematics was really the topic (or subject) being taught.
I ’m sorry that my memory isn’t better. 1 attended the program in l / 6 k — the first summer it was offered at OSU and 1 know that each year it has been improved. 1 feel that 1 missed a great deal by not living on campus. 136 I don't know whether or not you do it now, but there is a lot of sophisticated mathematics which could be done in the computer field. I do not necessarily mean teaching a programming language, but rather such topics as computability, languages, numerical methods, etc.
One problem I had— perhaps because I did not live on campus and hence had less access to counselors— was the fact that I tried to do some things which were too difficult to jump into with no help at all. I am referring to the logic seminar given (I think) by a Father Thomas. He jumped into completely unfamiliar ground immediately and without counselors available at night (I lived at home) I was never able to catch up. I dropped it about a week later. This was very disturbing because with enough help to let me understand my notes, I think I could have gotten somewhere.
The reason I have not graduated and am only a junior is because I served three years in the army between 6? & 70.
The material was interesting at first but I will admit I became lost towards the end. Also the material was not presented again until my second or third year of college at which time much of the material had been forgotten. 137 1>63
Enjoyed summer— pace about right— lectures occationally hard to follow— enjoyed meeting others in program— haven't met as interesting a group since.
Looking back, I really enjoyed the summer for my exposure to mathematics and to a college environment. In fact, I liked the set-up of the SSTP that I went to a similar NSF Institute the following summer at Northern Arizona University at Flagstaff. I made up here for some of the activities and student to student interaction I missed at OSU because I commuted. Drs. Walter and Butchart of the NAU Math Dept, were outstanding as, of course, was Dr. Ross. We went on several trips (to the Grand Canyon, the Painted Desert, etc. Northern Arizona has a much greater store of natural resources which serve as excellent places to go on field trips than does central Ohio). Also there were only 30 of us, 10 girls 20 guys, and as one of the 10, I couldn't argue about that. If you would like a longer comparison between the two, I would be glad to help you. I'm living at lS6l Indianala here in Columbus and my phone number is 2>'4-3l6l (Don't think it's a wrong number if someone answers "Theta House") I did begin at OSU as a math major and took one honors math course which I really didn't enjoy, probably because, as much as I liked the stress on theory in our class, we still had to (on our ovm) keep up with the regular section problem solving and take their tests which I disliked. Oh well, I do like French and I still remember quite a bit (I think). As a result of my summer at OSU, I did a math related science project which I took to the State Science Fair on Diophantine Equations.
This is the first questionnaire that I can recall having fully completed. I completed it only because of your request— it was difficult and meaningless to me as all the others I have attempted. I generally contradict myself in question naires because I don't like the way the questions are phrased and because I don't like rating anything. I generally answered the questions on the basis of my experience as a 1st year student (except IV (3). I have been a 2nd year student and counselor as well in the program, and therefore I can say that the experiences are very different. Perhaps you should have considered this.
Best course I ever took!
I'm being married in June t o ______whom I met at the summer program. 138 The program undoubtidly made me a worse student and foot ball player since I discovered that many things I had previously cared about no longer mattered. I had played football as an outlet for rage and hate for my o;vn incompetence. The summer convinced me that I had some intrinsic worth. It also provided the contrast to complete my model of the high school as a complete academic waste of time.
The program could probably use more publicity. Not very many high school students hear about the NSF courses. As far as 1 know no one from my high school other than myself has attended anything of this nature.
This happened long ago and there is very much 1 don't remember about it. However, these were the best math courses 1 ever took, best taught, most informative, most stimulating. Since then I have gotten bogged down with calculus to the degree that 1 have very little to do with it and am mostly interested in the arts. Sometimes though, 1 think 1 would like to go back to math and if 1 ever do, it well be because of the program at Ohio State. Also if 1 do, 1 will probably try to go wherever Dr. Ross happens to be.
1 have tried to be as thorough as 1 could be in filling out this questionnaire. However, it seems ^ long since 1 was at OSU. 1 was very glad 1 was able to participate in the program. 1 do thinY I felt lost a lot as far as the math goes. Think 1 would have advanced more if 1 had a little more self confidence and the approach was a little slower and more "rigorously" presented for me. 1 did find the counselors very helpful and available but think I would have benefited much by a more detailed presentation Tn the lectures instead of for example, being told to figure out how to solve Dia- phantine Equations. 1 realize for others this was very chal lenging and they did it, for me it got more and more frus trating. 13 V l-;66
I wish to speak somewhat about V. 20, 21, 22. When I returned to school as a junior I ran into a very peculiar sort of problem. My school had no advanced track or A.P. mathematics program, and I had basically covered most of the second-year algebra course on my own, so I petitioned to take senior math. The algebra teacher (the teacher who first told me about the program) and the senior math teacher, both thought the petition was a reasonable idea. My teachers did not consider me a threat, but the administration did. I was not allowed to advance. Summarily they stated that they could not make such exceptions! My sympathetic algebra teacher let me work on other topics, including proof-reading a paper she had written on non-euclidean geometries.
The program showed me the limitations and my ability in mathematics. I am grateful for the opportunity to partici pate in the program, and I think it is an excellent one for people interested in math.
Next year I am going to Harvard Graduate School in Mathematics. From the Wilson Foundation I won independent study money for the summer. I am attending a seminar in Algebraic Geometry in Oslo, Norway, and the International Mathematics Conference in Nice, France.
In the two terms I visited Ohio State, I took the fol lowing, Number Theory— as I stated earlier, the choice of text was poor, and the handout on "reduced inventory" took a great deal of time (the No. of exercises was absword) to make a point (isomorphism of union and intersection with LCM and GOD) which, properly viewed, was trivial. Some of the exercises (especially the Steinhaus formula) were highly unrealistic, and (sometimes) ambiguously stated. The set of problems sent out to applicants was quite challenging, but several were misstated. Algebra: At the time I found the definitions unmotivated, but their study undeniably prepared me for their use in college courses. Logic: When I took this course, a book by Hugues Leblanc was used which is still my candidate for all-time worst math book. I think some effort should be made to discuss the Godel incompleteness theorem, recursive functions, and axiomatic logic, and fragments of propositional calculus, strongly recommend topics in Analysis and Topology: This was an ambitious course not primarily for SSTP participants, quite a lot of the time I did not know what was going on, but it provided an introduction to certain theorems and ideas (axiom of choice, general 140 topology) which I have found quite interesting. Analysis (Prof. Saltzer): This course was somewhat weird. Some of the material involved (elementary proofs of Stinings formula, etc.) v/as quite interesting, but somehow the lectures always got bogged down on trivial points. Perhaps it would be better to suggest some previous accquaintance with calculus as a prerequisite. It was very enjoyable to spend two summers with a group of people with a common interest. It generated a subculture, complete with its own language and its own inside jokes. (Example; "What happens when you stand in front of a six- inch howitzer and pull the trigger?" Answer: Cannonical decomposition)
The program has definitely had great effect on my studies in mathematics and should not be discontinued.
The program did not have as much future influence as you think. 141 1/67
I often wonder about what might have happened had I attended a different program the second year, or none at all. I was seriously thinking about Illinois Inst. Of Technology, with a program in computer science and statistics. The conflict between attending the third year and getting a job was also strong. The second and third years were in some ways more difficult than the first; especially the second year, I tried to do too much, and I also felt a barrier, a communications gap, between myself and first year students. My biggest disappointment was the non-availability of the computer time-sharing APL for Exp. Number Theory the second year. On the whole, the experience is one of the greatest I have ever had, especially for working with others of similar talent and interests, and I think this is the most important aspect of the program.
OSU was a deeply affecting and meaningful and I think decisive point in my life. It introduced me to many people and notions and emotions I ’ll always cherish. I firmly hope OSU continues and offer my complete aid, if possible, to any efforts to sustain it.
I think that there is a lot of potential to learn things in non-math areas that is not being used. You have some very gifted and multi-talented young people there and a lot could be gained from interpersonal contacts and bull sessions. There wasn’t enough time for this. The load should be lightened on weekends to allow for it.
The social life is not all that tremendous at Ohio State but an effort is made. I had a significant social life but only 4 or 5 boys had much of a social life at all. Still I think this may be due to the amount of work as well as the lack of girls.
I think Congress would be making a serious mistake in cancelling aid to OSU. The way of thinking I learned at OSU has immensely helped me in my present schoolwork. It was a worthwhile challenge.
The summer was my first subjection to such a mental torture. I reacted with a proper amount of activity— but it was a piecemeal self-preservation of doing homework problems. A great deal of the continuity of succession of topics was lost to me. It was possible to do this since I had a minimal amount of contact with floor counsel, discussion group leader, or the faculty. Most of the benefits of the summer came by reviewing the experience and using the discipline and "acuter perception, intuition" I got, after the program was over. 142 If nothing else, the program did enable me to more critically evaluate the math department here at Michigan, and find that there is at least one area where Ohio State is superior to Michigan. However, even with this edge, OSU is going to have to go a long way before it can seriously hope to challenge Michigan on the football field. Q.E.D.
Yes, please notify me if, when, and where your study will be published.
The entire program could have been more meaningful if there had been some reinforcement at high school. On the contrary, I felt the students and decidedly the faculty used this as a starting point in hating me, actually discouraging me from returning the second year, and using every means to prevent me from continuing a vital interest in mathematics. As a result, I began very much to feel superior to the people at home, and yet inferior (especially the second summer) to those at OSU, so that a social problem got started I am still struggling with. Also I became glib and sententious with my new-found vocabulary upon returning home, and I found myself professing knowledge about things I didn’t understand at all. Although I did get a vital spark that summer, I don’t think I ’ve yet been able to adjust to the fact that normal people in a normal place, and even me in another place, can’t possibly have this intensity or singleness in purpose. Perhaps I was just too young and emotionally/intellectually too immature for this program, but is was really an over whelming experience, almost too much for me to handle at the time.
The program was extremely rewarding and I regret that I could not return the second summer for personal reasons. It greatly increased my appreciation of mathematics and my "feeling" for it. However, I do wish that there had been more of a follow up of suggested readings and problems. l/i3 lv6Ü
Re; Question 23 - Part VIII— My appreciation of mathe matics was increased, but not my interest. I saw that I could never be a good mathematician, and this realization is probably what gave the program its effect alone. I have since decided to be a psychologist, an occupation to which 1 well take all the skills taught me by the SSTP program— as indeed those skills would be valuable to any occupation. Although 1 did far from spectacularly in the program, it taught me to think clearly and logically, and more important, not to be afraid of really hard intellectual work. Since attending the program, my grades have improved phenomenally. 1 now hold second place in a class of 400, first place being held by a boy who also attended the institute. I think that says more for the program than 1 can.
During the program, 1 wanted very much to do more than 1 actually did. 1 thought that some of the problems were very hard and that there was a lot of pressure present. Although at the time 1 complained about the amount of homework, 1 don't think 1 would change it at all. 1 pushed myself and did more work than 1 would have if there was less homework. For as long as 1 didn't understand the material, 1 was dis pleased with the textbooks. Once the material sank in, the proofs appeared remarkably clear and simple. 1 hope that this questionnaire will help you in your work. If you want me to elaborate on any item or fill out another questionnaire please feel free to write.
1 think this questionnaire is a very good idea. If possible, 1 would like to see the results of your research. My experiences at Ohio State were among the most valuable 1 have ever had. 1 hope the program continues, and 1 hope it continues to improve.
1 feel that the SSTP was an important influencing factor in my life thus far. It added a new dimension to my life and I think it helped me to understand what my future in four years of college would be. 1 am indebted to Dr. Ross for allowing me to participate in this program.
Gave great insight to college life.
1 feel that perhaps more flexibility could be instilled in the program by leaving number theory for perhaps one summer and turning towards a field such as algebra. 1 think the rigidity of subject matter somewhat hampers the effect of being dynamic. 1 think the competitive atmosphere of the program should be lowered still, in order to preserve the emotional well-being of the participants. U h I found the program most valuable both in my intellectual and personal development. I learned much about mathematics, but even more about the scope of my mind and how to best attempt to utilize it. I learned much about people by being in close contact with a diverse group of young people. I also was shown a preview of college and feel that my summer at O.S.U. was responsible for making my transition into college so easy. While I am not majoring in math, O.S.U. did not turn me away from it, but rather strengthened my interest in mathematics. All I can say is that O.S.U. was a fantastic program bringing together a fantastic group of faculty and students within an intellectually and socially challenging atmosphere and was a major influence in my life. I think the program should definitely be continued.
I think that the most important feature of the program was the fact that students with similar interests were in contact with each other almost 24 hours a day which was (1) a challenge (2) a help because of discussion on some problems. This kind of total involvment rendered studying easier and much more pleasant.
The summer was the most profitable of my life. The lessons I learned have been well applied this year in college. I'm happy I attended the college program that summer and hope it continues.
The summer helped me decide not to major in math in college which I had never seriously considered anyway. The reason I consider the summer a very positive thing is that it helped me learn to think in a certain way and I hope eventually to follow it up with more study of pure mahtematics.
I have only the deepest respect and gratitude for the students and professors, especially Dr. Ross, who participated in the program along with myself.
Enjoyed program very much.
As I have stated before, I think all participants should be required to live in the dorms because a great deal of discussion of problems and techniques takes place there. A student who knows how to do the problems and knows the theory behind them finds that teaching another student will clarify and reinforce these ideas in his own mind. As a resident student now, I find many ideas become clear in a midnight bull session. When I was a commuter, I found that going home would put me in an environment that was not conducive to mathematics. Even though I have forgotten many cf the fine details of number theory, I have found that the ideas and techniques have been extremely helpful after the program. 145 1)6;
My mathematical intellect is only one part of my total identity. I found development in all other areas (perhaps even the physical) v/as sacrificed for mathematical develop ment, and I do not consider this justifiable. As far as homework goes, much of the work was nonessential for basic understanding of the subject matter— merely frill for the imagination. Some of the "frill", however, was quite chal lenging and took away time from more worthy problems. I feel at least a slight reduction in homework is in order, and certainly it should be indicated to the students just how essential each problem really is. The nonessential problems are recreation; perhaps most students would at least occasion ally prefer to spend their recreation in other ways. Psy chologically the summer was very trying. For one thing, I found very little release from the pressure. Another thing that was a bit shocking was that I wasn't even in the same ball park with the people in the top or so of the N.T. class. I was totally outclassed, whereas in my large high school at home I was first in class rank and one of the leading students in several departments. I actually did become slightly ill at the end of the program, due I think to fatigue. I was used to high achievement, so I pushed myself practically to my limits. In fact, I am convinced that I could have done significantly better if I had had proper rest, for fatigue has an almost quantifiable effect on my intel ligence. One of the major things I did take away from the program was a strong feeling for mathematical rigour.
To me the greatest single thing about the program was that it helped me find my peak potential.
I worked pretty hard, but not as hard as I could and now I regret that I did not take better advantage of my summer. But considering I am a perennial goof-off, the summer was good for me. I learned a lot about math and it increased my interest tremendously. It even helped me get the highest score on camnus in the Putnam Contest although I'm only a freshman. In short. I'm very glad I went and sorry I didn't do better (Because now I can't come back as a counselor).
I feel that Dr. Ross's method of teaching by asking questions was excellent. It stirred a great deal of interest in me, and caused me to look forward to answering the questions on the problem sets and any others that came to mind.
I felt that the SSTP math program at O.S.U. was a very fine program. Its value came from a realization (presumably on the part of Dr. Ross) that the S-week experience could be most beneficial not as a stepping stone to higher mathematics but as a perch from which to look at various "simple" mathe- l/,6 niatical systems. Dr. Ross tried to show some of the inter relationships in mathematics, and I think he was successful.
The Ohio State Math SSTP was one of the finest experiences I have had. If I can be of additional help, please let me know.
I would not have been able to attend the lyS^j SSTP if it were not for the funds provided by the NSF. I feel the money provided for these programs is extremely well invested and should definitely be continued or expanded. The program was an extremely beneficial and maturing influence on me. APPENDIX K
LETTERS FROM PARENTS
1/.7 14Ü LETTERS FROM PARENTS
1^65
Benjamin ____ enjoyed the contact with the instructors, counselors, and students this past summer. He came away wanting to become a mathematician, philosopher and teacher. He's been bursting with math and "logic". He’s determined to teach some of his Number Theory and other items learned at Ohio State to his classmates (with his math teacher's blessing). He's on a rampage to get the school to beef up its math program. In short he's been bitten by you math bugs and is full of "mathitis". It was a wonderful opportunity for Benjamin to be included in this program— to be exposed to this able group of young people— to have been influenced by you and Mr. Broivn.
What way did the summer program influence my daughter? 1) Realization that the discipline of mathematics has a creative as well as a utilitarian aspect. 2) Realization that the "impersonal" university has a warm and human side. 3) Developement of confidence and increased skills in meeting and dealing with new people and situations. 4) A feeling of continued involvement in the learning pro cess. 5) In an age where kindergardeners "graduate" in caps and gowns I thought your final assignment of problems (to be handed in by Christmas) and simple "good luck to you all parting message" was a deft stroke of psychology. 6) As for the continued challenge during the comming school year...so far all Melany has mentioned is that she is to be graded separately in Algebra II and her instructor hopes to have some extra time to work with her on some advance problems.
We feel that Richard's participation in this program has been one of the highlights of his life and naturally, as parents, we were pleased to know that his performance in Number Theory was Excellent. Richard is now a freshman at Ohio State University and is enrolled in mathematics 440 class. ...
Both Alan and Philip have profited very greatly by the experience. First, they have been exposed to and have learned something about a type of mathematics that extends their fields of thinking a great deal. Second, they have had the valuable experience of meeting the working with other top- notch students from other areas. The total exnerience has resulted in both boys solidifying an already strong interest in math. Alan, of course, has been more strongly affected at this point because of his previous experience in the NSF summer program and the courses he took on campus last school year. The genuinely friendly and helpful interest that you 14v and others on your staff have sho\m have been of great value to both boys.
Replying to your letter of September 13, Carol's participation in the summer program at Ohio State has given her a deeper insight into the study of mathematics. It also presented a great challenge to associate with such gifted students which we believe has provided incentive for her studies in general at school, and in mathematics in particular.
We believe the summer program has awakened some interest in mathematics in John. He has expressed interest in discussing Number Theory with others familiar with the subject. But unfortunately this has been rather difficult to do in our area. He found the work hard, difficult but not impossible, a challenge that could be met. His fellow students impressed him not only with their high degree of intelligence but also with their wide range of knowledge on many subjects and thoughts. Quite different from the average student here. He gained confidence in his ability to perform well in mathe matics. 150 1/66
In reply, I should like to state that you can't possibly realize the good that your program did a student like Bruce. He loved the challenge that he received there, the activating of his brain was good, and he only wished that the grades to the other two subjects that he carried had been included on the letter. He loved the college teaching much more over that in high school, and this year he finds his college Calculus extremely easy— in fact, boring. As to what the school is doing to stimulate his summer interest..I think that they are doing all that is humanly possible for an average school to do...in fact, with thoughts on college now and the testing programs, Bruce is so concerned that he will find a mediocre program, and he longs for one like that summer seminar. They caught him doing the physics problems for the seniors in the lunchroom, so they have left him carry physics in addition to his honors course of 6 subjects: theology, English, History, Latin III, College Calculus, Chemistry and now Physics. Upon his complaint at not learning anything in chemistry, they left him take College Chemistry I at Xavier University on independent study. This is the most that we can hope for. Next year at 15 when he is a senior, he will only sprnd & day in high school (he has exhausted the math and science program) and he will try for a fev/ more credits in college.. .then in 1966 when he graduates properly from LaSalle, we hope he will pick wisely his choice of college, and scholarship limitations. Also, he is on the tutoring program in high school, and will tutor 6-9 boys after school. He is building a computer for the science fair, so I think we have much to thank your program for.
In answer to your question about how Peter will maintain his work in mathematics, for your records I would like to indicate the following. Peter is now a freshman at Columbia College and after an interview by the Mathematics Department is now taking advanced calculus for one semester. After he completes this in February, he will be admitted to the Graduate School of Mathematics. He is also in the physics program. I think from my observation that Peter is intensely interested in mathematics and I am sure that the ten weeks that was spent at The Ohio State University will add a great deal in providing background for his future work. We wish to thank you again for including our son in your urogram and we do believe that it is one of the finest of this variety in our country.
I believe that the summer program in mathematics was very helpful to Michael in fostering his interest in the subject. He feels that he learned a great deal and is now thoroughly convinced that he wishes to major in mathematics in college. He is not yet 17 and his ideas may change but at the moment 151 he believes he would like to pursue a career in theoretical mathematics or physics with the intention of teaching and/or doing research. During the present academic year he is study ing trigonometry which ho finds boring, and calculus which he considers very stimulating.
Your summer program had a profound influence on Doug. The college approach to mathematics was a new and invaluable experience for him. The association with students, counselors, and professors of such high caliber in this field has done much to help him prepare for college life. The social activities at the Union with students other than those in this particular course, the realization of the vast expanse of the field and how much more there is to learn, and the increased incentive to push further into this field of study are only a few of the ways you have helped him.
I should just like to commend you on the terrific program that Dr. Ross has in the summer National Science Foundation program in which my son, Bruce, was a member from June 20- August 12. Not only was he possibly the youngest at 14, but he carried more subjects than necessary, because he wanted to "milk" all the knowoedge possible and he came back home with glowing reports of OSU and his desire to go there. He has worked on math "to mail in" since he has been home, signed for a correspondence course, and still has the stars in eyes over the summer program. Also the discipline I felt was extremely good, and this speaks well for the type of child interested, and for you and your staff in presenting the program. I can't say enough good things for Dr. Ross and his staff and what they did for our son, Bruce.
Thank you for the privilege you accorded Doug by permitting him to attend the S.S.T.P. course this summer. Not only did he find your lectures stimulating and challenging, but the comments and hints to problem solving on his papers were especially useful to him. Inasmuch as this course has opened many new areas of study to him, his intense interest in mathematics and nuclear physics continues. He is exceedingly anxious to study the mathematics books by Smirnov.
As far as the influence that your summer program had on Mark, we find that an already serious and studious boy has even been made more aware of his desire to excel and to make the most of every minute of the day. Ho found that there were a lot of fine young men in the program at Ohio State that were on a par with him and this certainly made him aware of the challenge that will be facing him when and 152 if he enrolls in one of the highly competitive eastern schools in which he is currently interested. We have also found that in his reading at home Mark now works in more reading of books dealing with math than before and he is currently reading "Calculus and Analytical Geometry" by Fisher and Zieber a book he purchased while at Ohio State. If it has not been said before, my wife and I would like to congratulate you on the manner in which your program was carried out and extend our personal thanks for the part you played in moulding our son Mark.
It is difficult for us, too, to evaluate the course in Number Theory that Douglas participated in this summer. I am sure there are many benefits which will not immediately be apparent. At present, he is taking what is generally termed the conventional course in trigonometry and therefore not using any of the theory he learned this summer. However, he cer tainly gained knowledge and ability in thinking with abstract numbers which will enrich his entire career as far as any further Mathematics courses are concerned. He is seriously considering the field of Physics as a career, and the summer course he had at your University should aid him in the problems he might encounter in that field. Unfortunately Douglas did not enjoy his weeks spent at O.S.U. as much as we had hoped. He found recreation very limited, not because the facilities were not there, but because so many of the students he came in contact with were students only and did not care to participate in any of the sports, or even attend church or movies. This we thought was the only weak point in the program. It was a challenge for him to be among such high calliber students there, and I am sure he realizes now that competition for the top place can be a reality.
You asked how we think the summer Math program has in fluenced Ralph. It has made him more sure of himself. He has always been a very shy person, very rarely joining in, even a family discussion. Now, he does not hesitate to add his well worded ideas, that usually leave little room for arguement. He is also more at ease when meeting people.
It is with great pleasure that we write to you of your program and its effects on our son, Michael ____ . Mike was just entranced with the program. He found that he had to work very hard and v;as very hapny to realize that he could do so. He learned a lot, found the associations very enjoyable and just had a great time. His one comnlaint might be that there was too little other activity, that there was D.ittle to do except enjoy the program, and he, for one, needed more variety. 153
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V/e think that Faith’s participation in your program last summer was of inestimable value to her. For the first time in her life, she was in the company of children of her own intel lectual ability and with interests similar to hers. She also had her first test of herself against people of this caliber. I feel that it opened windows for her into the broader world of the intellect, that she received her first taste of the joy of scholarship and also her first taste of really working to achieve. She was enchanted by the library, by the type of classes, by the companionship and really interested in the subject matter she was taught. I also think that she felt she would never do anything really creative in mathematics herself although she enjoys it very much.
V/e are not in a position to judge the influence which John's participation had on the amount of mahtematical know ledge which he has, nor can we judge whether his facility in using mathematical information and concepts improved as a result of his participation in your program, intuitively, v;e are sure he benefited in both areas. V/e believe the most important benefit was a broadening of both his intellectual and social horizons and a significant gain in maturity. V/e attri bute this growth to the opportunity you provided for him to spend the summer and work with persons of similar interest, intellectual capacity, and motivation.
How participation in your program last summer influenced David I don’t rightly know, largely because of the communi cation gap between generations. But my impression is that it v;as an immensely stimulating experience (socially as well as intellectually) and that his development was greatly advanced. His mother and I - and David himself, I think - are very grateful to you and your colleagues for last summer and for your acceptance of him this summer.
It is rather difficult to assess the influence of the program on Cameron. Academically, he was permitted to advance into the senior mathematics course at his high school without taking Algebra II and Trigonometry. The year’s work has caused no difficulty for him and he plans to take Calculus at Muskingum College in the fall if scheduling permits. He, independently, has been reading and working problems at a higher level which the theory v;ork made possible. Personally, I think lie benefited from his association witli the heterogeneous group represented since our village is rather smail and conservative.
It was a challenging program for him and we have noticed that his canacity for abstract mahtematical tliought has grown with the effort invested. The diversity of subject matter 15 k and the way it was presented were a new experience for him and opened new vistas. He has been taking Trig, and Algebra III (the General Theory of Equations) in high school this year. Unfortunately he has already learned most of what they are teaching in the Algebra III book and galloped thru the Trig, book on his own by Christmas. I asked him what he does in class and his answer is that "he sits there and spoils the teacher’s sur prises" .
It was a marvelous experience for Ed— he matured a good deal, found that he really did like math and that living away from home was a pleasant experience that fostered independence.
Bonn enjoyed his program last summer immensely. He praised highly all the teachers and programs. He emoted especially about the wonderful feeling of working hard and achieving gains in the knowledge of mathematics. 155 1 ;6Ü
Carol has already obtained early admission to the University of Chicago and will enter that school in Septem ber lv6,. She is tentatively planning to major in physics. I attribute her now found enthusiasm for a physical science (as opposed to art, her earlier love) at least in part to her summer at O.S.U. You may recall that another one of my dauchters, Clair Frances , attended O.S.U. mathematics summer school in ly'66 and 1, 67. Clair is now in her second year at the Uni versity of Chicago. She is majoring in mathematics.
Needless to say, I personally very much appreciate the existance of your summer school and I feel that my two oldest children, Clair and Carol, definitely benefit from attendance at the school. I want to thank you and Dr. Ross for this fine experience that you are making possible for those young people. 156 i;6v
The influence of the summer program on Frank was consider able and was good. Preparing the application itself was the first occasion on which he had ever perceived the significance of a record of achievement, or even of achievement itself beyond the minimal, V/e think that the depth and intensity of the course, and the contact with many outstanding students and instructors, continued to reinforce that new perception. It is certain that he worked harder than ever before, and thus knows that he can. It is also certain that he enjoyed the course, was exhilarated and stimulated by the very challenge of it, was not overwhelmed as we had feared. V/e felt that Frank matured rapidly during this period and at last was motivated. These aspects are of more immediate concern to us than the specific amount of mathematical knowledge and technique he mastered, but that should be of lasting importance and we should like to know your evaluation of it.
Thomas’ participation in the If'6y summer mathematics program has influenced him very much. He is more mature, poised and has more confidence in his ability to accomplish his school work. He is a junior at Aquinas High School. He has skipped Math III completely and even Math IV is not the challenge he needs. Part of the time he teaches the class. Looking in the future, he hopes, during his senior year, to take classes in Math at La Crosse State University.
At the start, when he sav/ the caliber of the students enrolled, he had few misgivings as to his ability to participate in such a program. As the course progressed, his confidence increased as he realized that dedicated study and perser- verence would enable him to keep up with his class. His counselors were also a source of inspiration. It is our opinion that the program has helped him early in life to aim for a goal in mathematics and also helped him to estimate his potential in this field.
In answer to your request, I feel that Jay's participation in the summer program was useful in introducing him to a higher level of competition from his peers. In high school Jay had no effective competition from the class, he would finish the class work, and then go on to his own projects. This left him no idea of what he would meet in college. The situation this summer was good intellectual and social preparation for the situation he now finds himself in at M.I.T. To quote Jay, "I am still continuing the work we did this suimr.cr. . .1 I’oally did learn a lot, I look at my early problem sets and die ].aughing. The main thing we learned was heuristics ...I may even feel inspired to write a DTO starting with 157 something as basic as Peano's postulates, although to be creative I ’ll try to come up with another nostulate system. But they were right, they did overwork us, expect too much of us, depress all of us, and thoroughly baffle and ]ose us by tlio end. But I ’m glad they did, and would like to go back again."
Paul’s participation in your summer program was the finest intellectual experience he has yet encountered. If he was possessed before witli a determination to pursue some phase of mathematics as his life’s work, he is now doubly possessed with such determination. I know that a young person’s future plans are many times fleeting and transitory, changeable innumerable times, yet I do believe Paul will stay with some phase of the broad area of mathematics as his life’s study and work. I-iy wife and I and Paul feel that this past summer was an experience for him which he will never forget.
As we are not mathematically inclined as our son is, we are really unable to make a valid judgment of Glenn’s progress in this field. V/e do feel, however, that he was able to broaden his field of interest and found ample opportunity to test his ability while at Ohio State. It is wonderful that Glenn was able to meet and study with such qualified faculty and also to share interests with students of his ovm age. V/e feel that Glenn is qualified to evaluate his progress and he has felt that your classes were extremely challenging and exciting and he feels that he has obtained a mountain of knowledge and that the instructors were creative and very talented. The classes have stimulated his interest even more and he spends much time in search of further knowledge. He is eagerly anticipating the next year’s program and has every hope of again being accepted at Ohio State.
I am certain that the summer program which David attended at Ohio State University has been most beneficial in his progress, not only in the study of mathematics, but also in the sudden development of maturity and self confidence he has displayed recently. David has also matured greatly. Living on his ov/n for eight weeks, and participating in a challenging program has definitely increased his desire to undertake university study.
The SSTP program was of value to Jack in the broad sense of new experiences, people and study materials. He was challenged and worked harder than at any time prior to last summer. Often he felt that studies were not a challenge to him and he indicated that he worked hard. The greatest influ ence of the program was to reinforce correct clioices in several areas. BIBLIOGRAPHY
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