Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1972 A Study of Mathematics Education in the Public Secondary Schools of Louisiana. Francis Pollard Woods Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Woods, Francis Pollard, "A Study of Mathematics Education in the Public Secondary Schools of Louisiana." (1972). LSU Historical Dissertations and Theses. 2369. https://digitalcommons.lsu.edu/gradschool_disstheses/2369 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact gradetd@lsu.edu.
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; I. 73-13,693 \. WOODS, Francis P ollard, 1924- A STUDY OF MATHEMATICS EDUCATION IN THE PUBLIC SECONDARY SCHOOLS OF LOUISIANA. i The Louisiana S ta te U n iversity and A gricultural I and Mechanical C ollege, Ed.D., 1972 Education, general ; University Microfilms, A XEROXCompany, Ann Arbor, M ichigan THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED
A STUDY OF MATHEMATICS EDUCATION IN THE PUBLIC SECONDARY SCHOOLS OF LOUISIANA A D is s e r ta tio n Submitted to th e G raduate F a cu lty of th e L ouisiana S ta te U n iv e rsity and A g ric u ltu ra l and M echanical C ollege in p a r t i a l f u lf illm e n t o f th e requirem ents fo r th e degree o f D octor in E ducation in The Departm ent o f E ducation by F ran cis P o lla rd Woods B.S., L ouisiana S ta te U n iv e rs ity, 1949 M.Ed., L o u isian a S ta te U n iv e rs ity, 1953 December, 1972
PLEASE NOTE: Some pages may have ind ist inet print. Filmed as received. University Microfilms, A Xerox Education Company
ACKNOWLEDGMENTS The w r ite r w ishes to ex p ress h is a p p re c ia tio n to th e m athem atics te a c h e rs, p r in c ip a ls and p a ris h su p e rv iso rs whose co o p e ra tio n and a s s is ta n c e made t h i s study p o s s ib le. G ra te fu l acknowledgment i s extended to th e members of h is d o c to ra l com m ittee, Dr. Sam Adams, Dr. Fred Smith, Dr. W illiam Sm ith, Dr. E ric T hurston and Dr. A lvin B ertran d. He i s e s p e c ia lly g r a te f u l to h is m ajor p ro fe s s o r, Dr. G. C. G ibson, whose encouragem ent, p ro fe s s io n a l guidance, ancl frie n d s h ip were in v a lu a b le. A p p recia tio n i s extended to Mr. Malcom McNaylor of th e L o u isian a S ta te U n iv e rsity Computer C enter fo r h is c o n trib u tio n to th e stu d y. F in a lly, th e w r ite r w ishes to ex p ress h is h e a r t f e l t thanks to h is lo v e ly w ife o f tw e n ty -fiv e y e a rs, B etty Thompson Woods, and to h is son D avid, fo r th e i r p a tie n c e, u n d erstan d in g, and encouragement throughout th e stu d y. ii
TABLE OF CONTENTS Page ACKNOWLEDGMENTS... 11 LIST OF TABLES... v i ABSTRACT........ ix CHAPTER 1. INTRODUCTION... 1 The Problem... 3 S tatem ent o f th e P r o b l e m... 3 D e lim ita tio n o f th e P r o b le m... 4 Im portance o f th e Study.. < >.. 4 D e fin itio n o f Terms U s e d... 5 Sources o f D a t a... 3 P r o c e d u r e... 6 2. REVIEW OF RELATED LITERATURE........ 7 S tu d ie s o f Teacher C h a r a c te r is tic s and P re p a ra tio n «. «.... o o.... o o. 7 S tu d ie s o f th e Secondary M athem atics C urriculum.............. 19 S tu d ie s o f Methods and In n o v ativ e Programs. 24 S tu d ie s in L ouisiana............ 25 3. DESIGN OF THE STUDY... 29 P lanning Procedure... 29 Data G athering P ro ced u re.... 30 M ailin g Procedure........ 31 i i i
CHAPTER Page Follow -up Procedure.............. 32 4. PRESENTATION AND ANALYSIS OF nata... 33 Background...... 33 C h a r a c te r is tic s o f M athem atics T eachers... 35 Age and Sex o f th e Q u estio n n a ire P o p u la tio n... 35 Age, Sex, and Race o f th e Q u e stio n n a ire P o p u la tio n... 35 E xperience and S a la rie s o f M athem atics T eachers........ 36 Teaching E xperience... 38 S a la rie s o f M athem atics T eachers... 38 P re p a ra tio n o f M athem atics T eachers... 40 T eacher C e r t if ic a tio n....... 41 D egrees Held by M athem atics T eachers... 43 Sources o f B ach e lo r's Degrees... 44 C la s s if i c a ti o n as to M athem atics M ajor, M inor, U n q u a l i f i e d... 45 C la s s if i c a ti o n by U ndergraduate M ajor and M i n o r... 48 M a ste r's Degrees of M athem atics Teachers. 51 M a ste r's Degree M a jo rs.... 51 G raduate M athem atics Courses... 54 N a tio n a l S cience F oundation I n s t i t u t e s.. 55 P ro fe s s io n a l Membership in M athem atics O rg an izatio n s.... 57 M athem atics Teaching A ssignm ents.... 58 B asal M athem atics Textbooks Being Used by M athem atics Teachers... 61 iv
CHAPTER PaSe G eneral M a th e m a tic s... 62 A lgebra I......... 63 G e o m e t r y... 64 A lgebra I I... o. 65 Advanced M a t h e m a t i c s... 66 Trigonom etry......... 67 S en io r A rith m etic.... 68 B usiness A rith m e tic... 69 Methods o f S e le c tio n o f Textbooks... 69. O rg a n iz a tio n a l P rocedures U tiliz e d in M athem atics Programs... 70. I n s tr u c ti o n a l P rocedures U tiliz e d in Teaching M a t h e m a t i c s... 73 E xperim ental M athem atics I n s tr u c ti o n a l M a te ria ls and P r o g r a m s... 76 Student M athem atics Clubs.... 78> 5. SUMMARY AND CONCLUSIONS... 79 Summary... 79 C o n c lu s io n s... 84 LITERATURE C ITE D... 86 A PPEND ICIES... 89 A. Q u e s tio n n a i r e... 89 B. Cover L e tte r to P r in c ip a ls o f Schools.... 93 C. L e t te r to S u p erv iso r o f A d m in istra tiv e U n its. 94 D. Follow-Up L e tte r to S u p erv iso rs o f A d m in istra tiv e U n its... 95 VITA... 96 v
LIST OF TABLES T able Page 1. Number o f Schools and Number o f M athem atics T eachers by School S ize.....34 2. Q u e stio n n a ire P o p u la tio n by Age and S e x... 36 3. Q u e stio n n a ire P o p u la tio n by Age, Sex, and Race. 37 4. E xperience o f M athem atics Teachers a t P re se n t School w ith T o ta l E xperience....... 39 5. S a la rie s o f M athem atics T eachers... 40 6. Number and Types o f Teaching C e r t if ic a te s Held by M athem atics T eachers... 43 7. Number and Types o f Degrees Held by M athem atics T eachers... 44 8. Number of B a c h e lo r s Degrees by Year and S ta te P u b lic I n s t i t u t i o n s G ranting... 46 9. Number o f B a c h e lo r s Degrees by Year and S ta te P r iv a te I n s t i t u t i o n s G ranting... 47 10. M athem atics T eacher Q u a lific a tio n s as to M athem atics M ajor, M inor, o r U n q u alified... 49 11. B achelor's Degree M ajor and Minor o f th e Q u e stio n n a ire P o p u la tio n....... 50 12. Number of M a s te r's Degrees o f M athem atics Teachers by Year and I n s t i t u t i o n G r a n t i n g... 52 13. M a s te r's Degree M ajors o f th e Q u e stio n n aire P o p u l a t i o n... 54 14. Number o f G raduate M athem atics Courses Completed by th e Q u e stio n n a ire P o p u la tio n... 55 15. Number and Types o f N atio n al Science Foundation I n s t i t u t e s A ttended by th e Q u estio n n aire P o p u la tio n........... 36 16. P ro fe s s io n a l Membership in M athem atics O rg an iza tio n s o f th e Q u e stio n n a ire P o p u latio n. 57 vi
Table Page 17. Number o f M athem atics C lasses Taught by M athem atics Teachers............. 59 18. M athem atics Courses Taught by the Q u e stio n n aire P o p u latio n... 60 19. S u b jec ts Taught in A ddition_to M a th e m a tic s... 61 20. M athem atics Textbooks Used in G eneral M athem atics and th e P ercen t o f S tu d en ts Using Each T e x t b o o k... 62 21. M athem atics Textbooks Used in A lgebra I and th e P e rc e n t o f S tudents Using Each Textbook... 63 22. M athem atics Textbooks Used in Geometry and th e P ercen t o f S tudents Using Each Textbook... 64 23. M athem atics Textbooks Used in A lgebra I I and th e P e rc e n t o f S tudents Using Each Textbook... 65 24. M athem atics Textbooks Used in Advanced M athem atics and th e P ercen t o f S tu d en ts Using Each T e x t b o o k... 66 25. Mathematics Textbooks Used in Trigonometry and th e P ercen t o f S tudents Using Each Textbook. 67 26. M athem atics Textbooks Used i n S en io r A rith m etic and the Percent of Students Using Each Textbook............... 68 27. Mathematics Textbooks Used in Business A rith m etic and th e P ercen t o f S tu d en ts Using Each Textbook................ 69 28. Q u e stio n n aire P o p u latio n by Methods o f S e le c tio n o f Textbooks and Teacher Q u a lific a tio n s... 71 29. Q u estio n n a ire P o p u latio n U tiliz in g C e rta in O rg a n iz a tio n a l P rocedures in M athem atical Programs.......... 72 30. Q u estio n n a ire P o p u latio n U tiliz in g C e rta in I n s tr u c tio n a l P rocedures in the Teaching o f M a t h e m a t i c s... 75 31. Q u estio n n aire P op u latio n Using E xperim ental M athem atics I n s tr u c ti o n a l M a te ria ls and Programs............ 77 vii
Table 32. Page Number of Schools w ith S tudent M athem atics Clubs........ 78 viii
ABSTRACT The purpose of th i s study was to analyze the c h a r a c te r i s t ic s of m athem atics ed u ca tio n in th e p u b lic secondary schools in L o u isian a in r e l a t i o n to te a c h e rs, program s, and methods o f te a c h in g. The d a ta were o b tain ed from th e 1971-1972 Annual School R eports to the S ta te Departm ent of E ducation and from a q u e s tio n n a ire se n t to 1759 secondary m athem atics te a c h e rs. There were 1517, or 86.3 p e rc e n t, u sab le q u e s tio n n a ire s re tu rn e d. Of th e q u e stio n n a ire p o p u la tio n 52.7 p e rc e n t of th e te a c h e rs were male as compared to 47.3 p e rc e n t fem ale. F if ty - s ix p e rc e n t of th e te a c h e rs were younger than 35 y ears o f age. Female te a c h e rs were in th e m a jo rity in th e under 25 and over 55 age b ra c k e ts. The r a t i o of C aucasian te a c h e rs to Negro te a c h e rs was 1070 to 447. F orty p e rc e n t of the m athem atics te a c h e rs had le s s than s ix y ears o f te a c h in g ex p erien ce. F o rty -th re e p e rce n t were new in t h e i r p re s e n t sch o o l. Temporary te a c h in g c e r t i f i c a t e s were h e ld by 8.5 p e rc e n t of th e mathem atics te a c h e rs. B ach elo r s degrees had been earned by 98.7 p e rc e n t of th e te a c h e rs. Of th e s e te a c h e rs, 33.4 p e rc e n t had a lso earned m a ste r s d eg ree s. A pproxim ately 70 p e rc e n t of th e se degrees were earned in th e p u b lic c o lle g e s and u n iv e r s i tie s o f L o u isian a. F if ty - e ig h t p e rc e n t of th e te a c h e rs were c l a s s i f i e d as m athem atics m ajo rs, 16 p e rc e n t as m athem atics ix
m inors, and 11 p e rc e n t as u n q u a lifie d. There were 42.9 p e rc e n t of th e te a c h e rs who had n o t taken a s in g le grad u ate course in m athem atics. This compared to 14.7 p e rc e n t who had taken n in e or more co u rses. Membership in th e N atio n al C ouncil of Teachers o f M athem atics was h eld by 319 te a c h e rs. The two s t a t e p ro fe s s io n a l m athem atics o rg a n iz a tio n s showed a combined membership of 329. In fo rm atio n on teach in g assignm ents re v e a le d th a t 54.1 p e rc e n t o f th e te a c h e rs ta u g h t fiv e c la s s e s of m athem atics. A l i s t of th e b a s a l textbooks and p e rc e n t o f s tu d e n ts u sin g them was o b ta in e d. The most fre q u e n t method of s e le c tin g th e se textbooks was by a d m in is tra tiv e u n it committee recommend a tio n ; however, 35.3 p e rce n t of th e te a c h e rs had no knowledge of who s e le c te d tex tb o o k s. Seventy-seven p e rc e n t of th e m athem atics te a c h e rs re p o rte d th a t t h e i r schools had m athem atics departm ents w ith departm ent chairm en. Only 6.5 p e rce n t in d ic a te d th a t they u t i l i z e d team te a c h in g. About o n e -h a lf of th e te a c h e rs s ta t e d th a t homogenous grouping of s tu d e n ts was used in m athem atics c o u rs e s. T h re e -fo u rth s o f the te ach ers re p o rte d th a t they used th e " t e l l, show, su p erv ised study" method of teach in g and used e x tra d r i l l m a te ria ls. Some 56.5 p e rce n t s ta te d th a t they in d iv id u a liz e d t h e ir in s tr u c tio n. Programmed m a te ria ls and a u d io -v is u a l m edia, w ith th e ex cep tio n of the overhead p r o je c to r, were used in fre q u e n tly. x
School M athem atics Study Group m a te ria l had been ta u g h t by 19.8 p e rc e n t of th e te a c h e rs. Only te n te a c h e rs were experim enting w ith in s tr u c tio n in computer s c ie n c e, w h ile the use o f te le v is io n in in s tr u c tio n was zero. The fin d in g s o f th i s stu d y in d ic a te th e fo llo w in g c o n c lu sio n s: 1. M athem atics was b ein g tau g h t by m athem atics te a c h e rs who were e q u ally balanced by se x, w ith a ra c e r a t i o o f seven to th re e of Caucasian to Negro. 2. The r a t e of tu rn o v er o f m athem atics te a c h e rs appeared high sin c e 40 p e rce n t of the te a c h e rs had le s s than s ix y e a rs teach in g ex p erien ce. 3. There e x is te d a sh o rta g e of m athem atics te a c h e rs in c e r ta in areas of th e S ta te as judged by th e number of tem porary c e r t i f i c a t e s issu e d. 4. E ighty-seven p e rce n t of th e s tu d e n ts were ta u g h t by m athem atics m ajors and m inors. 5. A g r e a te r number of m athem atics te a c h e rs e le c te d scien c e as a teach in g minor th an any o th e r s u b je c t f i e l d. 6. There was l i t t l e p a r t i c i p a t i o n in p ro fe s s io n a l m athem atics o rg a n iz a tio n s by th e m athem atics te a c h e r s. 7. The " t e l l, show, su p e rv ise d study" method of teach in g p re v a ile d. 8. Very l i t t l e use was being made o f a u d io -v is u a l media w ith the ex cep tio n of th e overhead p r o je c to r. 9. The degree of use of th e com puter o r te le v is io n in in s tr u c tio n was n e g lig ib le. xi
C hapter 1 INTRODUCTION Since th e m id -1 9 5 0 's, th e re has been c o n s id e ra b le n a tio n a l em phasis on m athem atics e d u c a tio n, p a r t i c u l a r l y a t th e h ig h school le v e l. T here have been commission re p o rts and experim ents sponsored by p r iv a te and government foundatio n s aimed a t im proving in s tr u c tio n in m athem atics. Im p o rtan t f i r s t ste p s have been ta k e n to u p d ate th e s u b je c t m a tte r competence o f m athem atics te a c h e rs through c o l le g ia te i n s t i t u t e s u n d e rw ritte n by th e N a tio n a l S cience F oundation. C ontrary to th e p o p u la r b e l i e f th a t th e re v o lu tio n in school m athem atics had i t s in c e p tio n w ith th e launching o f S putnick I by th e R ussians in 1958, i t s beg in n in g can o f f i c i a l l y be tra c e d to a re p o rt o f a com mission ap p o in ted in 1955 by th e C ollege E ntrance Exam ination Board. This re p o rt su p p lie d th e spark th a t ig n ite d a movement th a t swept th e c o u n try, as many groups worked to revamp th e m athem atics c u rric u lu m. These groups sh ared a common aim: to develop a cu rricu lu m th a t would meet th e needs o f an in d iv id u a l in a s o c ie ty o f ever in c re a s in g te c h n o lo g ic a l advances. G. G ailey P ric e (1961), Chairman o f th e M athem atics Departm ent o f th e U n iv e rsity o f Kansas s ta te d : The changes in m athem atics in p ro g ress a t th e p re se n t tim e a re so e x te n siv e, so fa r-re a c h in g in t h e i r im p lic a tio n s, and so profound th a t th ey can be d e sc rib e d only as a re v o lu tio n.
P ric e (1961) co n tin u ed by s ta t in g th re e causes o f th e re v o lu tio n : (1) re s e a rc h in m athem atics, (2) autom ation, and (3) autom atic d i g i t a l computing m achines. Though n a tio n a l a t te n ti o n was n o t focused upon th e developm ent o f new c u r r ic u la in m athem atics u n t i l passage o f th e N a tio n a l D efense E ducation Act by th e E ig h ty - f if th Congress in 1958, a t l e a s t two groups were a lre a d y organized and experim enting w ith c u r r ic u la r e v is io n s. The U n iv e rs ity o f I l l i n o i s C urriculum Study in M athem atics was e s ta b lis h e d in December, 1951. A y e a r l a t e r, ex perim ental m a te ria l was in u se as a r e s u l t o f th e work o f th i s group. In 1953, The Boston C ollege M athem atics I n s t i t u t e began a program o f modem m athem atics a t th e freshman and sophomore c o lle g e le v e ls. This program le d im m ediately to th e r e a l iz a t io n o f th e need fo r re te a c h in g secondary school m athem atics te a c h e rs. O ther cu rric u lu m development groups who gained im petus from N a tio n a l D efense E ducation Act and N atio n al Science Foundation were th e G re a te r C leveland M athem atics Program, th e Syracuse U n iv ersity -W eb ster C ollege Madison P r o je c t, th e U n iv e rs ity o f M aryland M athem atics P ro je c t, th e School M athem atics Study Group, and th e B all S ta te T eachers' C ollege E xperim ental Program. The developm ent o f m a te ria ls by th e se groups and th e im plem entation o f th e m a te ria ls by th e schools o f th e n a tio n n e c e s s a r ily a f f e c te d th o se whose r e s p o n s ib ility i t became to te ach them. Teacher p re p a ra to ry i n s t i t u t i o n s had to v ary
t h e i r program s, and te a c h e rs a lre a d y in s e rv ic e had to a l t e r t h e i r methods and become acq u a in te d w ith new co n cep ts and new m a te r ia l. The teach in g and re te a c h in g o f te a c h e rs o f m athem atics became a prim e concern in th e im plem entation o f new c u r r ic u la. S ch u lt and A bell (1963) re p o rte d th a t in s p ite o f th e accep tan ce o f th e new m athem atics programs by th e schools o f th e n a tio n, o n ly 30,000 o f th e 100,000 secondary school te a c h e rs o f m athem a tics in th e U nited S ta te s had a tte n d e d one o r more o f th e N a tio n a l Science Foundation I n s t i t u t e s. The c o lle g e s and u n iv e r s i t i e s o f th e n a tio n accep ted th e c h a lle n g e, and provided th e le a d e rsh ip needed to implement th e new m athem atics m a te r ia ls, and to re te a c h th e m athem atics te a c h e rs. THE PROBLEM Statem ent o f th e Problem What are th e c h a r a c te r i s t ic s o f m athem atics ed u c a tio n in th e p u b lic secondary schools in L o u isian a in r e l a t i o n to te a c h e rs, program s, and methods o f teaching? Data concerned w ith th e follow ing item s w ere c o n sid ere d : (1) te a c h e r c h a r a c t e r i s t i c s o f age, sex, ra c e ; (2) te a c h e r exp erien ce and s a l a r i e s ; (3) te a c h e r p re p a ra tio n ; (4) te a c h e r membership in p ro fe s s io n a l o rg a n iz a tio n s ; (5) te a c h in g assignm ents (6) b a s a l m athem atic textbooks being u sed ; (7) i d e n t i f i c a t i o n o f te a c h in g tech n iq u es and procedures used by th e te a c h e rs ; (8) s p e c ia l o r in n o v a tiv e programs in m athem atics.
D e lim ita tio n of th e Problem This study was lim ite d to th o se te a c h e rs in L o u isian a p u b lic secondary schools who were te a c h in g one o r more of th e follow ing s u b je c ts d u ring 1971-1972: (1) G eneral M athem atics, (2) A lgebra I, (3) Geometry, (4) A lgebra I I, (5) Advanced M athem atics, (6) Trigonom etry, (7) S enior A rith m e tic, and (8) B usiness A rith m etic. Im portance of th e Study No study has been made of t h i s n a tu re concerning th e m athem atics programs in th e p u b lic secondary school s u b je c ts in th e S ta te of L o u isian a p r io r to t h i s tim e. In view of th e tremendous changes th a t have taken p la c e in th e cu rric u lu m, th e v a s t amount of money th a t has been expended by th e N atio n al Science Foundation upgrading m athem atics te a c h e rs, and th e change from r a c i a l l y seg reg ated to u n ita r y school system s, a study i s needed. The d a ta o f th i s study have re le v a n c e and p o te n tia l as background in fo rm atio n to improve m athem atics e d u c a tio n, m athem atics program s, and m athem atics in s tr u c tio n in L o u isian a, and h o p e fu lly, t h i s re p o rt w ill be used by members of school b o ard s, p ro fe s s io n a l e d u c a to rs, and in te r e s te d c itiz e n s fo r th is purpose.
DEFINITION OF TERMS USED M athem atics Teacher The term "m athem atics te a c h e r" w ill be in te r p r e te d in t h i s study to mean any person g a in fu lly employed in th e occupatio n o f teach in g in a p u b lic secondary school in L o u isian a who was re sp o n sib le fo r in s tr u c tin g a c la s s in one o f th e follow ing s u b je c ts : (1) G eneral M athem atics, (2) A lgebra I, (3) Geometry, (4) A lgebra I I, (5) Advanced M athem atics, (6) T rigonom etry, (7) Senior A rith m e tic, and (8) B usiness A rith m e tic. Secondary School The term "secondary school" w ill r e f e r to any p u b lic sc h o o l, in c lu d in g th e n in th grade le v e l or above, whose academic program in c lu d e d some or a l l o f th e co u rses l i s t e d above. SOURCES OF DATA Records on f i l e w ith th e L o u isian a S ta te Department of E ducation served as th e source fo r much of th e d a ta of th i s study. The Annual School R eports fo r th e academic school y ear 1971-1972 y ie ld e d such in fo rm atio n a s : (1) a d m in is tra tiv e u n it, (2) sc h o o l, (3) s iz e of sch o o l, (4) p r in c ip a l, and such in fo rm atio n on te a c h e rs a s : (5) name, (6) e x p e rie n c e, (7) c o lle g e tr a in in g, (8) c e r t i f i c a t i o n, (9) s u b je c ts ta u g h t, and (10) s a la r y. O ther d a ta were o b ta in ed by q u e s tio n n a ire s com pleted by th e m athem atics te a c h e rs of th e p u b lic secondary sch o o ls.
Data included: (1) age, (2) sex, (3) race, (4) textbooks used, C5) jnethods o f te a c h in g, (6) in - s e r v ic e tr a in in g and N a tio n a l Science Foundation I n s t i t u t e s, (7) grouping p ro c e d u re s, (8) teach in g p ro ce d u re s, (9) membership in p ro f e s s io n a l m athem atics o rg a n iz a tio n s, and (10) use o f exp erim en tal m a te ria ls o r ex perim ental program s. PROCEDURE Survey cards were used to c o l le c t d a ta from th e 1971-1972 Annual School R eports on f i l e in the L o u isian a S ta te D epartm ent of E ducation. Q u e stio n n aires were s e n t to a su p e rv is o r of i n s tr u c tio n in each o f th e a d m in is tra tiv e u n it s, who in tu rn, forw arded them to school p r in c ip a ls. The p r in c ip a l of each school is su e d th e q u e s tio n n a ire s to h is m athem atics te a c h e rs and c o lle c te d th e com pleted form s. The q u e stio n n a ire s were then c o lle c te d by th e su p e rv iso r of in s tr u c tio n and forw arded to th e re s e a rc h e r. The d a ta were then coded fo r th e com puter, and cards were punched a t th e Computer C enter, L o u isian a S ta te U n iv e rs ity.
C hapter 2 REVIEW OF RELATED LITERATURE The g re a t i n t e r e s t c re a te d by th e n a tio n a l im petus on "modern m athem atics, combined w ith th e em phasis on s c i e n t i f i c developm ent, has in flu e n c e d to some degree th e m athem atics ta u g h t in our n a t i o n 's h ig h schools to d ay. S ev eral re s e a rc h p r o je c ts have been conducted which a re r e la te d e i t h e r d i r e c t l y o r i n d i r e c t l y to t h i s problem. These s tu d ie s a re summarized w ith in t h i s c h a p te r u nder fo u r subheadings: (1) S tu d ie s o f T eacher C h a r a c te r is tic s and P re p a ra tio n, (2) S tu d ie s o f Secondary M athem atics C urriculum, (3) S tu d ie s o f Methods and In n o v a tiv e Program s, and (4) S tu d ies Made in L o u isia n a. S tu d ies o f T eacher C h a r a c te r is tic s and P re p a ra tio n N elson (1959) conducted a study to determ ine th e c h a r a c te r i s t ic s o f o u tsta n d in g secondary school m athem atics te a c h e rs in N ebraska. By u sin g a r a tin g form w hich was m ailed to p r in c ip a ls and s u p e rin te n d e n ts, a l i s t o f 154 m athem atics te a c h e rs who w ere r a te d as o u ts ta n d in g, s u p e rio r, o r above average was conducted. The c h a r a c t e r i s t i c s of th e se te a c h e rs were id e n t i f i e d by u sin g q u e s tio n n a ire s, in te rv ie w s, and classroom v i s i t a t i o n s. The fin d in g s o f th e study in clu d ed a l i s t i n g s o f some o f th e d is tin g u is h in g 7
c h a r a c t e r i s t i c s o f th e o u ts ta n d in g secondary m athem atics te a c h e rs. The fo llo w in g c h a r a c t e r i s t i c s were c ite d : (1) th e o u tsta n d in g te a c h e rs w ere p rim a rily m a rried men o r s in g le women, (2) 68.4 p e rc e n t o f th e se te a c h e rs recognized th e in flu e n c e o f a h ig h school o r c o lle g e te a c h e r in making t h e i r c a re e r c h o ic e, (4) th e prim ary reaso n g iv en fo r choosing m athem atics te a c h in g as a c a re e r was a lik in g fo r m athem atics, (5) th e m a jo rity o f th e s e te a c h e rs rece iv ed t h e i r degrees from s t a t e u n i v e r s i t i e s o r teacher's c o lle g e s and had m athem atics m a jo rs. N eilsen (1955) s tu d ie d th e s ta t u s o f th e m athem atics «cu rricu lu m in th e h ig h sch o o ls o f Iowa. He in terv iew ed te a c h e rs in 60 randomly s e le c te d h ig h sc h o o ls. The m athem atics co u rses ta u g h t in Iowa h ig h sch o o ls w ere u s u a lly based upon a s in g le te x tb o o k. L i t t l e r e v is io n and m o d ern izatio n o f th e m athem atics cu rric u lu m had ta k en p la c e in th e 25 y ears p r io r to 1955, except in g e n e ra l m athem atics c o u rs e s. However, a growing i n t e r e s t in m odernizing th e m athem atics cu rricu lu m was a p p a re n t. A ll o f th e te a c h e rs in te rv ie w e d had b a c h e lo r s d eg rees; ov er 80 p e rc e n t had some g ra d u a te w ork, and more th an o n e -th ird o f th e te a c h e rs h e ld m a s te r 's d eg ree s. N early o n e -th ird had m ajors in m ath em atics, and over o n e -th ird had work exceeding th e req u irem en ts f o r a m inor in m athem atics. The m athem atics te a c h e rs devoted th e m ajor p o rtio n o f th e in s tr u c tio n a l p a r t o f t h e i r c la s s p e rio d s to d isc u ssio n s c e n te re d around te a c h e r e x p la n a tio n s and d em o n stratio n s.
Osbourn and Brown (1960) made a stu d y o f c h a r a c t e r i s t i c s o f te a c h e rs on a re g io n a l le v e l. The fin d in g s re v e a le d th a t 7.1 p e rc e n t o f th e te a c h e rs who ta u g h t one o r more c la s s e s o f m athem atics in th e t h r e e - s t a t e a re a had ta k e n no c o lle g e m athem a tic s. The p erce n tag es ranged from 3.6 p e rc e n t i n New J e rs e y to 1 2 p e rc e n t in M aryland. The co u rse m ost g e n e ra lly ta u g h t by th e se p ersons was G eneral M athem atics, and in no c a se w ere th e se people devoting t h e i r f u l l tim e to m athem atics te a c h in g. The average number o f sem ester hours o f m athem atics earned by th o se in d iv id u a ls te ach in g m athem atics was 23. In depth o f s u b je c t m a tte r stu d y, 39 p e rc e n t o f te a c h e rs who w ere te a c h in g one o r more co u rses in m athem atics had n o t had C alculus n o r a more advanced co u rse in m athem atics. A n aly sis o f th e degrees h eld showed th a t 64 p e rc e n t o f th e p ersons te ach in g m athe- m ath ics had b a c h e lo r 's d e g re e s. M a s te r's degrees w ere h e ld by 32.7 p e rc e n t, w h ile le s s th a n 2 p e rc e n t w ere re p o rte d as having no d eg ree. The type o f i n s t i t u t i o n in w hich m athem atics te a c h e rs re c e iv e d t h e i r academic tr a in in g re v e a le d th a t 57.3 p e rc e n t had a tte n d e d a l i b e r a l a r t s c o lle g e, w h ile 35.5 p e rc e n t and 4 5.6 p e rc e n t had a tte n d e d te a c h e r s ' c o lle g e s and c o lle g e s o f e d u c a tio n, r e s p e c tiv e ly. This in d ic a te d th a t many m athem a tics te a c h e rs a tte n d e d more th a n one ty p e o f i n s t i t u t i o n. O n e-h alf o f th e se te a c h e rs had re c e iv e d t h e i r tr a in in g o u ts id e th e s t a t e in w hich they w ere te a c h in g. The p erce n tag e o f m a th em a tic s.te a c h e rs who ta u g h t m athem atics f u l l tim e was 47, w h ile 12 p e rc e n t had one fr e e p e rio d ; a n o th e r 23 p e rc e n t
XV spent one h o u r perday keeping stu d y h a l l s. Some a d m in is tra tiv e d u tie s were perform ed by 16 p e rc e n t of th e m athem atics te a c h e rs, w h ile 15 p e rc e n t ta u g h t some o th e r s u b je c t in a d d itio n to m ath em atics. The ty p e o f s u b je c t m ost fre q u e n tly ta u g h t in a d d itio n to m athem atics was s c ie n c e, follow ed by p h y sic a l e d u c a tio n. In a l a t e r stu d y, on a n a tio n a l b a s i s, Osbourn and Brown (1963) n o ted th a t approxim ately 118,298 te a c h e rs in th e secondary sch o o ls w ere te a c h in g one or more p erio d s o f m athem atics each day. These te a c h e rs c o n s titu te d about 20 p e rc e n t o f th e secondary te a c h in g fo rc e o f th e n a t i o n 's p u b lic sc h o o ls. The stu d y re v e a le d t h a t in th e S o u th east re g io n, o f which L ouisiana was a p a r t, 58.1 p e rc e n t o f th e m athem atics te a c h e rs tau g h t fo u r o r more p e rio d s o f m athem atics d a ily ; 27.1 p e rce n t tau g h t m athem atics two o r th re e p e rio d s d a ily ; w h ile th e rem aining 20,2 p e rc e n t ta u g h t only one m athem atics c la s s d a ily. A pproxim ately 20 p e rc e n t o f a l l m athem atics te a c h e rs w ere new to th e school in w hich they w ere te a c h in g i n 1961. This c o n d itio n p re v a ile d re g a rd le s s o f s iz e and lo c a tio n o f th e sch o o l. I n a stu d y made by M ills (1963), sponsored by th e N a tio n al S cience F oundation, fo r th e y e a r 1960-1961, i t was found th a t m athem atics te a c h e rs w ere predom inantly m ale. Of those who ta u g h t m athem atics b u t no s c ie n c e, 63 p e rc e n t w ere m ales. Males c o n s titu te d 73 p e rc e n t o f th e te a c h e rs who ta u g h t b o th sc ie n c e and m ath em atics. In th is stu d y, th e n a tio n was d iv id e d in to fo u r re g io n s w hich w ere: N o rth e a st,
N orth C e n tra l, South, and West. L o u isian a was included in th e S outhern re g io n. The sex r a t i o of m athem atics te a c h e rs was lo w est in th e South where 63 p e rc e n t of th e se te a c h e rs were men. The r a t i o was th e h ig h e st in th e West where men made up 81 p e rc e n t of th e group. In th e a n a ly s is of th e number of y e a rs of teach in g ex p erien ce of m athem atics te a c h e rs, th e stu d y re v e a le d th a t 49 p e rc e n t of th e se te a c h e rs in th e South had le s s than te n y ears of e x p erien ce. The number o f hours per week an average m athem atics te a c h e r sp e n t in classroom in s tr u c tio n and o th e r r e la te d a c t i v i t i e s was re p o rte d. The fin d in g s re v e a le d th a t th o se of th e West and South worked 52 hours weekly w h ile th o se of th e N orth C e n tra l and N o rth e a st re p o rte d 48 and 46 hours p er week, r e s p e c tiv e ly. The re p o rt o f scien c e and m athem atics te a c h e rs showed th a t th o se o f th e South to i le d 57 hours w eekly, w hile th o se o f th e W est, N orth C e n tra l, and N o rth east r e f le c te d 54, 52, and 51 hours in th a t o rd e r. Of th e m athem atics te a c h e rs in th e South, 60 p e rce n t of them ta u g h t fiv e or more c la s s e s p er day. This was th e h ig h e s t p erce n tag e in th e n a tio n, as th e N o rth east showed a p erce n tag e of 58, w hile th e N orth C e n tra l and West r e f le c te d 57 and 56 p erce n t r e s p e c tiv e ly. Fewer m athem atics te a c h e rs in th e South p o ssessed m a s te r 's degrees when compared to th o se in o th e r re g io n s. Of th e se so u th ern te a c h e rs, only 32 p e rce n t had m a s te r s d e g re e s. T e a ch ers c o lle g e s co n ferred 35 p e rc e n t of th e b a c c a la u re a te degrees on m athem atics te a c h e rs in th e N orth
C e n tra l re g io n, 32 p e rc e n t on th o se in th e South, 28 p e rc e n t i n th e N o rth e a st, and 20 p e rc e n t in th e Westo co n sid ere d grades 7-12 as secondary g ra d e s T his study Of th e secondary m athem atics te a c h e rs te a c h in g a t th e seventh and e ig h th grade le v e ls, 31 p e rce n t o f th o se who ta u g h t one o r two m athem atics c la s s e s d a ily had m a s te r's d eg rees; 27 p e rce n t who ta u g h t th r e e o r fo u r m athem atics c la s s e s d a ily had m a s te r 's d eg rees; w h ile 34 p e rc e n t o f th o se who ta u g h t fiv e o r more c la s s e s p er day had m a s te r 's d eg ree s. By re g io n, th e p erce n tag es o f secondary m athem atics te a c h e rs te a c h in g seventh and e ig h th grade m athem atics who h e ld m a s te r's degrees were as fo llo w s: N o rth e a st, 38 p e rc e n t; W est, 30 p e rc e n t; N orth C e n tra l, 29 p e rc e n t; and South 28 p e rc e n t. An a n a ly s is o f th o se secondary m athem atics te a c h e rs who were te ach in g grades 9-12 re v e a le d th a t 30 p e rc e n t o f th o se te a c h in g one o r two m athem atics p e rio d s d a ily had m a s te r 's d eg rees; w h ile o f th o se te a c h in g th re e o r fo u r p e rio d s and th o se te a c h in g fiv e o r more p e rio d s o f m athem atics d a ily, 41 p e rc e n t and 40 p e rc e n t, r e s p e c tiv e ly, had m a s te r 's d eg re e s. B urger (1960) s tu d ie d th e academic background o f th e m athem atics te a c h e rs in the s t a t e o f K ansas, b asin g h is fin d in g s on in fo rm a tio n g ath ered r e l a t i v e to th e school s e s sio n o f 1957-1958. T ra n s c rip ts o f 1,024 te a c h e rs were s tu d ie d. About 50 p e rc e n t o f th e m athem atics te a c h e rs ta u g h t in a re a s o r communities w ith a p o p u la tio n o f le s s than 1,000; 4 3.2 p e rc e n t ta u g h t in hig h schools w ith 100 stu d e n ts o r l e s s.
In excess of 66 p e rc e n t tau g h t in what was a "C lass A" sch o o l. The school o rg a n iz a tio n a l p lan in which 64.4 p e rc e n t of th e se te a c h e rs w ere employed was. th e 8-4 p la n. A n aly sis o f th e te ach in g assignm ents r e f le c te d th a t 236 te a c h e rs, or 22.8 p e rc e n t, ta u g h t only one course in m athem atics d a ily ; 410, or 39.5 p e rc e n t ta u g h t two o r more m athem atics c la s s e s and a ls o c la s s e s in o th e r s u b je c t a re a s. A few te a c h e rs who had a d m in is tra tiv e d u tie s were a ls o co n sid ere d in t h i s group. The o th e r 391 te a c h e rs c o n s titu te d 37.7 p e rc e n t o f th e t o t a l. and had f u ll- tim e assignm ents as secondary m athem atics te a c h e rs. In d eterm in in g th e source o f th e te a c h e rs of secondary m athem atics, th e stu d y r e f le c te d th a t 706, o r 67.1 p e rc e n t of th e group s tu d ie d, were graduated from Kansas high sch o o ls. The m ajor p o r tio n, 52.3 p e rc e n t, g rad u ated from high sch o o ls lo c a te d in towns whose p o p u la tio n was 2,000 or l e s s. The secondary m athem atics s u b je c t m ost fre q u e n tly ta u g h t was f i r s t y ear a lg e b ra w ith 692, or 66.7 p e rc e n t of th e te a c h e rs te a c h in g a t l e a s t one c la s s of th e s u b je c t d a ily. In second p la c e as th e most fre q u e n tly ta u g h t course was P lane Geometry. A pproxim ately 44.5 p e rc e n t, o r 461 te a c h e rs ta u g h t a t l e a s t one course o f th e s u b je c t d a i ly. A la rg e number of th e secondary te a c h e rs o f m athem atics in Kansas were 35 y ears old or l e s s. T his group was composed of 415 te a c h e r s, which re p re se n te d 40 p e rc e n t o f th e t o t a l. T his f a c t was a ls o of s ig n ific a n c e when i t was noted th a t 51.7 p e rc e n t of th e te a c h e rs had te n y e a rs o r le s s o f ex p erien ce and th a t 66.1 p e rc e n t had been in t h e i r p re s e n t sch o o l system s f iv e y ears o r l e s s. The
number o f m athem atics s u b je c ts ta u g h t was one o f th e c r i t e r i a s tu d ie d. The fin d in g s re v e a le d th a t 31.4 p e rc e n t o f th e te a c h e rs ta u g h t only a s in g le s u b je c t in m athem atics, and approxim ately tw o -th ird s o f th e se ta u g h t only a s in g le s e c tio n o f th e s u b je c t, th e rem ainder o f t h e i r sch ed u le being in o th e r f i e l d s. Two m athem atics s u b je c ts w ere ta u g h t by 38.2 p e rc e n t o f th e te a c h e rs, w h ile 20.6 p e rc e n t ta u g h t th re e m athem atics co u rses d a ily. The rem aining 9.7 p e rc e n t ta u g h t fo u r o r more m athem atics s u b je c ts d a i ly. A pproxim ately 27.2 p e rc e n t o f th e secondary m athem atics te a c h e rs in Kansas re c e iv e d t h e i r b a c c a la u re a te d eg rees from o u t - o f - s t a t e i n s t i t u t i o n s. A high p e rc e n ta g e, 4 5.9, o f th e se te a c h e rs te a c h in g secondary m athem a tics had earned t h e i r degrees in th e te n -y e a r p e rio d im m ediately p rev io u s to th e stu d y. The study re v e a le d th a t m a s te r 's degrees were q u ite fre q u e n tly h e ld. They were p o ssess by 39.5 p e rc e n t o f th e group. The m ajor p o rtio n, 55.1 p erce n t o f th e s e w ere earned in th e te n -y e a r p e rio d p reced in g th e stu d y. Of th e perso n s engaged in th e te a c h in g o f secondary m ath em atics, 32.7 p e rc e n t had earned m athem atics m a jo rs. Of th e m athem atics te a c h e rs who had earned m a s te r 's d eg re e s, 69.4 p e rc e n t had earned degrees in ed u ca tio n w h ile 12.5 p e rc e n t had earned degrees in m ath em atics. The number o f sem ester hours earned i n m athem atics r e f l e c t e d th a t th e re was s t i l l a sm all number, le s s th an 3 p e rc e n t, o f te a c h e rs te a c h in g m athem atics who had re c e iv e d no c o lle g e m athem atics t r a i n in g. In excess o f 40 p e rc e n t o f th e te a c h e rs had earned more th a n 24 hours o f c r e d i t in c o lle g e m ath em atics. About 31 p e rc e n t o f th e
te a c h e rs had earned between 1 and 14 sem ester h o u rs, w hile th e rem ainder, approxim ately 26 p e rc e n t, showed between 15 and 24 hours of m athem atical s tu d ie s. S ixty-tw o p e rc e n t o f th e m athem atics te a c h e rs tau g h t some s u b je c ts in f i e l d s o th e r than m athem atics. T w enty-three p e rce n t tau g h t on ly a s in g le c la s s in m athem atics. W alter E. Regula (1965) made a study of th e p re p a ra tio n of th e m athem atics te a c h e rs in th e p u b lic secondary sch o o ls of West V irg in ia. The purpose of h is study was to d e sc rib e th e c u rre n t s itu a tio n in th e se sch o o ls w ith re s p e c t to c e r t a in f a c to r s r e la te d to th e academic p re p a ra tio n and to th e te a c h in g assignm ents o f m athem atics te a c h e rs. In t h i s survey of 75.9 p e rc e n t of a l l m athem atics te a c h e rs in 1963-1964, u sin g 18 hours as th e minimum requirem ent fo r adequate m athem atics p re p a ra tio n, he found th a t 31.7 p e rc e n t had in ad eq u ate p re p a ra tio n ; 8.8 p e rce n t had no c r e d it in c o lle g e - le v e l m athem atics. The median p re p a ra tio n was 22 sem ester h o u rs. Only 25.9 p e rc e n t had 30 hours o r more. M a s te r's d eg rees were held by 34 p e rc e n t of th e se te a c h e rs, w ith 4.2 p e rc e n t h o ld in g m a s te r s degrees in m athem atics. R e g u la 's recom mendations were: 1. Reduce th e number of in a d e q u a te ly prepared m athem atics te a c h e rs. 2. Urge a d m in is tra to rs to study a v a i l a b i l i t y of q u a lif ie d te a c h e rs and r e - a s s ig n. 3. I n s t i t u t e g rad u ate programs in m athem atics and m athem atics ed u catio n designed to meet th e needs of th e se te a c h e r s.
l b 4. Improve competence through in - s e r v ic e tr a in in g a t s t a t e and lo c a l le v e ls. 5. Encourage te a c h e rs to p re p are them selves to use new c u r r ic u la m a te r ia ls. 6. S tren g th en c e r t i f i c a t i o n req u ire m en ts. Smith (1966) c o n c e n tra te d on th e d u tie s and p e rso n a l c h a r a c te r i s t ic s of m athem atics te a c h e rs, t h e i r academ ic background, and th e p re s e n t hig h sch o o l cu rric u lu m in I l l i n o i s. He se n t q u e s tio n n a ire s to o n e -h a lf of th e hig h school te a c h e rs in th a t s t a t e. The academ ic p re p a ra tio n of th e te a c h e rs was checked fo r v a l i d i t y a t th e o f f ic e o f te a c h e r c e r t i f i c a t i o n. His fin d in g s were as fo llo w s: The m athem atics te a c h e rs in sm all high sch o o ls sp en t more tim e in th e classroom and re c e iv e d le s s pay than th o se in la r g e r s c h o o ls. More b eg in nin g te a c h e rs were in th e sm all sch o o ls th an in th e la rg e ones. O ne-fourth of th e se te a c h e rs in sm all sch o o ls sp en t more time on e x tra c u r r ic u la a c t i v i t i e s than th e i r c o u n te rp a rts in la rg e sch o o ls. O ne-half had academ ic p re p a ra tio n as recommended by th e Committee on th e U ndergraduate Program in M athem atics. O n e-th ird had a tte n d e d a t l e a s t one N a tio n a l Science Foundation I n s t i t u t e. F o rty p e rc e n t of th e c la s s e s were judged modern. Programmed in s tr u c tio n was used in only 43 p e rc e n t of th e sc h o o ls. The g e n e ra l sequence of m athem atics co u rses was: A lgebra I, Geometry, A lgebra-t rigonom etry, and A n aly sis. Dye (1966) re p o rte d on m athem atics e d u ca tio n in the schools in the s t a t e of M innesota, b asin g th e study on th e
1965-1966 school y e a r. The stu d y in c lu d e d a t o t a l o f 1,096 te a c h e r s, o f w hich 988 w ere from independent school d i s t r i c t s, te n from s p e c ia l d i s t r i c t s ; and 98 w ere te a c h in g in a c a teg o ry named u norganized d i s t r i c t s. One to p ic in th e study was th e a tte n d a n c e o f secondary te a c h e rs a t summer o r academic y e a r i n s t i t u t e s. One hundred n in e ty - f o u r te a c h e rs a tte n d e d a summer i n s t i t u t e durin g th e two summers p r i o r to th e stu d y, w h ile 27 te a c h e rs had a tte n d e d academic y e a r i n s t i t u t e s durin g th a t p e rio d. A n aly sis o f th e p re p a ra tio n a l s ta tu s of- th e p a r ti c ip a n ts in th e stu d y r e f le c te d th a t 811 te a c h e rs had u n d erg rad u ate m ajors in m ath em atics, 210 had u n d erg rad u ate m in o rs, and 75 had n e i th e r m ajor nor m inor in m athem atics. The ty p e s o f degrees earned by M innesota m athem atics te a c h e rs showed th a t 774, o r 71 p e rc e n t, h eld b a c c a la u re a te d e g re e s, w hile 269, o r 24 p e rc e n t, h eld m a s te r 's d e g re e s, w ith 53 te a c h e rs, o r 5 p e rc e n t c la s s e d i n th e c a te g o ry as " o th e r." E a s te rly (1967), on th e b a s is o f a q u e s tio n n a ire u t i l i z e d in th e study o f te a c h e rs o f Alabama, found th a t 24 p e rc e n t o f th e secondary m ethem atics te a c h e rs were m ale, w h ile 69 p e rc e n t w ere fem ale. The rem ainder f a ile d to in d ic a te t h e i r sex when r e tu rn in g th e q u e s tio n n a ire. The m ajor p o r tio n, 62.5 p e rc e n t, o f th e secondary te a c h e rs o f m athem atics h e ld a C lass B, o r fo u r-y e a r c e r t i f i c a t e ; ap p ro x im ately 26.9 p e rc e n t h e ld a C lass A o r f iv e -y e a r c e r t i f i c a t e. C e r t i f i c a t i o n o f th e rem aining te a c h e rs was in c a te g o rie s l i s t e d as a d m in is tra tiv e c e r t i f i c a t e s, guidance c e r t i f i c a t e s, s p e c ia l e d u ca tio n c e r t i f i c a t e s, and emergency
c e r t i f i c a t e s. The m ajor p o rtio n o f th e se w ere emergency c e r t i f i c a t e s, numbering 7.5 p e rc e n t o f th e t o t a l secondary m athem atics te a c h e r s. The average number o f y ears o f te a c h in g m athem atics was re p o rte d as 7.1 y e a r s 9 and th e median number o f y e a rs in th e p re s e n t p o s itio n was 3.4 y e a rs. The m edian fo r th e fem ale te a c h e rs in th e same p o s itio n exceeded th e m edian o f th e male te a c h e rs by 1.3 y e a rs, th e range being 3.8 fo r fem ale to 2.5 y ears fo r m ale. An e f f o r t was made to determ ine w h ether th e co u rses in th e secondary m athem atics c u rric u lu m w ere being ta u g h t by q u a lif ie d p erso n s, th a t i s, th o se having m ajors o r m inor in m athem atics. The follow ing fin d in g s w ere n o ted : 81.4 p e rc e n t o f G eneral M athem atics te a c h e rs met th e c r i t e r i o n ; 82.3 p e rc e n t o f th o se teach in g Shop o r B usiness A rith m e tic were m ajors o r m inors; 85 p e rc e n t who ta u g h t b eg in n in g A lg e b ra, 92.5 p e rc e n t o f th e A lgebra, second c o u rse ; 87.6 p e rc e n t o f th e Geometry te a c h e rs, and 95.4 p e rc e n t o f th e Advanced M athem atics te a c h e rs w ere in th e m ajor- m inor c a te g o ry. I n v e s tig a tio n o f th e m ajor-m inor com binations o f secondary m athem atics te a c h e rs showed th a t about o n e -s ix th o f th o se re p o rtin g had a n o th e r m ajor in a d d itio n to m athem atics. The le a d in g a re a in th e double m ajor was s o c ia l sc ie n c e, follow ed in o rd e r by s c ie n c e, E n g lish, fo re ig n language, and b u sin e ss e d u c a tio n. The m inors earned by th o se te a c h e rs w ith m athem atics m ajors w ere in th e fo llo w in g o rd e r o f frequency: E n g lish, s o c ia l s tu d ie s, p h y s ic a l s c ie n c e, n a tu ra l sc ie n c e, b io lo g ic a l sc ie n c e, p h y sic a l e d u c a tio n, and b u sin ess e d u c a tio n. The m athem atics te a c h e rs who w ere te a c h in g w ith m inors in
m athem atics u s u a lly m ajored in th e b io lo g ic a l s c ie n c e s. O ther a r e a s, in th e o rd e r o f t h e i r o ccu rren c e were p h y s ic a l s c ie n c e, s o c ia l s tu d ie s, E n g lish, elem entary e d u c a tio n, b u sin e ss e d u c a tio n, and n a tu r a l sc ie n c e. N a tio n a l S cience Foundation I n s t i t u t e s had been a tte n d e d by 39.8 p e rc e n t o f th e te a c h e rs who ta u g h t secondary m athem atics. A la rg e p o rtio n o f th e se had a tte n d e d a t l e a s t one i n s t i t u t e s in c e 1962. T w o-thirds o f th o se who a tte n d e d i n s t i t u t e s a tte n d e d th o se h e ld a t an Alabama c o lle g e o r u n iv e r s i ty. T eachers who ta u g h t o th e r s u b je c ts in a d d itio n to m athem atics named p h y s ic a l sicen ces as th e s u b je c ts most fre q u e n tly ta u g h t. G eneral sc ie n c e and p h y s ic a l ed u ca tio n were a ls o ranked high in th e t o t a l l i s t o f 15 a re a s. About 65 p e rc e n t o f th e m athem atics te a c h e rs h eld b a c c a la u re a te d eg rees; 23 p e rc e n t had m a s te r 's d e g re e s. Of th e rem aining 12 p e rc e n t, 3 p e rc e n t were re p o rte d as having no d eg ree. A pproxim ately 25 p e rc e n t o f th e secondary te a c h e rs in d ic a te d th a t they had earned c r e d i t i n co u rses e q u iv a le n t to th o se l i s t e d in th e le v e l th re e recommendations o f th e Committee on th e U ndergraduate Programs in M athem atics. S tu d ie s o f th e Secondary M athem atics C urriculum Alspaugh (1970) chose a sample o f 50 randomly s e le c te d p u b lic secondary schools in M isso u ri and a sample o f 50 m athem atics te a c h e rs. The sample o f 50 m athem atics te a c h e rs c o n s is te d o f one randomly s e le c te d from each o f th e secondary schools in th e sam ple. The data w ere c o lle c te d by in te rv ie w in g each te a c h e r in th e sam ple, and by in te rv ie w in g a te a c h e r o f each