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AN INVESTIGATION OF TRENDS IN THE MATHEMATICS CURRICULUM IN THE JUNIOR COLLEGES OF CALIFORNIA AND WASHINGTON

A Thesis Presented to the Faculty of the School of Education The University of Southern California

In Partial Fulfillment of the Requirements for the Degree Master of Science in Education

by Jack Levaughn Rowe June*1950

UMI Number: EP56154

All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion.

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E±

'SO

T h is thesis, w r it t e n u n d e r the d ire c tio n o f the C h a irm a n o f the candidate’s G uid a n ce C o m m itte e a n d a p p ro v e d by a l l members o f the C o m m itte e , has been presented to a n d accepted by the F a c u lt y o f the S c h o o l o f E d u c a tio n o f the U n iv e r s ity o f S o u th e rn C a lif o r n ia in p a r t i a l f u l f i l l m e n t o f the requirem ents f o r the degree o f M a s t e r o f Science in E d u c a tio n . D a te .......................

D ean Guidance Committee

TABLE OF CONTENTS CHAPTER

PAGE

I. THE PROBLEM AND ITS IMPLICATIONS . ......... Importance and implications

• • • •

........

1 2

Implication of trends in the conventional college preparatory course in mathematics. •

2

Implication of trends in terminal and applied courses in mathematics

...........

2

Implication of trends tov&rd a required mathematics curriculum for graduation in the junior c o l l e g e s ................. Summary

............

. . . . . . .

4

P r o c e d u r e ...................

II.

4

Method of obtaining d a t a ...................

4

Organization of the investigation

••••«•

5

........

7

ANALYSIS OF PREVIOUS INVESTIGATIONS

.

Original function of junior c o l l e g e .........

7

Recent trends as reported in the literature ...

8

Summary of recent trends III.

3

...................

12

THE QUESTIONNAIRE UTILIZED IN THIS S T U D Y ........

15

Criteria used In construction of the questionnaire 15 The questionnaire in this Investigation Procedures............... . •. •

• • • • ........

Organization of the questionnaire......... IV.

17 17

18

TABULATION AND ANALYSIS OF COURSE TITLES IN JUNIOR COLLEGE MATHEMATICS

.

.....................

22

ill CHAPTER

PAGE Source of data . . . . . . .

. • •

21

Analysis of course t i t l e s

• • •

22

Comparison of results with

previous studies

Chapter summary and general conclusions V.

.

26

• « .

26

THE HIGH SCHOOL MATHEMATICS COURSES IN THE CURRI CULUM OP JUNIOR COLLEGES OP CALIFORNIA AND 29

.

WASHINGTON . . . . . ................. Analysis of offerings in bulletins and answers to questionnaire Comparison of results with

29

......... previous studies

.

36

Summary of the chapter.......... ........... VI.COLLEGE MATHEMATICS AND PURE MATHEMATICS

34

COURSES .

37

Analysis of offerings in catalogues and answers to questionnaire............... . • Comparison of results with

previous studies

•

Summary of chapter.............. ........... VII.

VIII.

TERMINAL AND APPLIED MATHEMATICS COURSES......

37

40 42 44

Analysis of course titles in the catalogues .

44

Results of questionnaire • • • • • • • • • • *

45

Chapter summary. • • • • .

49

.............

ANALYSIS OP ENROLLMENTS IN MATHEMATICS COURSES IN THE JUNIOR COLLEGE

...........

Enrollment In mathematics courses as a whole .•

52 52

Enrollment in the high school mathematics courses 53 Enrollment in college mathematics

.........

57

iv CHAPTER

PAGE Enrollment in terminal and applied

IX.

mathematics courses •

58

Chapter summary • • • » • » • • • • • • • . .

58

.............

61

CONCLUSIONS AND RECOMMENDATIONS Conclusions...............

61 .

6l

• . • .

62

Review of results of recent investigations Survey and analysis of course titles

High school mathematics courses • • • • • • •

62

College mathematics and pure mathematics courses » • • • • • • • • » • * . • • • • • Terminal and applied mathematics courses

• •

63 63

Enrollment in the junior colleges • « • • • •

64

Recommendations . » • • • • • • • • • • • • • •

64

BIBLIOGRAPHY........................................

67

APPENDIX............................................

73

LIST OP TABLES TABLE I.

PAGE Number of Junior Colleges in California and Wash ington Offering Certain Courses in Mathematics; Fifty-four Institutions Reporting.........

II.

23

Summary of Total Number of Mathematics Courses Offered and Total Number of Units of Instruction Offered in Mathematics by School

III.

.............. 27

Summary of Courses in High School Mathematics Offered by Fifty-four Junior Colleges in California and Washington

IV.

32

Summaryof Part I of Questionnaire.................. 33

V.

Studies of Mathematical Offerings in Junior Colleges

VI.

Summary of College Mathematics and Pure Mathematics

35

Courses Offered by Fifty-four Junior Colleges in California and Washington VII. VIII.

............... 39

Summary of Part III of Questionnaire..........

4l

Summary of Terminal and Applied Mathematics Courses Offered by Fifty-four Junior Colleges in Califor nia and Washington

IX. X.

........• • • • . ........... 46

Summary of Part II of Questionnaire

• • • . • • • •

50

Enrollment of Students in the Various Courses In Mathematics as Reported in Part IV of Questionnaire 54

XI.

Summary of Enrollments as Reported by Thirty-five Junior Colleges of California and Seven Junior Colleges of Washington...........

56

Vi TABLE XIX.

PAGE Summary of Percentages as Outlined in Chapter VIII

60

CHAPTER I THE PROBLEM AND ITS IMPLICATIONS There Is no question hut that the mathematics curricu lum in junior colleges of today is undergoing fundamental changes*

It is common knowledge among most educators that

the once important function of junior colleges to provide a stepping stone to advanced work in senior colleges and uni versities is becoming less and less the sole aim of such institutions*

These changes have been more pronounced during

the past few years.

Some of the factors producing these

changes include the following:

the great number of veterans

now returning to school who are deficient in mathematics; the greater emphasis being placed on science and mathematics in the junior college as a direct influence of our participation in the late war; and trends for more and more terminal educa tion to be offered in the junior colleges, particularly in the business field* It is the purpose of the present study to investigate and interpret present trends in the mathematics curriculum of the junior colleges of California and Washington; to review and interpret past trends as revealed by a study of previous similar investigations found in publications and the litera ture; and to compare the present trends with those found in the literature.

2 A.

IMPORTANCE AND IMPLICATIONS

In considering trends of the mathematics curriculum it is convenient to group them under the following general head ings:

1#

Trends in the conventional college preparatory

courses in mathematics; 2*

Trends in terminal and applied

courses in mathematics; 3*

Trends toward a general minimum

curriculum of mathematics required hy all junior colleges for graduation. Implications of trends in the conventional college preparatory courses in mathematics. Several questions con cerning trends of college preparatory courses in mathematics curriculum of junior colleges are important.

What are the

number and type of strictly college preparatory courses offered at present in the junior colleges as compared with those of fered five or ten yearsago?

What are the number and type of

courses in mathematics, formerly classified as high school subjects, now offered in the mathematics curricula of the junior colleges?

In view of the fact that many students in

junior colleges, how great and widespread is the tendency for junior colleges to offer more and more courses which used to be regarded as high school courses and were not formerly a part of the junior college curriculum? Implications of trends in terminal and applied courses in mathematics ♦ During the past fifteen years the trend for

3 more and more terminal and applied courses in the junior colleges has been very marked*

By 19419 Hill reported that

since 1916 over 4000 terminal courses were offered in the junior colleges of California**1* The question of how far ter minal curricula in mathematics have conformed with this growing trend becomes important. Implications of trends toward a required mathematics curriculum for graduation in the junior colleges ♦

It is a

fact that most high schools today require a minimum of one year of some type of mathematics before graduation.

There

are many leading educators who believe that this minimum re quirement is inadequate.

H* H* Douglass, Dean of the College

of Education, University of Colorado, in an address to the high school teachers of mathematics at a section meeting on mathematics in Chicago, Illinois, said: Everyone should study mathematics in high school and should have at least a year of mathematics beyond the tenth grade, and in all* not less than two years of high school mathematics. 2 The question as to whether the junior colleges will require a minimum mathematics program for graduation becomes pertinent.

Merton L. Hill, "History of Terminal Courses in California,” Junior College Journal. 12:311-313» February, 1942. o■ ■ ' Harl R. Douglass, "Mathematics for all and the Double Track Plan," School Science.and Mathematics. 45:425-434, May, 1945*

4 As early as 1937, Georges believed that mathematics should be a part of the junior college required curriculum, although he stated that it would be several years before the junior col leges would make it a requirement•3

Hannelly also favored a

general course in mathematics for all college students, es4 pecially terminal students* Summary* Consideration of the importance of the problem indicates that trends in the college preparatory courses and in terminal and applied courses in the mathematics curriculum of junior colleges are significant• The question of a required mathematics curriculum for graduation in the junior colleges is one which definitely is becoming more important. B.

PROCEDURE

Method of obtaining data.

This investigation was con

ducted by an analysis and study of information from several sources.

First, a careful study was made of the titles and

descriptions of courses offered in the mathematics curriculum of forty-six public junior colleges in the State of California and eight junior colleges in the State of Washington.

The

3 j. s. Georges, “Mathematics in the Junior College,” School Science and Mathematics. 37:302-305, March, 1931. 4 t, M R. J. Hannelly, Mathematics in the Junior College, American Mathematical Monthly. 4 6 :5 81 -5 8 5 , Hovember, 1939.

5 description and titles of such courses were obtained from the 1948-49 catalogues as published by the various junior colleges. Second, analysis and comparison were made of the trends, find ings, and other pertinent information as reported by previous similar investigations.

Information covering previous similar

investigations was obtained from periodicals and publications over the past ten years.

Third, an analysis was made of ans

wers to a questionnaire which was sent to the chairmen of the mathematics departments of the various junior colleges referred to previously.

A copy of the questionnaire used is included

in the appendix of this report. Organization of the investigation. For convenience and clarity of understanding the final chapters of this investiga tion were organized under the following divisions:

Chapter

Two is concerned with a survey and an analysis of the trends and findings of similar investigations conducted during the past ten years. Chapter Three presents a brief discussion of the question naire method in general as a means of obtaining data and how it was utilized in getting pertinent information for this study. Chapter Four considers the tabulation and analysis of the various courses in mathematics offered in the junior col leges of California and Washington as described in their cata logues.

A comparison was made between results of investigations

6 found in the literature and those found in considering the survey of the various catalogues* In Chapters Five, Six, and Seven the study and analysis of the mathematics courses offered in junior colleges were broken down into three main divisions*

Chapter Five considers

the trends and implications of high school courses now offered in junior colleges• Chapter Six is concerned with the college preparatory and advanced courses in pure mathematics.

In

Chapter Seven there is the presentation of pertinent facts con cerning terminal and applied mathematics courses* Chapter Eight presents the trends as revealed by the present enrollments in the different types of mathematics courses.

In the concluding chapter there are presented the

summary and general conclusions* follow*

A bibliography and appendix

CHAPTER II ANALYSIS OP PREVIOUS INVESTIGATIONS By a review and analysis of the results of several pre vious studies it is intended that this chapter will point out several trends in the mathematics curriculum of junior colleges which appeared during the past ten years* Original function of junior college *

In order to estab

lish just what were the recent trends in the curriculum of junior colleges, it might be well to consider what were the original functions of junior colleges*

The subject matter in

the field of mathematics in the junior college has been rather well defined and fixed until recently*

One of the principal

reasons for such a stable curriculum in mathematics can be associated with the original function of the junior colleges. Several leading authorities of recent years have stated: The early history of the junior college shows it to be an attempt to take over the first two years of the four year liberal arts college.-** The attention of junior colleges since their incep tion has been devoted largely to provide two-year periods of academic training which will enable a grad uate to enter the senior college. 2 1

William A. Gager, Terminal Business Mathematics in the Junior College,” (unpublished Doctor^ dissertation, George Peabody College for Teachers, Nashville, Tennessee, 1940) p. 15 o R. W. Goddard, "Junior College Serves Community Needs, Junior College Journal. 4:308-311, March, 1931*

8 Mathematics courses in the junior colleges have generally heen patterned after the lower.division courses In the university prior to 1940.^ Recent trends as re-ported in the literature# Closely related to the recent trend of junior colleges to offer courses leading to terminal training, the curriculum of mathematics has also undergone certain changes along this line.

Several studies

have heen made which definitely show these changes. In 1928 Hoy conducted a survey of the eourses in mathe matics offered by thirty-three junior colleges of California.1* He found that very few junior colleges offered such high school subjects as plane geometry, intermediate algebra, solid geometry, shop mathematics and business arithmetic.

The main part of the

mathematics curriculum consisted of strictly college subject matter. Hills In 1929 conducted a survey to find out what the public junior colleges of the United States were offering in mathematics at that time.

5

Out of eighty-eight junior colleges

responding to his questionnaire, he found that the academic courses in mathematics were practically the only ones being taught.

Trigonometry (eighty-four), college*algebra (eighty-

3 F. E. Hills, "Junior College Mathematics,** School Science and Mathematics. 2 9 :880 -8 8 5 , November, 1 9 2 9 . ^ E. A. Hoy, "Junior College Mathematics in California, 11 School Review. 3 6 :370-373> May, 1928. ^ F. E. Hills, op. cit., p. 880.

three), analytical geometry (eighty), differential calculus (seventy-six), and integral calculus (seventy-one) are the subjects listed in the order of frequency*

In addition he

found that practically all of the junior colleges were satis fied with their programs*

This survey seems to show that the

curriculum in mathematics at this date was well standardized with no provision for terminal or cultural mathematics* Apparently not until 1 9 3 6 -3 7 was there further investi gation along these lines*

An analysis of the mathematics cur

riculum of twenty-six California junior colleges by Adams in 1 937 vas significant in that he found practically all offered

elementary algebra, elementary plane geometry, intermediate algebra, trigonometry and solid geometry in addition to the traditional college algebra, plane and solid analytical geometry differential and integral calculus.

6 More than half of the

junior colleges reporting offered mathematics of investment* Finally, it was found that although the mathematic courses were numbered and patterned after those offered by the University of California, there was little uniformity in the content of such courses• Schmidtke in October, 1937# published results of his findings which showed from a study of one hundred and fourteen colleges in the United States that there was on the average 6

L. J. Adams, "Mathematics in California Junior Colleges Junior College Journal. 7:194-195, January, 1937*

10 only a slight gain from 1 9 2 1 -1 9 3 0 In the number of courses in mathematics offered in junior colleges.*^

Prom 1930 to 1935 there

was a distinct increase in the number of such courses offeredj it rose from 21.4 semester hours of mathematics to 25^6 semester hours.

This investigation brought out an interesting fact that

California junior colleges offered 3^*7 semester hours of mathe matics as compared to the average of 2 5 *6 semester hours for the group as a whole.

Although this study did not determine

which of the courses in mathematics were terminal and which were not, the conclusion drawn from the entire investigation was that junior colleges with large enrollments were offering a greater variety of courses, including both terminal and college prepara tory. In 1937 Poston found that in only seventy-four institu tions out of three hundred and seventy-eight studied were there any evidences of a trend toward unified mathematics— i.e., mathematics of a terminal nature.® In a study of mathematics courses offered in 159 public junior colleges in which every state in the union was represen ted > Hannelly in 1940 found the following facts:

7 F. E. Schmidtke. "Trends in Terminal Offerings, 11 Junior College Journal, o:22, October, 1937# ® J. H. Poston, "Mathematics Curricula of the Junior Colleges of the United States,” (unpublished Master#s thesis, George Peabody College for Teachers, Nashville, Tennessee, 1937)-

11 (1)

One junior college offered eighty-four semester hours of mathematics.

(2)

Average public junior college gave twenty-three semester hours of mathematics.

(3)

Several junior colleges offered high school mathe matics courses for credit.

(4)

Very few courses offered were terminal or cultural mathematics outside of business mathematics.9

Hannelly*s conclusions were that traditional courses in junior colleges in mathematics were being broken down even if slowly and that the boundary line between the junior college and high school mathematics courses was not so well defined as it formerly was. In 1940 Gager, after comparing the results of his study with those of several similar studies, stated that there ap peared to be a general downward trend in the four traditional mathematics courses in the junior colleges:

i.e., college

algebra, trigonometry, analytical geometry and calculus.1^ Terminal business mathematics and unified mathematics showed an upward trend.

However, Gager reported that in spite of the

downward trend of these traditional courses the curriculum then primarily continued to be composed of the same mathematics courses which were introduced at the beginning of the junior college movement.

9 R. J# Hannelly, "Mathematics Offerings in Junior Col leges," Junior College Journal. 10:260, January, 1940. William A. Gager, o£. cit.♦ p. 15*

In a study published in 1942 by Ahern it was found that out of eighty-two junior colleges reporting seventy-seven of fered analytical geometry, fifty-seven gave differential calculus and fifty-three gave integral c a l c u l u s T h u s , the traditional college preparatory courses were still in preponderance#

Sig

nificantly, this study also found that the tendency for junior colleges was to offer those mathematics courses which formerly had been considered the prerogative of the high schools.

Ahern

also found that mathematics courses whiGh were described as survey or general courses were comparatively popular and that, often special mathematics courses were being added for students who were preparing for specific professions or vocations. Summary of recent trends♦ Careful analysis and considera tion of the results of previous investigation as reported in recent literature revealed the following facts: 1.

As of 1942 the greatest number of mathematics courses offered by junior colleges in the United States were college preparatory courses.

2.

Until approximately 1937 there appeared to be very little change in the offerings of mathematics courses in the junior college.

3.

By 1940-41 there was a definite trend toward offering

Lorella Ahern, "Scope of Mathematical Offerings in Junior Colleges," Mathematics Teacher. 35:18-22, January, 1942.

more and more terminal courses in mathematics, but there still existed a lack of suitable terminal courses in mathematics in junior colleges* By 1942 there was a distinct tendency to offer all the courses in mathematics formerly included exclu sively in the high school curriculum* Of all the terminal courses in mathematics offered in junior colleges up to 1942, the greatest prepon derance was in the field of business mathematics* There was no evidence of junior colleges establishing a minimum required program of mathematics for graduation.

CHAPTER III THE QUESTIONNAIRE UTILIZED IN THIS STUDY Investigators in many fields of education frequently turn to the questionnaire method in order to obtain informa tion which cannot best be secured by other methods*

Although

it has been proved that in many instances the questionnaire method for obtainingdata has been indiscriminately used with very poor techniques

employed, the author has attempted to

follow accepted methods in utilizing this technique to obtain pertinent data*'*'

The purpose of this chapter is to present a

few of the important aspects of the questionnaire method uti lized in this study* A.

CRITERIA USED IN CONSTRUCTION OP THE QUESTIONNAIRE The history of the rise and eventually unpopular use

of the questionnaire

techniquefor obtaining answers to a host

of problems in the wide fields of education is now rather well known*

Leonard V. Koos has quite clearly outlined this interest

ing picture of the wide application of the questionnaire method for obtaining data in his treatise, The Questionnaire in Educa tion*^ However, many educators, including Koos, believe that

Leonard V. Koos, The Questionnaire in Education (The Macmillan Company, New York, 1928), p* I7 8 * 2 Ibid.

15 for some problems and In some fields of Investigation there Is no better method than the one employing questions and answers, provided the technique has been properly carried out*

In fact,

Phillips has pointed out In her discussion of the problems of questionnaire investigations that 11this method Is thought in dispensable by many school executives for purposes of gathering material concerning educational practices and procedures."^ Although it was not the intention here to write a treat ise on the questionnaire technique, certain significant suggest ions regarding this technique were considered.

Koos believed

that two important criteria for establishing the validity of a questionnaire were ”ability” and ”willingness,” that is, ability and willingness of the person approached to make reliable ans wers.^

It is believed that in this study both of these criteria

were satisfactorily met.

Willingness of the recipients to make

responses to the questionnaire was obtained by mailing a postcard prior to sending the questionnaire.

Upon receiving an affirma

tive reply of agreement to cooperate, the author mailed out the questionnaire.

Since the recipients in every instance were

either the chairmen of the mathematics departments in the junior colleges or experienced instructors in the department, the

^ Marjorie Phillips, "Problems of Questionnaire Investi gation," Research Quarterly of the American Association.for Health; Physical Education and Recreation. 12:528-37*" October,

19*H • 4

Koos, op. cit., p. 99*

16 criteria of ffability to make reliable answers" was established in this survey. Herbert A. Toops listed the following important elements which should be attained in order that a questionnaire be effective: 1.

Select topics regarding which the recipients are vitally interested in knowing the answers.

2.

Send the blank to those persons who because of a knowledge of your professional repute will feel a personal obligation to answer.

3.

Use the best possible technique in writing questions.

4.

Make it easy for the recipient to reply.

3.

Use objective, unequivocal but "sensible” questions.^

One of the best and most complete discussions of the questionnaire technique in education is volume eight of the Research Bulletin of the National Education Association.

The

criteria established in this publication included the following: 1.

Questions should be simply and clearly worded.

2.

Question-

nairs should be such that answers may be expressed by yes or no, check mark or very short answers. as short as possible.

4.

deal with matters of fact. given a preliminary tryout.

3 . Questionnair should be

The questionnaire should preferably 5*

The questionnaire should be

6 . The questionnaire should meet

^ Herbert A. Toops, "Predicting the Returns for Question naire,” Journal of Experimental Education. 3:204-15, March, 1935. 0 National Education Association, Research Division, "The Questionnaire,” Research Bulletin. 8:1-51, January, 1930*

17 certain standards of mechanical form*

7.

The purpose of the

investigation should he stated* In so far as possible the questionnaire used in this investigation has followed these accepted criteria and methods. B.

THE QUESTIONNAIRE IN THIS INVESTIGATION

Procedures. Strictly speaking, the questionnaire organ ized and used in this study consisted for the most part of a check list of administrative practices and procedures in the mathematics curriculum in the junior colleges of California and Washington.

A few questions were included which required ex

pressions of opinions from the recipients. As a preliminary procedure, several members of the mathematics department in Bakersfield Junior College were asked to respond to the questions in the first draft of the question naire.

Several minor changes in wording and questions were

then made before the final form was decided upon. Questionnaires were mailed to fifty-seven junior colleges in the states of California and Washington.

The respondents

in every case were considered experts in their field— they were the chairmen of the mathematics department or instructors in that department.

Out of fifty-seven questionnaires sent, forty-

two responses were received; this represents a return of approxi mately seventy-four per cent.

The high degree of response was

attributed in part to two factors:

(1 ) follow-up letters for

18 those who failed to respond at the first request and (2 ) the interest of the respondents in helping to obtain answers to the problem outlined in the investigation. Organization of the questionnalre. The questionnaire (or check list of administrative practices, which more ac curately describes the instrument) was organized into four general divisions.

In Part I there were four questions'relating

to the inclusion of elementary mathematics in the junior college. The first question in Part I was divided into three sub-questions: (a) a question of fact regarding the giving or not giving junior college credit for the elementary mathematics courses of algebra, geometry and arithmetic; (b) two questions of opinion as to whether certain elementary mathematics courses and/or certain advanced courses in mathematics should be a permanent part of the curriculum of the junior college.

Question two was one of

opinion as to whether or not every student should take some course in mathematics as a graduation requirement.

The third

question was another one of opinion in which it was asked if every student should be required to pass a test in arithmetic fundamentals before graduation from junior college.

Question

four asked what elementary course (choice of several) in mathe matics should be required if every student had to take at least one course before graduation. The seven questions in Part II were principally designed to produce more information on the terminal mathematics curriculum

19 In the junior colleges.

The first question asked an opinion

as to whether terminal courses or college preparatory courses in mathematics were being emphasized*

Question two requested

whether or not terminal students were required to take a course in mathematics before graduation and, if so, what course?

The

third question was related to number two in that it asked whether or not the recipient would require a mathematics course for terminal students for a graduation requirement.

Questions

four, five, six and seven were all concerned with the terminal mathematics curriculum in the junior college at the present time:

(4) Do you believe that the terminal courses in mathe

matics in your junior college which are required for certain vocational preparations are adequate?

(5 ) What courses in mathe

matics designed for the terminal student have been added to the curriculum during the past few years?

(6 ) What additional ter

minal courses in mathematics do you think should be added to the curriculum?

(7 ) Of the various terminal courses in mathematics

now offered in your junior college, name the one which in your opinion is best serving the needs of terminal students. The three questions in Part III were general questions concerning the curriculum in mathematics as a whole.

The first

asked whether or not the respondent was satisfied with the pre sent curriculum in mathematics and, if he was not, to suggest what changes should be made*

The second asked him to name and

briefly describe any new courses in mathematics which were to

20 be added to the curriculum next term.

The third question in

this section asked for an opinion concerning whether or not emphasis on the college mathematics (such as college algebra, analytic geometry, calculus and others) was too great. In Part IV the respondent was asked to furnish data concerning enrollments in the junior college— total enrollment, total enrollment in all mathematics courses, total enrollment in the terminal courses in mathematics and enrollment in each of several, particular courses in mathematics.

These particu

lar courses in mathematics were grouped so that enrollment was reported as follows:

first, for the so-called "high school11

courses in mathematics by course:

solid geometry, elementary

algebra, plane geometry, intermediate algebra and trigonometry; second, enrollment in the college courses (college algebra, analytic geometry, calculus, etc.); third, business mathematics fourth, trade and shop mathematics; fifth, cultural or general mathematics; sixth, slide rule; and, finally, enrollment in any other mathematics courses. *

A copy of the questionnaire used is included in the appendix.

Analysis of results of the questionnaire and how

they affected this study will be revealed in succeeding chapters.

CHAPTER IV

TABULATION AND ANALYSIS OP COURSE TITLES IN JUNIOR COLLEGE MATHEMATICS It Is the purpose of this chapter to tabulate and make an analysis of the course titles in the mathematics courses taken as whole as found in the catalogues of the junior col leges in the states of California and Washington*

Also, a

comparison will be made between the results of similar Investi gations as found in the literature and the analysis of the course titles in this study*

In Chapters Five, Six and Seven

a more detailed analysis of the course titles in junior col lege mathematics will be made, in which the course titles are broken down into the sub-divisions of high school mathematics, college courses, and terminal or applied mathematics courses* Source of data.

In order to obtain information as to

the type and number of courses in mathematics which were being offered in the junior colleges of California and Washington, a request was made to each school for a copy of the latest cata logue or bulletin announcing the courses offered for the year 19^8-49•

Out of fifty-seven requests for catalogues, a total

of fifty-four junior colleges responded.

Forty-six of the

schools were In California and eight (which included all in the state) were in the state of Washington.

Analysis of course titles. A compilation of the offer ings of all the mathematics courses as listed in the bulletins from the various junior colleges revealed that a total of fortyfive different courses in mathematics were given by the junior colleges reporting.

Since not all junior colleges in California

were represented in this investigation, it is' possible that if data from all had been available the total number of mathematics courses would have been found to be even greater. Prom among the forty-five different courses offered, the following twelve courses in mathematics were given by sixtyseven per cent or more of the schools represented in this study: intermediate algebra; plane geometry; first, second and third courses in calculus; analytic geometry, plane trigonometry, college algebra, solid geometry, elementary algebra, business mathematics, and mathematics of finance.

A complete list of the

mathematics courses and the number of schools offering each course is shown in fable I on page 2 3 . A listing of the number of different courses in mathe matics and the total number of units credit granted for these courses for each school revealed that fifty per cent of the schools studied offered fifteen or more different courses which totaled forty or more units of credit in mathematics.

Also, it

was found that three junior colleges offered mathematics courses for which over one hundred units of credit were granted.

The

average number of semester hours instruction in mathematics

23 TABLE

I

NUMBER OF JUNIOR COLLEGES IN CALIFORNIA AND WASHINGTON OFFERING CERTAIN COURSES IN MATHEMATICS; FIFTY-FOUR INSTITUTIONS REPORTING Name of course

Total number of schools offering course

1.

Intermediate algebra

52

2.

Plane trigonometry

52-

3.

First course in calculus

51

4.

Second course in calculus

51

5.

Plane analytic geometry

51

6.

Plane geometry

49

7.

College algebra

47

Solid geometry

47

Elementary algebra

45

10.

Business mathematics

41

11.

Third course in calculus

3S

12.

Mathematics of finance

36

13.

Slide rule

24

14.

Arithmetic

16

15.

Engineering mathematics

16

16.

Spherical trigonometry

16

17.

Elementary statistics

14

IS.

Differential equations

13

9.

(To be continued)

24 TABLE

I

(Continued)

NUMBER OF JUNIOR COLLEGES IN CALIFORNIA AND WASHINGTON OFFERING CERTAIN COURSES IN MATHEMATICS; FIFTY-FOUR INSTITUTIONS REPORTING Name of course

Total number of schools offering course

19.

Technical mathematics

20,

Solid analytical geometry

7

21.

Projective geometry

6

22.

Shop mathematics

6

23.

Vector analysis

6

24.

Applied mathematics

5

25.

Cultural mathematics

5

26. General mathematics

10

5

27.

Mathematical analysis

5

23.

Vocational mathematics

5

29.

Commercial algebra

3

30.

Mathematics of accounting

3

31.

Nursing mathematics

3

32.

Pre-engineering mathematics

3

33.

Advanced mathematical analysis

2

34.

Algebra theory

2

35.

Analytic mechanics

2

36.

Mathematics for elementary teachers

2

37.

Non-euclidean geometry

2

(To be continued)

25

TABLE

I

(Continued)

NUMBER OF JUNIOR COLLEGES IN CALIFORNIA AND WASHINGTON OFFERING CERTAIN COURSES IN MATHEMATICS; FIFTY-FOUR INSTITUTIONS REPORTING Name of course

Total number of schools offering course

3$. Advanced business mathematics

1

39. Applied trigonometry

1

40. Constructions of mathematics

1

41. Industrial statistics and control charts

1

42. Logarithmic curve fittings and determinants

1

43. Radio mathematics

1

44. Simplified calculus

1

45. Survey of mathematics

1

26 offered by a junior college in California and Washington in 1948 was found to be forty-six, and all fifty-four junior col leges offered over twenty-five units.

Table II on page 27 gives

a summary of the listing of schools, the number of different courses in mathematics offered (by school) and the total units of credit granted. Comparison of results with previous studies. Compared with the facts brought out in 1940 by Hannelly, who showed that out of 159 junior colleges studied one school offered eightyfour semester hours of mathematics and that the average junior college gave only twenty-three semester hours, the junior col leges at the present time offer considerable greater variety and number of courses in mathematics.^

Although Schmidthe

found that in 1937 an average of thirty-five semester hours of mathematics were offered by junior colleges of California, this average had increased to forty-six units in the present study. 2 Chapter summary and general conclusions. Analysis of course titles in mathematics indicated that forty-five different courses were offered by junior colleges in California and Wash ington.

It was found that the average number of semester hours

instruction in mathematics was forty-six and that fifty per cent of the schools offered fifteen or more different courses in

^ R. J. Hannelly, 0£. cit.. pp. 260-61. 2 F. E. Schmidtke, op. cit.. pp. 22-23.

27 TABLE

II

SUMMARY OF TOTAL NUMBER OF MATHEMATICS COURSES OFFERED AND TOTAL NUMBER OF UNITS OF INSTRUCTION OFFERED IN MATHEMATICS BY SCHOOL School

1 2 3 4 5 6 7 3 9 LO LI L2 L3 L4 L5 L6 L7 L3 L9 >0 >1 >2 J3 >4 15 >6 17 averages

Number of different courses in mathematics

32 29 23 27 26 24 22 21 21 21 21 19 19 13 13 13 17 17 16 16 16 16 16 16 15 15 14

Total units of instruc tion in mathe matics 107 90 104 102 73 65 62 61 60 60 55 57 46 53 53 44 52 44 47 45 45 44 43 41 50 44 44

School

23 29 30 31 32 33 34 35 36 37 33 39 •40 41 42 43 44 45 46 47 43 49 50 51 • 52 53 54

Number of different courses in mathematics

12 14 14 14 13 13 13 13 13 12 12 12 12 11 11 11 11 10 10 10 10 9 9 9 9 9 3 154

Total units of instruc tion in mathe matics 42 41 33 37 45 40 39 37 36 46 40 36 33 33 31 31 30 33 30 30 29 31 30 27 27 24 26

28 mathematics . The general conclusions are that the trend of junior colleges is to offer more and more courses in mathematics and that junior colleges at present are offering a greater number and variety of courses than ever before in the brief history of junior college instruction*

CHAPTER V

THE HIGH SCHOOL MATHEMATICS COURSES IN THE CURRICULUM OF JUNIOR COLLEGES OF CALIFORNIA AND WASHINGTON One important consideration in determining trends in the mathematics curriculum of junior colleges is to examine any change in the extent, type and variety of courses offered in mathematics now as compared with courses offered in past years* As previously cited, Hills found in the junior colleges in 1929 a rather stable, uniform curriculum in mathematics, consisting primarily of college subjects.

In the present chapter It is

intended to present an analysis of the titles of mathematics courses offered in junior colleges which were formerly classi fied as high school subjects and to compare the findings of this study with results of previous similar Investigations.

A

study of course titles as given In the junior college bulletins and the results obtained from Part I of the questionnaire will be utilized in making the analysis* Analysis of offerings in bulletins and answers to ques tionnaire * A compilation of the offerings of the so-called high school mathematics courses in the junior college catalogues re vealed a number of facts.

From a total of fifty-four junior

colleges reporting, fifty-two offered plane trigonometry and

1 F. E. Hills, o£. cit., pp. 8 8 0 -8 5 .

30 fifty-two, intermediate algebra.

Plane geometry was offered by

forty-nine junior colleges, followed by forty-seven schools giving solid geometry and forty-five institutions offering elementary algebra.

Arithmetic was offered for junior college

graduation credit by sixteen schools, but only five schools indicated a course in general mathematics. In considering the high school courses of elementary algebra, plane geometry, intermediate algebra, plane trigono metry and solid geometry as a whole, this analysis indicated that eighty-five per cent or more of all the junior colleges studied offered such subjects for college credit#

Results of

this study revealed that by 1948 nearly all of the junior col leges had definitely added to their curriculum all the mathe matics courses which were formerly given exclusively by the high schools. Results of the answers to question one, part a, in the questionnaire corroborated the findings in the catalogues# Only twelve schools reported that no credit was given for inter mediate algebra; twenty schools (less than forty per cent) re ported that no credit was granted for elementary algebra and plane geometry#

Because so few junior colleges offered solid

geometry and general mathematics in their curriculum, the report for these latter two courses was not significant# Not only had the junior colleges formally added the high school subjects to their mathematics curriculum by 1948, but

31 eighty per eent of the experts in the schools reported in the questionnaire that they believed these subjects should be there and should remain as a permanent part of the mathematics curri culum*

The only exception was general mathematics; even so,

fifty per cent believed it, also, should be included as a part of the mathematics curriculum* One of the interesting facts revealed by this study was the great variability among junior colleges in the amount of credit granted for courses in mathematics.

Although only seven

of the junior colleges operated class schedules for the year on a four quarter basis (three quarters being a normal school year), instead of the usual two semesters per year, great variability in credit granted for a particular course was evident. example:

For

out of forty-five schools offering elementary algebra,

thirty gave three units credit, one allowed four units, nine schools granted five units, one school gave six units, three schools allowed eight units, and one granted ten units*

A second

example to illustrate this inconsistency was the varying amount of credit granted for solid geometry.

Out of forty-seven schools

reporting, nineteen gave two units, eighteen gave three units, three schools allowed four units credit, and seven granted five units.

Similarly, the same situation was true for the subjects

of trigonometry, intermediate algebra, and plane geometry. Table III on page 32 summarizes the results of the ana lysis of the course titles and Table IV on page 33 shows the results of answers to Part I of the questionnaire.

32 TABLE III SUMMARY OF COURSES IN HIGH SCHOOL MATHEMATICS OFFERED BY FIFTY-FOUR JUNIOR COLLEGES IN CALIFORNIA AND WASHINGTON Name of course

Number of Units credit Schools for course granting this credit

1. Plane trigonometry

2 3 4 5

3 43 1 5

52

3 4 5 6 8 10

36 1 9 2 3 1

52

no credit 3 4 5 6 S 10

2 31 2 9 1 3 1

49

2 3 4 5•

19 18 3 7

47

30 1 9 1 3 1

45

2 3 4 5

4 7 4 1

16

2 3 5

1 2 2

5

2. Intermediate algebra

3. Plane geometry

4. Solid geometry

5. Elementary algebra

6* Arithmetic

7# General mathematics

Total number of schools offering course

3 4 5 6 8 ID'

TABLE

IV

SUMMARY OF PART I OF QUESTIONNAIRE 1* a. Courses for which credit is not given.

b. Elementary courses which should be a permanent part of curriculum.

No. of schools "No" Elementary algebra Plane geometry Intermediate algebra Solid geometry General mathematics

20 20 12 10 10

2. One course in mathematics required for graduation 3. Everyone required to pass test in mathematics or take refresher course before graduation

Yes General mathematics 'Elementary algebra Plane g eometry Intermediate algebra

No IB B

11 3

Advanced algebra Solid geometry Trigonometry

..Yesr Number 12

Per cent 29

No Number 29

Per cent 71

22

54

19

46

4. Best course which might be required for graduation Business mathematics Trade or shop mathematics General or survey mathematics Arithmetic (fundament als) Choice of any of above

24 31 30 37

c. Advanced courses which should be a permanent part of curriculum. Yes

No

37 37 41

5 5 1

Number of schools reporting for each course 7 1 19 7 6

34 Comparison of results with previous studies#

In com

paring the offerings of high school mathematics courses in the junior colleges at the present time with those of ten or twenty years ago the results of several previous similar studies were obtained#

It was found that trigonometry is the only subject

that has been offered consistently by a high percentage of all the junior colleges*

This fact was revealed by the results of

a number of studies conducted in 1 9 2 9 # 1 9 3 1 # 1935# 1 9 3 9 # a&d the present study#

Results of these previous studies indicated

that up to 1939 elementary algebra and plane geometry were not offered at all or were offered by less than ten per cent of the junior colleges#

By converting the restilts of this study, which

are shown in Table III into terms of percentage, it appeared that elementary algebra and plane geometry were offered by eighty-three per cent and ninety-one per cent, respectively, of the junior colleges reporting.

During the period 1929-1939#

there was a steady increase in the percentage of junior colleges which offered solid geometry and intermediate algebra# the figure never exceeded thirty per cent#

However,

Results of the pre

sent investigation indicated that by 1948 ninety-six per cent of the junior colleges offered intermediate algebra as part of their curriculum and eighty-seven per cent offered solid geo metry.

A summary of results of previous studies and the per

centages of schools offering the several high school subjects in mathematics are shown in Table V, page 35#

35 TABLE

V

STUDIES OF MATHEMATICAL OFFERINGS IN JUNIOR COLLEGES Title of course

Percentage of schools offering the course Carpenter fs PostonsT GagerTs Present Hillfs study study study study study (360 (33 (378 (274 (54 schools) schools) schools) schools schools .12.31? ... ..... 1.93.53... ....1939k. ....194&5.J..929,1 _

Trigonom etry

95

Solid geometry

83

74

96

16

28

23

37

Intermed iate algebra

32

26

23

96

Plane geometry

11

4

9

91

4

6

33

Elementary algebra

89

lj. E. Hills, "Junior College Mathematics," School Science and Mathematics, 29:330-335, November, 1929. ^W. W. Carpenter, "Curriculum Offerings in Missouri," Junior College Journal, 2:13-24, January, 1931 • 3j. H. Poston, "Mathematics Curricula of the Junior Colleges of the United States," (Masterfs thesis, George Peabody College for Teachers, Nashville, Tennessee, 1937). A. Gager, "Terminal Business Mathematics in the Junior College," (Doctor!s dissertation , George Peabody College for Teachers, Nashville, Tennessee, 1940). ^Data taken from Table III of this study.

Summary of the chapter* The study of previous investi gations revealed that ten to twenty years ago very few, if any, junior colleges offered for credit the high school subjects of algebra, plane geometry, intermediate algebra, trigonometry and solid geometry.

The trend during the recent years was that

more and more junior colleges were offering these mathematics courses.

The results of the present study indicated that

junior colleges today universally offer the so-called high school courses as a part of their mathematics curriculum. Experts agreed that these elementary mathematics courses should become a permanent part of the junior college curriculum. Finally, it was found that there is great variability in the amount of credit given by junior colleges at present for these same high school subjects.

CHAPTER VI

COLLEGE MATHEMATICS AND PURE MATHEMATICS COURSES Since one of the early functions of junior colleges was to offer certain courses in preparation for university training, it is the purpose of this chapter to study the offerings of junior colleges in the field of college mathematics and pure mathematics.

It is intended that particular attention will he

drawn to the presence or absence of any long term tendencies or trends as exhibited by the college and pure mathematics courses.

Information in making the-study of college courses

was obtained by analysis of course titles as listed in the junior college catalogues and by use of the answers in Part III of the questionnaire. Analysis of offerings in catalogues and answers to questlonnalre. The compilation and examination of the offer ings of'the college and pure mathematics courses in the junior college revealed several facts#

Twenty-one or nearly fifty per

cent of all the mathematics courses offered by the junior col leges were college or pure mathematics courses.

Thirty-eight

(seventy per cent) or more of the schools listed offered the conventional junior college courses in mathematics consisting of the following subjects:

analytical geometry, first, second

and third courses in calculus and college algebra.

However, in

addition to these latter courses sixteen other purely college

courses were listed as available for eredit.

Of the new mathe

matics courses, recently added to the curriculum of junior colleges, engineering mathematics, spherical trigonometry, differential equations, vector analysis, projective geometry and mathematical analysis are a few of the most frequently listed in the catalogues. As it has been shown in Chapter Five, there is consider able variation in the number of units credit granted by the different junior colleges even for college mathematics courses. For example, in the standard college algebra course two schools granted two units credit, seven schools offered four units credit, five schools allowed five units, and thirty-three junior colleges granted three units credit.

A complete summary of the

college courses offered by the junior colleges and the units credit offered for each by school is shown in Table VI, page 3 9 . >

It has been pointed out previously that junior colleges have been adding more and more terminal and applied courses to their curriculum? during the past few y e a r s I n order to learn what instructors of mathematics in junior colleges felt concern ing this growing tendency, several pertinent questions were asked.

Results of answers to Part III of the questionnaire re

vealed that despite this growing tendency forty (ninety-eight per cent) of the schools reporting indicated that too much

1 Merton L. Hill, oj>. cit., pp. 3H-313»

TABLE

VI

SUMMARY OF COLLEGE MATHEMATICS AND PURE MATHEMATICS COURSES OFFERED BY FIFTY-FOUR JUNIOR COLLEGES IN CALIFORNIA AND WASHINGTON

Name of course

Number of Units credit Schools granting for course this credit

1. Plane analytic geometry

Total number schools offering course

3 4 5 6

41 2 6 2

51

3 5 6

39 'a 4

51

3 5

44 7

51

2 3 4 5

2 33 7 5

47

3 5

31 7

33

2 4 6 10

5 6 1 4

16

1 2 3

a 7 1

16

S. Differential equations

2

13

13

9. Solid analytical geometry

2 3 4

4 2 1

7

10. Vector analysis

2

6

6

11. Projective geometry

3

6

6

6 a 10 15

1 2 1 1

5

2 15

1 2

3

10

2

::2

15. Algebra theory

3

2

2

16. Non-euclidean geometry

2 6

1 1

2

17* Mathematics for elementary teachers

3

2

2

IS. Analytic mechanics

3

2

2

19. Constructions of mathematics

3

1

1

20. Logarithmic curve fitting and deter minants

2

1

\1

21. Survey of mathematics

6

1

1

2. First course in calculus

3. Second course in calculus 4. College algebra

5. Third course in calculus 6. Engineering mathematics

7. Spherical trigonometry

12. Mathematical analysis

13. Pre-engineering mathematics 14• Advanced mathematical analysis

.

v r\ >iJ

40 emphasis was not being placed on college mathematics in the junior colleges. Approximately fifty per cent of the instructors indica ted that they were not satisfied with the present curriculum in mathematics and that changes were necessary.

Those who in

dicated dissatisfaction offered fifteen possible changes in curriculum.

The changes which would affect the terminal and

applied curriculum in mathematics will be discussed in Chapter VII.

The following were suggested changes concerning the tra

ditional college courses in mathematics:

1.

Establish a five

or six unit course in analytic geometry and calculus for engi neers in the first semester. equations. students.

34.

2.

Add a course in differential

Rearrange the mathematics courses for engineering Add a course in advanced calculus.

3*

Replace

the conventional elementary algebra and plane geometry by a single, new mathematics course. In reply to the question of what new courses were to be added to the mathematics curriculum next term, respondents to the questionnaire indicated ten different courses. four college courses were among the ten:

The following

differential equations;

a sequence of four courses in engineering mathematics; elementary vectors; and solid geometry.

Table VII, on page 4l lists a sum

mary of answers to Part III of the questionnaire. Comparison of results with previous studies.

In Chapter

II it was pointed out that in 1929 Hills found that practically

TABLE

VII

SUMMARY OF PART III OF QUESTIONNAIRE Yes 1. Satisfied with present curriculum in mathematics Suggested changes for the ,rNotf answers above: a. Require all students to take course in review of arithmetic fundamentals (four schools re quested this change). b. Add more terminal mathematics courses. c. Establish five or six unit course in analytic geometry and differential calculus for en gineers in first semester. d. Add a course in differential equations. e. Replace algebra and geometry with a survey course for non-engineers. f. Add suitable mathematics courses for the general student. g. Rearrange'mathematics courses for the engin eering students. h. Add a general or survey course in mathematics. i. Add a course in mathematics of finance. j. Add a course in advanced calculus. k. Stress terminal mathematics more and more. . 1. Reorganize whole four-year high school mathe matics curriculum. in. Establish more vocational applied mathematics courses (four schools requested this course). n. Require students to attend mathematics classes five hours per week but grant only three units credit. o. Replace conventional elementary algebra and plane geometry by a single new mathematics course.

22

No 19

2. New courses in mathematics to be added next term: Number of schools reporting this course Slide rule Differential equations Vocational mathematics Sequence of four courses in engin eering mathematics Elementary vectors Cultural mathematics (History and applicaations to statistics, algebra, geometry, etc., and calculus) Practical business mathematics Solid geometry Shop mathematics Insurance mathematics 3. Too much emphasis still being placed on college preparatory mathematics. Yes No

1

40

2 2 2 1 1 2

1 1 1 1

•pM

42 the only mathematics courses being offered by junior colleges were the standard college courses in trigonometry, college alge bra, analytical geometry, differential equations and calculus.2 He also reported that nearly all the schools were satisfied with their curriculum in mathematics.

Adams in 1937,3 Hannelly in

19402* and Ahern in 1942^ found approximately the same facts, namely, college courses in mathematics in the junior colleges continued to be in predominance with little change and consisted almost entirely of the standard courses mentioned above. sults of the present study revealed considerablechange situation from 1929 to 1942 as just outlinedabove.

Re in the

It is true

that at the present time the standard college courses are still a vital part of the junior college programs, but considerable variation in number and type of college courses are now being offered.

Also, instructors have indicated that they are not

satisfied with present programs of instruction.

This can be

interpreted only to mean that the mathematics curriculum in junior colleges now is changing and probably will continue to change in the future. Summary of chapter. Analysis of answers to a questionnaire

2 F. E. Hills, op. cit., pp. 8 8 0 -8 8 5 . 3 L. J. Adams, op. cit.. pp. 194-195* ^ R. J. Hannelly, op. cit., pp. 260-1. ^ Lorella Ahern, pp. cit., pp. 18-22.

43 and study of course titles in college mathematics in junior colleges revealed that compared to previous similar studies the number and type of courses are undergoing considerable change*

Junior colleges at present are offering a greater

variety and number of college courses in mathematics than were offered ten to twenty years ago*

College courses in

mathematics are still an Important part of the junior college curriculum.

About fifty per cent of the instructors in the

junior colleges indicated that they were not satisfied with the program of instruction in mathematics and indicated several constructive changes which might be made.

CHAPTER VII

TERMINAL AND APPLIED MATHEMATICS COURSES The growth In the number and in the enrollment of junior colleges during the past few years has been very noticeable. Along with the increased emphasis on junior college instruction there has been a corresponding expansion of terminal and applied courses in the eurriculums of junior colleges.

It is the pur

pose of this chapter to point out the trend of terminal and ap plied courses in the mathematics curriculum of the junior col leges during the period of approximately the past ten years. Data and information for the analysis in this chapter were obtained from the same sources1as mentioned in Chapters V and VI— namely, study of course titles in the junior college bulletins and analysis of answers to the questionnaire. Analysis of course titles in the catalogues. Reference is made to the total list of all the mathematics courses offered by junior colleges in California and Washington as shown in Table I.

Analysis of this list shows that nineteen or forty-

two per cent of all the mathematics courses were terminal or applied.

A breakdown of these subjects showed that eight were

business mathematics; eleven were applied mathematics courses designed for particular vocational fields.

The courses in the

vocational field included radio mathematics, industrial statis tics and control charts, nursing mathematics, simplified

*5

calculus, vocational mathematics, shop mathematics, slide rule, applied trigonometry, applied mathematics, technical mathematics and cultural mathematics*

The several courses designed for the

business field were general mathematics, business mathematics, 4 mathematics of finance, elementary statistics, advanced business mathematics, arithmetic, mathematics of accounting and commercial algebra• Of all the terminal and applied courses offered, those in the business field were in the majority; business mathematics, mathematics of finance, arithmetic and elementary statistics being offered by thirty per cent or more of the junior colleges reporting*

Table VIII lists all the terminal and applied mathe

matics courses shown

in the catalogues of the fifty-four junior

colleges studied* Results of ques tionnaire * Analysis of answers to ques tions in Part II of the questionnaire revealed several pertinent facts regarding terminal mathematics courses*

Although it ap

pears that terminal and applied courses in mathematics have been increasing recently in the junior college curriculum, opinions of experts were unanimous in expressing that emphasis on terminal and applied courses was not so great as to slight the regular college courses*

Forty-one instructors (representing one hun

dred per cent of the replies) stated that too much emphasis was not being placed on terminal mathematics*

TABLE

VIII

SUMMARY OF TERMINAL AND APPLIED MATHEMATICS COURSES OFFERED BY FIFTY-FOUR JUNIOR COLLEGES IN CALIFORNIA AND WASHINGTON

________ Number o f ___________

Name of course

Units credit for course

1. Business mathematics

3. Slide rule 4. Arithmetic

2

12 19 3 3 4

3 5

6 1 2 2 3 4 5

5. Elementary statistics

2 3 4 5

6.'

6.

Technical mathematics

'3 ‘4

6

7. Shop mathematics

9. Cultural mathematics

10. Applied mathematics

11. General mathematics

course

41

32

2 2 20 4

■ 36 24

4 7 4

1 1 9 2 1 1 6 1 3

16

14

• 10

6

6 8

3

5

3 4 5

1 2 1

3

6

:1

5

3 4 8 10

1 2 1 1

5

2 3 5

1 2 2

5 3

12. Commercial algebra

3

3

13. Nursing mathematics

2

1 2 1 2 1 1 1 1 1

3 14. Mathematics of accounting

Total number

schools offering

1 3 2 1 1

3 5

6 S. Vocational mathematics

this credit

3 4 5

6

2f Mathematics of finance

Schools granting

1 3

15* Advanced business mathematics

2

16. Applied trigonometry

3

17. Industrial statistics and control charts

6

IS. Radio mathematics

3

19. Simplified calculus

6

3 3

1 1 .1 1 1

47

Of forty-one schools reporting, only one stated that Its terminal students were required to meet a specific course re quirement; this school required either three units of any mathe matics and a course in plane geometry or six units of any mathe matics.

However, fifteen instructors (representing forty per

cent of the replies) were of the opinion that a course in mathe matics should be required of all terminal students to meet gradua tion requirements • In considering mathematics as a course requirement for graduation for all students, terminal or otherwise, a majority (twenty-nine or seventy-one per cent) of the experts stated they were not in favor of such a requirement.

In this investi

gation It appeared significant that nearly thirty per cent of the answers were in favor of some required mathematics.

This

fact indicated that mathematics is becoming more important at the junior college level. In addition, experts who stated that a mathematics course should be required for graduation indicated that it should be a terminal or applied one.

Of the several courses listed, a survey

course or other general course in mathematics was mentioned most frequently as best for students to take as a graduation require ment.

Nineteen, or forty-eight per cent, listed the survey

course as best; seven, or twenty-eight per cent, listed business mathematics; and twenty per cent listed arithmetic fundamentals as the best course.

In other words, the experts* opinions were

48 that If junior colleges were to require a course in mathematics as a graduation requirement it should be, first, a general or survey course and, second, either business mathematics or arith metic fundamentals*

It was apparent that some basic course in

mathematics which would be of value and interest to all students was the one considered most desirable by nearly all the junior college experts in mathematics* Additional evidence that junior colleges now believe mathematics is becoming more important in their curriculum is illustrated by the responses to another question.

Twenty-two,

or fifty-four per cent, of the instructors replied that all junior college students should be required either to pass an examination in the fundamentals of mathematics or take a re fresher course. A number of instructors in the junior colleges expressed the opinion that the terminal courses in mathematics required for certain vocational preparation were not adequate.

Forty

per cent of the replies expressed dissatisfaction with these terminal courses.

Instructors were asked to state which termi

nal courses should be added to the curriculum. proved rather enlightening.

The answers

Business mathematics, vocational

mathematics and a survey or history of mathematics were the ones most frequently checked as being the most desirable.

The

fact that ten different terminal courses were mentioned as sub jects which should be added to the curriculum indicated that junior colleges were aware of the need for more of such courses

49 In the curriculum* 'Which terminal courses in mathematics are best serving the needs of terminal students was the essence of another ques tion asked*

Surprisingly, there were ten different mathematics

courses listed*

The courses most frequently mentioned as the

best were shop mathematics, business mathematics, general mathe matics, and technical mathematics*

Others mentioned were

mathematical analysis, petroleum mathematics and a survey of mathematics• The fact that junior colleges are very much interested and aware of the needs of terminal students was shown by the answers to the question of what terminal courses in mathematics have been added recently to the curriculum* courses were listed as new ones*

Thirteen different

Shop mathematics, business

mathematics, general mathematics and technical mathematics were the ones reported most frequently as having been recently added to the curriculum* Reference is made to Table IV and Table IX for the sum mary of answers to the questionnaire which pertain to terminal and applied mathematics courses* Chanter summary* Analysis of information obtained from junior college catalogues and results of the questionnaire re vealed the following facts:

1*

The trend in the curriculum

of mathematics in junior colleges is to offer more and more terminal and applied mathematics courses*

2*

Of all the

TABLE

IX

SUMMARY OF PART II OF QUESTIONNAIRE —

,

1. Too much emphasis on terminal mathematics 2. One course in mathematics required by all terminal students (One school required three units of any mathematics and geometry or six units in any mathematics) 3. Should one course in mathematics be re quired b y all terminal students 4. Terminal courses in mathematics now re quired in certain curricula are adequate (Two schools offered no terminal courses in mathematics)

Y e s

Wo

6

4T

1

40

15

24

21

15

5. Terminal courses in mathematics which have been added recently to curriculum: Course

Number of schools adding this course

Shop mathematics General mathematics Business mathematics Technical mathematics Business arithmetic Appreciation of mathematics Graphical methods Slide rule Related mathematics Statistics Mathematics for nurses Mathematics for radio Daily life mathematics

4 5 7 3 3 1 1 1 1 1 1 1 1

6. Additional terminal courses in mathematics which should be added Number of schools re porting this course Agricultural mathematics 1 Classical problems in mathematics 1 Shop mathematics 1 Vocational mathematics 2 Business mathematics 3 Technical mathematics 1 Survey and history of mathematics 3 Nursing mathematics 1 . Radio mathematics 1 Applied mathematics 1 7. Which course in mathematics is best serving needs of terminal students Number of schools re porting this course Shop mathematics General mathematics Business mathematics Technical mathematics Mathematical analysis Petroleum mathematics' Radio mathematics ’Survey of mathematics Trade mathematics Remedial mathematics

5 3 5 2 1 1 1 1 1 1

vn

O

51 terminal courses in mathematics offered by the junior colleges those In the business field were the most predominant.

3•

The

prevailing opinion of experts in junior colleges was that ter minal mathematics courses are still not adequate but that neces sary additions and curriculum changes are occurring to meet the growing demand.

4.

A majority of the junior colleges stated

that a required course in mathematics for all students was not desirable at present; however, there was a relative high per centage of instructors who did indicate the desirability of such a required course.

5.

Evidence that mathematics is in

creasingly becoming more and more important in the curriculum of junior colleges was shown by the responses of experts to the query concerning students being required to pass an examina tion in the fundamentals of mathematics or to take a refresher course as a graduation requirement.

6.

A high percentage of

experts stated that if students should be required to take a course in mathematics as a graduation requirement, it should be a terminal or applied course in mathematics.

7.

The termi

nal courses which are best meeting the needs of terminal students were found to be shop mathematics, business mathematics, general mathematics and technical mathematics.

CHAPTER VIII

ANALYSIS OF ENROLLMENTS IN MATHEMATICS COURSES IN THE JUNIOR COLLEGE In the previous chapters there has heen presented an analysis of the mathematics courses in junior colleges as re vealed by a study of course titles and results of answers to a questionnaire.

It is the purpose of this chapter to present

an analysis of student enrollments in the various mathematics courses in the junior colleges as revealed by answers to Part IV of the questionnaire.

Student enrollments will be studied

under the following divisions:

enrollment in the junior col

lege mathematics courses as a whole, enrollment in the high school mathematics courses, enrollment in traditional college mathematics courses and enrollment in terminal and applied mathematics courses. A.

ENROLLMENT IN MATHEMATICS COURSES AS A WHOLE

The summary of the results of student enrollments in the various mathematics courses as reported by forty-two junior colleges In California and Washington revealed that 20,092 stu dents out of a total enrollment of 55*325 were enrolled In mathematics . This represented thirty-seven per cent of all the students.

It appeared that the importance and impetus of mathe

matics as a junior college subject is well illustrated by this

53 figure, when more than one out of every three students were studying mathematics at this level* In considering the relationship between the number of students enrolled in all mathematics courses and the total enrollment in each school, it was found that there was con siderable variation from school to school*

For example, in

one school only eleven per cent of the total enrollment were talcing some type of mathematics.

On the other extreme, it

was found that in another school fifty per cent of the students were enrolled in mathematics.

Any attempt to explain this

wide variation would be difficult unless a detailed survey of the aims, interests, goals and community needs of the particular school were determined.

Table X gives the summary of students

enrolled in all mathematics courses by each school* A condensed summary which shows the total enrollments, enrollments for the mathematics courses as a whole, and enrollments in terminal and applied mathematics courses is presented in Table XI* B.

ENROLLMENT IN THE HIGH SCHOOL MATHEMATICS COURSES Probably the most startling figure revealed by an ana

lysis of enrollments was that 1 0 ,1 5 9 students, out of a total of 5 5 *3 2 5 enrolled in junior colleges, were talcing one or more of the so-called high school courses of elementary algebra, plane geometry, intermediate algebra, solid geometry or trigo nometry*

This figure represented eighteen per cent of the total

54 TABEE

X

ENROLMENT OF STUDENTS IN THE VARIOUS COURSES IN MATHEMATICS AS REPORTED IN PART IV OF QUESTIONNAIRE Junior college

TCT" —

Enrollments 1. Total enrollment as of March. 1, 1948

500

250

ioo

1 4 3 5 ? 240

TT

13

Hi

15

15

“17

W

1650

1250

1500

2400

300

2400

175

•11 44 46 59 37

14 20 24 61

200 120 200 140

10 10 6 12 12

29 100 180 334 80

20 200 2,50 400

144

125

22

n -----------

315

100

1150

80

160

1000

11 11

3 3 4

2 2 3 1 10

50

10

50 50 75 75

-16

22

3 2 2 5 8

5

35

41

20

13 7

200 25

11

120

T9

FT

11000

885

1150

300

34 30 3G 45

20 20 25 25 40

1000 210

115 90

4. Enrollment in the follow ing courses: Solid geometry Elementary algebra Plane geometry Intermediate algebra Trigonometry

8

16

30 10 30

9 10

College preparatory courses5|l00 Business mathematics 20 Trade or shop mathematics 20 General or cultural math. Slide rule

15

10

39

60 25 25

3. Total enrollment terminal mathematics courses**

35 73

5 21

Refresher mathematics Mathematics of finance Technical mathematics Statistics Arithmetic 2. Total enrollment all mathematics courses

8

60

4 5

3

25

110 100 100

60

8°

150

160 25

122 19 70

203

53 110

300 40 15

25

35

26

160

45 30 10

60

41 11 29

60

19 12

20 53

110 30 25

10

7 10

50

70

14

18 20

15

190 40

50

195

162

25

28

85

40

:'40

500

5

18

225

22

60

375

600

400

577

1160

140

1018

50

2500

354

287

10

75

25

125

163

215

40

130

32

335

164

55

*College preparatory courses included: college algebra, analytic geometry; first, second, and third courses in calculus; engineering mathematics and differential equations. **Terminal courses included: business mathematics, trade or shopmathematics, slide rule, cultural or general mathematics and arithmetic.

55

TABU

J.

(Continued)

ENROLLMENT OF STUDENTS IN THE VARIOUS COURSES IN MATHEMATICS AS REPORTED IN PART IV OF QUESTIONNAIRE

Enrollments 1. Total enrollment as of March 1, 1948

22

22

24'

725 668

350

29

200

520

2700

409 670 230

15

25 20 35 25

20 35 70 100 100

2 3 2 1 3

21 91 55 68 25

500

15

50 20

300

1 3

185 100 50

5040

500

30

Junior college 31 12 33 ’

28

""25.. ~ZS.. 2?

75 1300

850

Ik

38

39

200 1600

1958

200

18 42 55 91 80

20 25 22 40 36

2 3 3 2 11

171

60 20

30

5500

1700

29 295

30 25

150 50

330 460 317

20 55 55

35 45

3 2 6 3 10

80

707

260 100

100

10

800

W -- 41“

600 1200

42

650

4. Enrollment in the follow ing courses: Solid geometry Elementary algebra Plane geometry Intermediate algebra Trigonometry

12 46 24 25

22 39 90 54 22

College preparatory courses* 71 Business mathematics 48 Trade or shop mathematics 14 General or cultural mathematics Slide rule

11 22 8

12

11

Refresher mathematics Mathematics of finance Technical mathematics Statistics Arithmetic 2. Total enrollment all mathematics courses 3. Total enrollment terminal mathematics courses*?

70 256

12 30 15 25 10

88

10

150

44

25

120 90

24

50 45 50 75 20

12 25 30 18 20

75 100 50

100

33

11 103

33

21 26

10

25

50 35

6 25 42 37 28

24 32

30

30 1000 252 235

74

41

85

2430

275

40

200

800

15

700

500

3240

600

204

50

340

50

10

45

200

3

200

100

1000

140

24

25

490

250

50

185

485

210

33

20

26

150

25

^College preparatory courses included: college algebra, analytic geometry; first, second and third courses-in calculus; engineering mathematics' and differential equations. **Terminal courses included: business mathematics, trade or shop mathematics, slide rule, cultural or general mathematics and arithmetic.

56 TABLE

XI

SUMMARY OF ENROLLMENTS AS REPORTED BY 35 JUNIOR COLLEGES OF CALIFORNIA AND 7 JUNIOR COLLEGES OF WASHINGTON (SUMMARY OF PART IT OF QUESTIONNAIRE) Enrollments

Total number of students enrolled

Average for all junior colleges

Junior college as a whole

55,325

1,317*

All mathematics courses

20,092

47$

High school mathematics courses Elementary algebra Plane geometry Intermediate algebra Solid geometry Trigonometry Totals

1,900 2,273 3,341 477 2,16$ 10,159

43 54 $0 12 51 240

5,654

135

Terminal and applied mathematics courses Business mathematics 1,160 Arithmetic 1,093 Slide rule 912 Trade and shop mathematics 634 Mathematics of finance 360 Cultural or general mathematics 75 Statistics 45 Totals 4,279

2$ 26 22 15 9 2 1 103

College mathematics courses*

^College algebra, analytic geometry, first, second and third courses in calculus, engineering mathematics, and differen tial equations.

57 junior eolleg© enrollment or nearly fifty per cent of all those taking mathematics. One explanation for this situation might have been the fact that there were a great number of returned veterans of the last war who were deficient in elementary mathematics*

Many of

these people in returning to junior colleges had enrolled in curricula leading to semi-professional or professional vocations in which some elementary mathematics was required or highly recommended*

Other reasons which could have explained this

situation were poor educational programming or guidance in high school and the greater maturity of students leading to changed vocational plans* C.

ENROLLMENT IN COLLEGE MATHEMATICS

In the group of courses in traditional college mathematics, which included college algebra, analytic geometry, first, second, and third courses in calculus, engineering mathematics and dif ferential equations, it was found that 5 >654 students were en rolled.

This represented approximately ten per cent of all

those enrolled in junior colleges*

This figure was not surpris

ing; in fact, it was quite expected, since there is always a certain percentage of students preparing for the scientific or engineering fields in which this mathematical background is necessary.

58 D.

ENROLLMENT IN TERMINAL AND APPLIED MATHEMATICS COURSES In the terminal and applied mathematics courses, which

included business mathematics, trade or shop mathematics, slide rule, cultural or general mathematics, and arithmetic, only 4,279 students or eight per cent of the total were found to be enrolled.

It appears that contrary to trends of junior colleges

to offer more terminal and applied courses in mathematics, en rollment figures do not indicate that these courses are popular with the students.

However, these terminal courses were added

to the curriculum to meet the needs of students who pursue the terminal curriculum, but evidently such people were in the minority according to enrollment in mathematics as shown in the present study. Chanter summary* Analysis of the enrollments in the various mathematics courses in the junior colleges as reported in the questionnaire indicated the following conclusions:

1.

More than one out of every three students enrolled in junior colleges were enrolled in mathematics.

2.

Enrollment of

junior college students in the so-called high school courses in mathematics was the greatest--it represented nearly fifty per cent of the students who were enrolled in mathematics courses.

3.

Ten per cent of the students were enrolled in

the traditional college courses in mathematics • 4.

Eight

per cent of junior college students were enrolled in terminal

59 mathematics courses* Table XII presents a summary of the percentages as outlined in this chapter*

60

TABLE

XII

SUB-MARI OF PERCENTAGES AS OUTLINED IN CHAPTER- VIII Division of mathematics

Percentage of Total enrollment Enrollment in all mathematics courses

All mathematics courses

37

High school mathematics courses

1$

50

Traditional college courses

10

23

Terminal and applied mathematics courses

20

CHAPTER IX

CONCLUSIONS AND RECOMMENDATIONS It was the purpose of this study to survey the curriculum in mathematics of the junior colleges in the states of California and Washington in order to investigate and interpret general trends in these curricula.

In order to make this analysis

several procedures were used:

(1 ) a detailed study and analysis

of the catalogues of the junior colleges, (2 ) a review and inter pretation of the trends in the mathematics curriculum of the junior colleges as revealed by a study of investigations con ducted during the past several years, (3 ) and an analysis of answers to a questionnaire sent to responsible personnel in the junior colleges.

In this concluding chapter there will be pre

sented the general conclusions of the present report and recom mendations for future study. A.

CONCLUSIONS

Review of results of recent investigations« Conclusions which were based upon an analysis of recent studies were:

1.

Up to 19^2 most of the courses in mathematics in the junior colleges were traditional college courses.

2.

Until approxi

mately 1937 there was very little change in the mathematics courses offered in the junior colleges, but by 19^0-41 the trend was toward offering more terminal courses in mathematics.

62 3*

By 1942 there existed a trend, even though slight, for

junior colleges to offer some or all the courses in mathematics formerly taught only in the high schools.

4.

Of all the ter

minal courses in mathematics offered in the junior colleges the course in business mathematics was most frequent.

There

was no evidence of junior colleges desiring or attempting to establish a minimum required program of mathematics for gradu ation for any student. Survey and analysis of course titles. Conclusions which were found based upon a study and analysis of the course titles in mathematics offered by the junior colleges in the 1948-49 catalogues were:

1.

A total of forty-five different courses

in mathematics were offered by the junior colleges.

2.

There

is great variability among junior colleges in the amount of credit given for the same courses in mathematics.

3.

The aver

age number of semester hours instruction in mathematics courses was found to be forty-six hours, compared with an average of twenty-three semester hours found in*1940.

4.

A general con

clusion is that the trend of junior colleges is to offer more and more courses in mathematics and that the junior colleges at pre sent are offering a greater number and variety of courses than ever before. High school mathematics courses. Analysis of catalogues of junior colleges and answers to the questionnaire indicated

63 that the junior colleges by 19^8 had formally added the high school courses to their mathematics curriculum and had indi cated that these subjects should remain as a permanent part of the mathematics curriculum• College mathematics and pure mathematics courses• Re sults of the present study indicate that junior colleges now are offering a greater variety and number of college courses in mathematics than were offered ten years ago*

It was found that

in fifty per cent of the cases junior college instructors stated that they were not satisfied with the curriculum in college mathe matics and indicated a number of constructive changes* Terminal and applied mathematics courses♦ Analysis of information from the junior college catalogues and results of the questionnaire revealed several conclusions:

1.

The trend

in the mathematics curriculum was to offer more and more terminal and applied mathematics courses— the most predominant of these courses being in the business field.

2*

Experts in junior col

leges stated that terminal mathematics courses are still not adequate and that necessary additions and changes must be brought about to meet the growing demand#

3*

Up to the time of the

present study, no graduation requirement in mathematics existed; there was expressed, however, an opinion by thirty per cent of the junior colleges that there ought to be established a survey or a general course in mathematics as a graduation requirement.

64 4*

Evidence was found which pointed out that mathematics is

increasingly becoming more and more important on the junior college level. Enrollment in the .junior colleges. Conclusions based upon student enrollments in the mathematics courses indicated that:

1*

More than one out of every three junior college

students are enrolled in mathematics courses.

2.

High enroll

ment figures in high school mathematics courses in junior col leges showed definitely the trend of these courses to become an important, permanent part of the mathematics curriculum in the junior colleges.

3*

Traditional college mathematics courses

show an enrollment of ten per cent of the total junior college population.

4.

Enrollment in "terminal and applied mathematics

courses showed an unexpectedly low proportion of the total enrollment. B.

RECOMMENDATIONS

There is no doubt that the evidence supports the con clusion that junior colleges have accomplished much during the past few years in revising and adding to their mathematical curriculum in order to meet the changing needs of students. It is felt, however, that there is still much to be done.

As

early as 1940, suggested revisions and changes drawn up by the National Council of Teachers of Mathematics were goals for junior colleges to try to reach:

65 Junior Colleges should offer a range of Instruction that will meet the needs of hoth preparatory and termi nal students and should provide for: (a) first two years of general and liberal arts education, patterned in a manner acceptable to universities, (b) two years of gen eral and liberal arts education suitable for both termi nal students and those who may continue their study in semi-professional education for which there may be a community need* • • For the large majority of students who are terminal, it is recommended that curricula In mathematics be set up In the junior colleges for the following group of terminal students: A* Commercial B* Vocational C. Academic. Although it was found in this study that many junior colleges are doing a good job in offering many terminal and specialized courses In mathematics, it is easy to agree with R. W. Hart that there should be further re-organization of some of the subjects.

Hart believed that junior colleges

should include specially organized terminal courses In arith metic, algebra, geometry, trigonometry, mathematics of investo ment, use of tables, and graphical methods. He said that some or all of these topics, except mathematics of investment, could be offered in one five-hour course or in two three-hour courses. It is believed that if the junior college Is going to carry out one of its principal aims of serving the needs of the students of the community, a program of "selling” its terminal curriculum to such individuals must be instituted and carried 1

"Junior College Mathematics," Fifteenth Yearbook of National Council of Teachers of Mathematics. Teachers College, Columbia, Chapter VIII, 19^-0. 2 R. V. Hart, "Terminal Courses In Mathematics," Junior College Journal. 11:253~6 , January, 19^1*

66 out.

Joseph Seidlin very ably stated the problem when he said: Since the junior college is supposed to be serving principally the community, it seems that it should offer more terminal mathematics courses for the youth not going to college. . . Hence, it is up to the mathematics teachers not only to find time during these crowded days to develop terminal courses, but what is harder, to sell such courses to the youth of the community.3 In conclusion, it is recommended that a survey and an

analysis be made of the trends and courses of the mathematics curriculum in the junior college at the end of every five or ten year period and that results of these studies be made com mon knowledge among instructors and supervisors of mathematics in junior college.

Early information of such investigations

should provide understanding and knowledge as to what direct ions the mathematics curricula of the junior colleges are taking.

o Joseph Seidlin, "A Report of the Mathematics Committee of the California Junior College Association,” National Mathe matics Magazine, XI, No. 4, p. 3 8 7 , 1937*

BIBLIOGRAPHY

68 BIBLIOGRAPHY Adams, L. J., "Mathematics in California Junior Colleges,,f Junior College Journal. 7:194-5, January, 1937* This survey by Adams in 1937 was quite significant. His analysis showed that elementary courses in mathematics were being offered by junior colleges as part of their curriculum. Ahern, Lorella, "Scope of Mathematical Offerings in Selected Junior Colleges, Mathematics Teacher. 35:18-22, January, 1942. One of the later surveys of the offerings of junior col leges in the mathematical curriculum. This report was significant in that it showed that by 1 9 *1-1 there was a definite trend for junior colleges to offer the elementary mathematics course formerly given only in high school. Cloud, A. J., "The Junior College and the Community," Junior College Journal. 8:453*55, May 1933. One of the best articles published which outlines the role of junior colleges in California concerning their place in serving community needs. Lists the several junior colleges-and the distinctive program of courses for each. Cushman, Frank, "Junior College and Vocational Education," Junior College Journal, 8:417-19, May, 1938. Douglas, Harl R., "Mathematics for All and the Double Track Plan," School Science and Mathematics, 45:425*434, May, 1945. An address by a well-known expert in education in which there appears an important statement implying a required program of mathematics for all high school and junior college students. "Effects of Revision of Junior College-Mathematics," Editorial, School Review. 53:197-8, April, 1945. An article which gives evidence that the trend in mathe matical education in junior colleges during recent years has been away from the traditional pattern of college algebra, trigonometry, and the other pure mathematic courses.

69 Fifteenth Yearbook of National Council of Teachers of Mathe matics"! ^Junior College Mathematics,” Teachers College., Columbia, 1940. An excellent report containing recommendations for types of mathematics courses that should be offered in junior colleges to meet the needs of the commercial, vocational, and academic groups of students. Gager, W. A.. ’’Terminal Business Mathematics in the Junior College, .Unpublished Doetorfs dissertation, George Pea body College for Teachers, Nashville, Tennessee, 1940. Contains a summary of the findings of several studies of mathematical offerings in junior colleges throughout the United States. This dissertation contains information which is invaluable for studies similar to the present report. Georges, J. S., ’’Mathematics in the Junior College,” School Science and Mathematics. 37002-6, March, 1937* One of the earliest evidences indicating the desirability of including a required course in mathematics in the curriculum of junior colleges. Goddard, R. W., ’’Junior College Serves Community Needs,” Junior College Journal, 4:308-11, March, 1934. Goddard, R. W., ’’Shall We Accept the Challenge,” Junior Col lege Journal, 1 5 :388 -9 , May, 1945. Good, C. V., Editor, Dictionary of Education. Published under auspices of Phi Delta Kapa, 1945* An excellent source of definitions and terminology in the field of education. Hannelly, R. J., ’’Mathematics in the Junior College,” American Mathematical Monthly, 46:581-5, November, 1939. Gives a clear picture of one of the earlier functions of junior colleges in the field of mathematics. Suggests an effective program of instruction in mathematics for both the terminal and semi-professional student. Hannelly, R. J*, ’’Mathematics Offerings in Junior Colleges,” Junior College Journal. 10:260-3, January, 1940. First significant study of a great number of junior

70 colleges throughout the United States in which the number of semester hours instruction in mathematics was obtained. This study also gave evidence that by 1939 there was little mathematics offered in the cultural or terminal field in junior colleges. Hart, R. W., ’’Terminal Courses in Mathematics,” Junior Col lege Journal, 11:253-6, January, 1941. Suggests an important revision and re-organization of the mathematics curriculum in junior colleges in order that the program might become more effective for the terminal student. Hill, Merton E., "History of Terminal Mathematics," Junior College Journal. 12:312-313, February, 1942. A concise summary of the history and growth of terminal courses in junior colleges of California which indicates the growing trend of curricula in the terminal field. Hills, J. E., "Junior College Mathematics," School Science and Mathematics. 29:880-885, Hovember, 1929. One of the earliest surveys made to find out what the public junior colleges in the United States were offering in mathematics. An excellent source of information con cerning the mathematics offerings at that time. Hoy, E. A., "Junior College Mathematics in California," School Review. 36:370-3, May, 1 9 2 8 . A survey of courses in mathematics offered by junior col leges in^California during the year 1928. Results of this survey provide pertinent information concerning what courses were predominate in the mathematics curriculum at that time. Koos, Leonard V . , The Questionnaire in Education. Hew York: The Macmillan Company, 1928, 248 pp. One of the best references for students who intend to make up, use and interpret questionnaires as part of their re search techniques. Lefever, D. Welty, Turrell, A. M., and Henry L. Weitzel, Principles and Techniques of Guidance. Hew York: The Ronald Press Company, 1941, 522 pp. A basic text containing modern methods and techniques of

71 of guidance which provides an excellent reference in this field of education. Lounsbury, John L., “Junior Colleges are Not on the Wrong Path,” Junior College Journal. 1 5 :3 6 0 -3 7 1 * April, 1945. A useful article for comparison between the ideas of “junior" college and "city" college. McGrath, E. J., “The Junior College of the Future,11 Junior College Journal, 15:260-268, February, 1945* Has presented an excellent prediction of what the junior college of the near future must offer in the way of di versified curriculum in order to take care of the greatly increased enrollment. National Education Association, Research Division, “The Questionnaire," Research Bulletin. 8:1-15, January, 1930. A publication of the National Education Association in which pertinent problems in education are investigated and scientifically answered by a staff of experts. Phillips, Marjorie, “Problems of Questionnaire Investigation," Research Quarterly of the American Association for Health. Physical Education and Recreation. 12:528-37, October,

19417 A treatise which points out to students the problems and their solutions which may arise in the construction and use of the questionnaire. Poston, J. H., “Mathematics Curricula of the Junior Colleges of the United S t a t e s U n p u b l i s h e d Master*s thesis, George Peabody College for Teachers, Nashville, Tennessee, 1937Quite a significant survey. Results indicated that in only seventy-four out of 378 junior colleges studied were there evidences of a trend toward mathematics of a terminal nature. Reynolds, E. J., and W. W. Carpenter, "Terminal Curricula in Junior Colleges," Junior College Journal. 12:71-75, October, 1941. An excellent study of 241 junior colleges which showed that by 1941 there was a definite trend toward terminal curricula being offered in these institutions.

72 Schmidtke, F. E., "Trends in Terminal Offerings,” Junior Col lege Journal, 8:22-26, October, 1937* An excellent study of over one hundred junior colleges in the United States which showed that over a ten year period there was only a slight gain in the number of courses in mathematics offered in junior colleges. Seidlin, Joseph, "A Report of the Mathematics Committee of the California Junior College Association,” National Mathematics Magazine. XXI Ho. k , p1. 3 8 7 , 1937* An official statement of the Mathematics Committee of the California Juhior College Association indicating the im portance of an adequate program of terminal mathematics courses in junior colleges• Singer, C. Gregg, "Junior Colleges are on the Wrong Path," Junior College Journal. 15:67-70, October, 19^4. This article was quite significant' because the author has taken'a position opposing most educators. He states that junior colleges are being mis-led to offer terminal and technical training to a great degree and are not becoming junior colleges in a sense of providing a liberal education. Toops, Herbert A., "Predicting the Returns for Questionnaire," Journal of Experimental Education. 3:204-15* March, 1935* Gives a clear and concise picture of the important ele ments which should be attained in order that a question naire be effective.

APPENDIX

74

SURVEY QUESTIONNAIRE (Completion time: 20 minutes) An Investigation of Current Trends in Mathematics Curricula of t he Junior~ollegesoT California and WasKington Originator Jack L. Rowe Instructor, Engineering Mathematics Bakersfield College Mailing Address 1524 Pearl Street Bakersfield, California

Respondent [Name] (Junior college) (Location— City)

DIRECTIONS 1.

It is requested that the mathematics department head or other qualified representative answer all the questions as best possible with the information readily available.

2♦

Supplemental answer may be recorded in the space pro vided at the end of pertinent items.

3. Use the enclosed envelope to return the questionnaire to the originator. Definition and explanation of terms: In this questionnaire the term "terminal courses" refers to those courses that are designed for students who intend to complete their formal education at the end of the fourteenth year. "Terminal stu dents" are those students who intend to complete their formal education at the end of the fourteenth year. The term "junior college" refers to those institutions which grant some formal recognition upon the completion of a course of study at the end of the fourteenth year. PART I 1.

Many Junior Colleges now offer one or more of the socalled high school courses in mathematics. a.

Check below those courses now offered in your Junior College for which full junior college credit is not gi ven:

75 elementary algebra intermediate algebra plane geometry ____ solid geometry general mathematics (the review of fundamental arithmetic) b.

Check below which of the following elementary high school mathematics courses you think should be a permanent part of the junior college curriculum and which ones should not. Yes

No general mathematics (review of fundamental arithmetic elementary algebra ____ plane geometry intermediate algebra

c.

Check below which of the following more advanced high school mathematics courses you think should be a permanent part of the junior college curriculum and which ones should not. Yes ___

No ___ advanced algebra _____solid geometry , trigonometry

2.

Do you think that every student should be required to com plete at least a one-s:emester course in mathematics be fore graduation from Junior College? Yes No

3.

Do you think every student in Junior College should be required to pass a test in the fundamentals of arithmetic before graduation or else be required to take a short course in a review of arithmetic fundamentals before graduation? Yes No

4*

If your Junior College-were to require that every student complete at least one course in mathematics before gradua tion, check which one of the following you believe would be the best: business mathematics trade or shop mathematics a general or survey course in mathematics a review of arithmetic fundamentals other (please give brief description)

76 PART II 1,

Do you believe that so much emphasis is being placed on terminal courses in mathematics in the Junior College to the extent that traditional college preparatory courses in mathematics are being slighted? Tes No

2*

Does your Junior College require for graduation at least one course in mathematics for the terminal students? Yes No If the answer is nYesn to above question, please name the course required and give a brief description below*_____

3*

If the answer to the previous question is !tNon, do you believe your Junior College should require at least one course in mathematics for graduation for the terminal student? Yes No

4#

Do you believe that the terminal courses in mathematics in your Junior College which are required for certain vocational preparation are adequate? Yes No

5*

What courses in mathematics designed for the terminal stu dent have been added to the curriculum during the past few years? (Please list) (Give approximate date of addition;)

6. What additional terminal courses in mathematics do you think should be added to the curriculum? (Please list below and give brief description of each)

7#

Of the various terminal courses in mathematics now offered in your Junior College please name the one which in your opinion is best serving the needs of terminal students*

PART III Are you satisfied with the curriculum in mathematics now offered in your Junior College: Yes No If the answer is "No11 to the above question, please indi cate below briefly what change or changes you would make if it were possible.

What new course or courses in mathematics are planned to be added to the curriculum of your Junior College next fall? (Please list by name and give a brief description of each below.)

Do you think that too much emphasis is still being placed on the college preparatory courses in mathematics such as calculus, college algebra, analytic geometry, differential equation, etc., in your Junior College? Yes No FART IV What is the approximate total enrollment in your Junior College as of March 1, 1943?__ ______________ _ What is the approximate total enrollment in all mathematics courses in your Junior College?. . ___________ What is the approximate total enrollment in the so-called terminal courses in mathematics in your Junior College (shop math., business math., survey math., etc.) If possible and if the information is available it would be helpful to give below the approximate enrollment as of March 1, 1943 in each of the following classifications: ________________ elementary algebra

7& jplane geometry intermediate algebra [solid geometry trigonometry [college preparatory mathematics (calculus, analytic ’geometry, college algebra, etc.) business mathematics [trade and shop mathematics [cultural or general mathematics [slide rule ‘other (Please list and give enrollment in each.)