Utah State University DigitalCommons@USU All Graduate Theses and Dissertations Graduate Studies 5-1967 A Suggested Mathematics Curriculum for Preparation of Teachers of Modern Secondary School Mathematics in Utah Harold Nolan Philips Utah State University Follow this and additional works at: https://digitalcommons.usu.edu/etd Part of the Education Commons Recommended Citation Philips, Harold Nolan, "A Suggested Mathematics Curriculum for Preparation of Teachers of Modern Secondary School Mathematics in Utah" (1967). All Graduate Theses and Dissertations. 2976. https://digitalcommons.usu.edu/etd/2976 This Thesis is brought to you for free and open access by the Graduate Studies at DigitalCommons@USU. It has been accepted for inclusion in All Graduate Theses and Dissertations by an authorized administrator of DigitalCommons@USU. For more information, please contact [email protected]. A SUGGESTED MATHEMAT; cs CURR ULUM FOR PREPARATION OF TEA HERS OF MODERN Sl:. 0 DAR Y SCHOOL MATHEMATICS .iN UTAH by Harold No) H Phi 1 s A th S I S submiLt<. d in par tial fulfillm nt of the requn < ments for th degree of MASTER OF ARTS in Secondary School Teaching UTAH STATE UNIVERSITY Logan, Utah 1967 ACKNOWLEDGM NTS The writer 'W i~ h F. s to exp r t>bs his appr ciation to his major professor, Robert U. Hammond , for the suggestwns and assistance offered in the creation of this study, and to the othe.r me mb rs of the committee: Dr. Eldon M. Drake and Professor G. Leon Beutler . Appr ciation is alo;o expressrd to the writer's wife, Bonnie W. Phillips, for her pati nt assistanc and advice. ~ Harold Nolan Phillips ii TABLE OF CONTENTS P age INTRODUCTION AND PROBLEM STATEMENT 1 OBJECTIVES 3 Definition ..... 3 REVIEW OF LITERATURE 4 Striving for Excellence and Change . 4 Reasons for Change . • . 5 Cambridge Conference Report on School Ma thematics 9 Comments on the Cambridge Conference Report . 14 Implications . 17 New appr oach 17 New materials 19 New termini:>logy 19 Ne w Demands for Teache r Preparation 21 New Mathematics Teacher Education Programs 25 Evaluation of Proposed Curriculum Programs . 31 Recent Educational Research (Three Doc toral Dissertations). 36 METHOD 39 RESULTS 41 CONCLUSIONS AND SUMMARY 58 Evaluation of Results 58 Proposed Program . 62 LITERATURE CITED 66 APPENDIX 69 VITA 76 iii LIST OF TA BLE S Table Page 1. Per cent of institutio n ~ r -qu.r ing ma th ematics courses of prospective te achers majonng in ma the matics in selected years ...•. .. ... ..... ......... .. 6 2. P e rcent of teacber- Pdurah on In stitutions offering mathematics courses in sPl cted years 7 3. Recommended mathematJcR programs fo r secondary school te achers ........ •..•... .. ... • 32 4 . The value of courses 1n teaching s econd ary mathe matics by all te achers ..... ..•. ... .. .. 42 5. Th e five most valuable courses in teaching s condary school math maticR by all teachers . •. .. 43 6. Courses recommended as leaching major requirements by all teachers . .. .. .. .. ..•...... 44 7. The value of courses 10 teaching secondary school mathe matics by teachers who have a ma the matics teaching major or minor or a science-mathematics composite and who have taught modern mathematics 45 8. The five most valuable cou·rses in teaching secondary school mathematics by te achers who hav a mathematics major or minor , or a mathe matics-sci nee composite 46 9 . Courses recommended as teaching major requirements by teachers who have a mathe matics eaching major or minor, or a mathematics-science composite . .. .. 47 10. The value of courses in teaching secondary school mathe matics by teach rs who do not have mathematics majors or minors or who have not taught modern mathe matics .........•....•••. .. .. ... 48 iv LIST OF TABLES CONTINUED Table Page 11. The five most valuable courses in teaching secondary school mathematics by teachers who do not have mathe matics majors or minors or hav not "taught modern mathemati s .... .... .... ... 49 12. Courses r ecommended as teaching major requirements by teachers who do not have a mathemati cs major or minor or who have not taught modern mathe matics 50 13. Rank order of cours s according to their value in teaching secondary school mathematics 54 14. Rank order of cou ses considered to be in the five most valuable courses in teaching secondary school mathematics 55 15. Rank order of courses recommended for a teaching major in secondary school math ma tics ..... 56 v ABBRE\1ATlONS OF ORGANIZATIONS AAAS Ame ncan Association for the Advance me nt of Science AACTE Amencan Association of Collt>ges for Teacher Education BSCS Biological Sci.:; nce Curriculum Study CBA Chemical Bond Approach Project CCTSM Cooperab.ve Commit[ e on th e Teaching of Science and Mathe matics Chern Study Ch mical Education Mat rials Study CUPM Committee on the Undergraduate Program in Mathematics MAA Mathe matical Associallon of America NCTM National Coun il of Teachers of Mathematics NSF National Sci nc Foundation PSSC Physical Scitnl Study Committee SMSG School Matht' mah s Study Group UEA Utah Educational Assoc tatwn UICSM Uniwrsity of Jllmois Committee on School Mathematics UMMaP University of Maryla nd Mathematics Proj c t VI ABSTRACT A Sugg!'sted Mathemattcs Currtculum for Preparation of Teachers of ModHn Secondary School Ma the matics tn Utah by Harold Nolan P ht lhps, Master of Arts U tah Stai \Jmvel'stty , 1967 Major Professor: Rob r t G. Ha mmond Department: Secondary Education " New math" has drastically changed secondary mathematics and the demands on th e secondary ma thematics teacher. The changes and e ffects of changes w re studied with e mphas1s on suggested programs in teacher prepa~ · ration. Questionnaires were given to one hundred four secondary mathematics teachers in Utah. Fifty-e ight w rt: returned, of which fifty we re usable. The questionnaire contained twe nty-six mathe matics courses offered to mathematics education majors in Utah universities. The teachers indicated which courses were valuable to th e m in teaching secondary school mathematics. Rank order correlation coefficients were calculated among subgroups of the questionnaire to determine internal consis t ncy. All coeffi cients were above the 1 per cent significance level. The first fifteen courses listed in rank order according to vii the percentage of teachers who fe lt e ach course was valuable are: college algebra, trigonometry, analytic geometry, differ ential cal culus, modern algebra, metltods for secondary mathematics teachers, mathe matics for s econdary school teachers, foundations of mathe matics, integral calculus, number theory, history of matlte­ matics, foundations of geometry, solid geo metry, logic, and foundations of algebra. On the basis of the courses generally recommended for prospective modern matltema tics teachers by nationally interested groups and the r e sults of the evaluations of courses by Utah mathematics teachers, the following program in mathematics was proposed for prospective matltematics teachers in Utah. Mathematics education majors should take: College Algebra (or equivalent) Trigonomentry (or equivalent) Analytic Geometry Differe ntial Calculus Abstract Algebra (at least one course) College Geometry (a t least one course other than Analytic Geometry) Mathematics for Secondary School Te achers Methods course (may be taken under the Department of Education) After completing tltis basic program , teachers intending to teach grades seven, eight, or nine s hould choose three or more courses from tlte following: viii Foundations of Mathematics Additional courses in Abstract Algebra Additional courses in College Geometry (other than Analytic Geometry) Number Theory Logic History of Mathematics Probability and Statistics A teacher intending io teach grades ten, eleven, or twelve should complete integral calculus and choose three or more courses from the following: Foundations of Mathematics Additional courses in Abstract Algebra Additional courses in College eometry (other than Analytic Geometry) Number Theory Logic History of Math matics Probability and Statistics Additional Calculus courses (85 pages) ix INTRODUC T ON AND PROBLEM STATEMENT The past decade ( 1957-1967) has ushered in what many educators feel is th e largest seal education revo ution in th history of United Stated edu­ cation. Beginning with the adoption of "ne w math" in public schools, many new programs were initiated m other fields. Some programs, such as the Chemical Education Materials Study (Chern Study), Chemical Bond Approach Project (CBA), Physical Science Study Commtttee (PSSC), and th e Biological Science Curriculum Study (BS S), have changed pr1 marily the approach to the subject matter, while others, such as the new math and n w E nglish programs, have changed or added much newt rminology as well as changing the approach and structure. This study will b concerned with the n w mathematics program and the secondary school mathe matics teacher in the stat of Utah. The changes in th n w mathematics curriculum are so extensive in both new vocabulary and conte nt stT ucture that they place new and very different demands on classr oom teach r s . As th e initial presenta ti on of material to the students in the classroom is of great im,orlance to the ir motivation, understanding, and con­ cept formation , it is of gre at importanc that th e teach r be well prepared to function prope rly in hts role. The success of the new mathematics is highly dependent upon the skill and abtlity of th e teacher to present the program to the students in the spirit in which the p ogram was created and structured (Adler, 2 1966). For this r ason, most of the study groups responsible for the new programs in mathematics hav suggested a r vised university curriculum which they hope wi ll allow the te ache r to attain a preparation specifically adapted to th functioning of th ir program in the secondary school classroom.