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IR H...” “I! ”"1! {I .I‘IIII ' .11”;wa . , III I IISIII II.“ III “III “1‘13Rflfil‘l‘hhnf' :"II“(. '1, ”I,” IN I It IWII I I II‘,':II‘:'II‘I ' I' . I‘ III'II II IIII'I’ III IIIIHIUIHIIIIIlllllllllHllllllIllllillllllillHlllHllllM 3 1293 10422 8931 THESIS This is to certify that the thesis entitled AN EVALUATION OF THE MATHEMATICS CURRICULUM GIVEN AT THE COLLEGE OF EDUCATION, MECCA, FROM THE PERSPECTIVE OF THE TEACHERS WHO GRADUATED FROM THE COLLEGE IN THE YEARS 1976-1980 presented by Abdulwahab Ahmad Zafar has been accepted towards fulfillment of the requirements for Ph.D. Department of Adminis- deyeemTW—on and Curriculum Major: Curr1cu1um and Instruction 454W .1 Major professor Date February 12, 1982 0-7639 MSU LIBRARIES RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES wiII be charged if book is returned after the date stamped beiow. Cave-c 31/ j x?“ 3’9an AN EVALUATION OF THE MATHEMATICS CURRICULUM GIVEN AT THE COLLEGE OF EDUCATION, MECCA, FROM THE PERSPECTIVE OF THE TEACHERS WHO GRADUATED FROM THE COLLEGE IN THE YEARS 1976-1980 By Abdulwahab Ahmad Zafar A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Administration and Curriculum Major: Curriculum and Instruction 1982 ABSTRACT AN EVALUATION OF THE MATHEMATICS CURRICULUM GIVEN AT THE COLLEGE OF EDUCATION, MECCA, FROM THE PERSPECTIVE OF THE TEACHERS WHO GRADUATED FROM THE COLLEGE IN THE YEARS 1976-1980 By Abdulwahab Ahmad Zafar This study evaluates the mathematics curriculum of the College of Education, Mecca, Saudi Arabia, from the perspective of the mathe- matics teachers who have already graduated from the College. This is the first study of this nature ever conducted regarding an important specialty program. This study was able to enlist the participation of the entire Saudi graduate teachers who graduated from the College between 1976 and 1980 as teachers of mathematics in intermediate and high-school systems of Saudi Arabia. Design and Methodology The following procedure was used to conduct the study: 1. A questionnaire was administered to the entire group of Saudi teachers who had graduated from the College of Education with mathematics as their teaching specialty between the years 1976 and 1980. 2. Through factor analysis, the following twelve dimensions characterizing the mathematics program were developed: Understanding the Objectives of Teaching Mathematics, Understanding Basic Mathematics Abdulwahab Ahmad Zafar to Teach Mathematics, Preparation for Higher Mathematics, College-School Relations, Emphasis on Practical Problems, Preparation for School Teaching, Methods of Teaching Mathematics, Student Teaching, Educa— tional Thought, Curriculum Design, Educational Psychology, and Problems of Teaching Mathematics. 3. With analysis of covariance, eight hypotheses were tested regarding these twelve dimensions. Conclusions 0n the basis of the results, it may be affirmed: 1. A poor relationship between the courses in mathematics at the College of Education, Mecca, and curricula in mathematics for intermediate and high schools of Saudi Arabia. 2. A very positive relationship between the College program of teaching methodology for mathematics and the graduate teachers' effec- tiveness as teachers of mathematics. 3. Student teaching being a very effective program of the Mecca College of Education. 4. The mathematics curriculum of the College having helped the graduate teachers in a positive manner to teach mathematics at inter- mediate and high schools in Saudi Arabia. 5. The adequacy of education courses as having a positive effect on the teaching ability of the teachers. 6. The mathematics curriculum's failure to give adequate empha- sis to practical problem—solving aspects of mathematics in the mathe- matics program of the College. Abdulwahab Ahmad Zafar 7. The mathematics curriculum's failure to provide for inno- vations and experimentation in the teaching of mathematics. 8. The mathematics curriculum's failure to prepare teachers of mathematics adequately in the techniques of evaluating and grading. 9. A lack of adequate in-service programs and seminars for the College's past graduates. an H}; name 0/04[[a/I this most mztcifufand t5; most [ism/aunt Copyright by ABDULWAHAB AHMAD ZAFAR 1982 ACKNOWLEDGMENTS This dissertation is the outcome of the moral support, intel- lectual encouragement, concern, and prayers and devotion of all those who were intimately connected with this work and this investigator. This work would not have attained the measure of academic excellence that has been accorded to it without the direction, painstaking guid- ance, and encouragement of the Dissertation Committee, comprised of Drs. Ben Bohnhorst, John Lopis, Richard Gardner, and Howard Hickey. I am deeply indebted to each member of the Committee individually for their ever-readiness to discuss and comment on the issues that arose during the preparation of this dissertation, despite their heavy schedules of engagement. It is well-nigh impossible for me to find words to match my deeply felt gratitude to Dr. Ben Bohnhorst, the director of this dissertation, for the enormous amount of time he spent on various aspects of this work in guiding me at every stage of prepa— ration of this work, and to Dr. John Lopis, who guided and directed work on this dissertation in the initial stages of development. Dr. Lopis' loss to me and this work, because of his decision to move from Michigan State University, would have been too much to bear, had it not been for Dr. Bohnhorst's filling in with his direction. I would be remiss in my duty if I were not to acknowledge the help and cooperation I received from the Registrar's Office of 11 Umm Al-Qura University, Mecca, the Ministry of Education, the General Presidency of Schools for Girls, and the General Directorate of Educa- tion, Western Division, Saudi Arabia, for their timely and ready assistance in contacting the respondents and collecting the data. Completion of this work in record time is a living testimony to the help and cooperation not only of these official bodies, but, above all, also to the participating graduates who took time out of their heavy engagements to respond to the questionnaire with thought and understanding. Encouragement of my brothers and sisters, patience of my wife, Sana, and even the sacrifice of my children, Rahaf and Bassam, who willingly forewent their precious moments of fun and frolic in consid- eration of my need for quiet and peace, have always been a source of inspiration for me all through the writing of this dissertation. My parents (May their souls rest in peace!) have always been a source of strength for me. Their strict discipline and guidance are reflected in the effort that I have been able to generate in the pres- ent undertaking. Blessed are those who have had the fortune of having such parents! I hope I have met my obligation and gratitude to them as laid down by God in the Holy Qur'an: menace 1'! ‘5 :64 3.191834%} And lower unto them the wing of submission through mercy, and say: My Lord! Have mercy on them both as they did care for me when I was little! The Glorious Qur'an, Surah XVII, 24 TABLE OF CONTENTS Page LIST OF TABLES ........................ vi Chapter I. INTRODUCTION ..................... 1 Aims of the Study .................. 3 Need for the Study ................. 5 Purposes of the Study ................ 5 Research Questions ................. 6 Study Hypotheses .................. 7 Limitations of the Study .............. 8 Procedure and Organization of the Study ....... 9 II. EDUCATION IN SAUDI ARABIA ............... 11 III. REVIEW OF THE LITERATURE ............... 27 IV. PROCEDURE AND METHODOLOGY ............... 45 Research Questions ................. 45 Research Hypotheses ................. 46 Population of the Study ............... 48 The Survey Instrument ................ 50 Validity of the Research Instrument ......... 52 Reliability of the Research Instrument ....... 53 Data Collection ................... 55 Male Graduate Teachers .............. 55 Female Graduate Teachers ............. 55 Graduates Studying Abroad ............. 56 Data Analysis .................... 56 Summary ....................... 57 V. ANALYSIS AND INTERPRETATION OF THE DATA ........ 58 Tabulation and Analysis of the Survey Results . . . . 60 Personal Background ................ 61 Academic Performance ............... 62 Working Situation ................. 62 Education Curriculum ............... 63 Mathematics Curriculum .............. 63 iv College-School Relationships ........... 64 Open-Ended Responses ............... 65 Exploratory Factor Analysis and Reliability ..... 67 Testing of Hypotheses ................ 76 Analysis of Variance ............... 77 Summary of the Results ............... 84 VI. CONCLUSIONS AND SUGGESTIONS .............. 88 Suggestions ..................... 97 APPENDICES .......................... 101 A. ARABIC AND ENGLISH VERSIONS OF THE COVER LETTER AND QUESTIONNAIRE .................. 102 B. FREQUENCIES ...................... 123 C. EXPLORATORY FACTOR ANALYSIS .............. 141 D. RELIABILITY ANALYSES OF SCALES ............ 154 E. ANALYSIS OF VARIANCE ................. 172 BIBLIOGRAPHY ......................... 233 Table B-1.1. B-1.2. B-1.3. B-2. B-4. C-1. C-2. C-4. D-1. D-2. LIST OF TABLES Mathematics Graduates of Mecca College of Education, 1976 Through 1980 ................... Subscales, Clusters, and Coefficients of Reliability . . . Enrollment of Males and Females in Mathematics Department of Mecca College of Education, 1975-76 Through 1979-80 . Means and Standard Deviations of the 12 Dimensions . . . . Pearson Correlations Between 12 Scales Developed From Factor Analysis (N = 116) ............... Overview of Results of Testing the Hypotheses ...... Personal Background ................... Academic Performance ................... Working Situation .................... Education Curriculum ................... Mathematics Curriculum .................. College-School Relations ................. Means and Standard Deviations of Variables Entering the Factor Analysis .................. Correlation Coefficients ................. Factor Matrix Using Principal Factor With Iterations . . . Varimax Rotated Factor Matrix After Rotation With Kaiser Normalization .................. Reliability Analysis for Scale: Dimension l--Understanding the Objectives of Teaching Mathematics ......... Reliability Analysis for Scale: Dimension 2--Understanding Basic Mathematics to Teach Mathematics ......... Vi Page 49 54 61 74 75 78 124 125 126 127 131 137 142 144 150 152 155 157 D-3. D-4. D-6. D-7. D-8. D-9. D-11. D-12. D-13. D-14. D-15. E-1. E-2. E-3. Reliability Analysis for Scale: tion for Higher Mathematics Reliability Analysis for Scale: Dimension Dimension 3--Prepara- 4--College- School Relations .................... Reliability Analysis for Scale: on Practical Problems Reliability Analysis for Scale: Dimension Dimension 5--Emphasis 6--Prepara- tion for School Teaching ................ Reliability Analysis for Scale: Dimension 8--Student Teaching ........................ Reliability Analysis for Scale: Thought Reliability Analysis for Scale: Curriculum Design . Reliability Analysis for Scale: Dimension Dimension 9--Educational 11-- Educational Psychology ................. Reliability Analysis for Scale: Reliability Analysis for Scale: of Teaching Mathematics Reliability Analysis for Scale: Reliability Analysis for Scale: Reliability Analysis for Scale: Factor 13 Dimension Factor 15 Factor 16 Factor 17 Analysis of Variance of Dimension l--Understand the Objectives of Teaching Mathematics--By Sex and Graduated With 40 or 60 Credits Analysis of Variance of Dimension l--Understand the Objectives of Teaching Mathematics—-By Sex and Teaching at Which Level Analysis of Variance of Dimension l--Understand the Objectives of Teaching Mathematics--By Sex and Percent of Mathematics Teaching Duty .......... vii 160 162 163 175 E-4. E-6. E-8. E-10. E-14. E-16. Analysis of Variance of Dimension l--Understand the Objectives of Teaching Mathematics--By Year Graduated From Mecca College of Education (Male Teachers) Analysis of Variance of Dimension l--Understand the Objectives of Teaching Mathematics-—By Year Graduated From Mecca College of Education (Female Teachers) Analysis of Variance of Dimension 2--Understand Basic Math to Teach Mathematics--By Sex and Graduated With 40 or 60 Credits ................. Analysis of Variance of Dimension 2--Understand Basic Math to Teach Mathematics--By Sex and Teaching at Which Level ..................... Analysis of Variance of Dimension 2--Understand Basic Math to Teach Mathematics--By Sex and Percent of Mathematics Teaching Duty ............... Analysis of Variance of Dimension 2--Understand Basic Math to Teach Mathematics--By Year Graduated From Mecca College of Education (Male Teachers) ....... Analysis of Variance of Dimension 2--Understand Basic Math to Teach Mathematics--By Year Graduated From Mecca College of Education (Female Teachers) ...... . Analysis of Variance of Dimension 3--Preparation for Higher Mathematics--By Sex and Graduated With 40 or 60 Credits ..................... . Analysis of Variance of Dimension 3--Preparation for Higher Mathematics--By Sex and Teaching at Which Level . . Analysis of Variance of Dimension 3--Preparation for Higher Mathematics--By Sex and Percent of Mathematics Teaching Duty ..................... Analysis of Variance of Dimension 3—-Preparation for Higher Mathematics--By Year Graduated From Mecca College of Education (Male Teachers) .......... . Analysis of Variance of Dimension 3--Preparation for Higher Mathematics-~By Year Graduated From Mecca College of Education (Female Teachers) ......... Analysis of Variance of Dimension 4--College-School Relations--By Sex and Graduated With 40 or 60 Credits viii Page 176 177 178 179 180 181 182 183 184 185 186 187 188 E-17. Analysis of Variance of Dimension 4--College-School Relations--By Sex and Teaching at Which Level ..... 189 E-18. Analysis of Variance of Dimension 4--College-School Relations--By Sex and Percent of Mathematics Teaching Duty ..................... 190 E-19. Analysis of Variance of Dimension 4--College-School Relations—~By Year Graduated From Mecca College of Education (Male Teachers) ............... 191 E-20. Analysis of Variance of Dimension 4--College-School Relations--By Year Graduated From Mecca College of Education (Female Teachers) .............. 192 E-Zl. Analysis of Variance of Dimension 5--Emphasis on Practical Problems--By Sex and Graduated With 40 or 60 Credits ..................... 193 E-22. Analysis of Variance of Dimension 5--Emphasis on Practical Problems--By Sex and Teaching at Which Level . 194 E-23. Analysis of Variance of Dimension 5--Emphasis on Practical Problems--By Sex and Percent of Mathematics Teaching Duty ..................... 195 E—24. Analysis of Variance of Dimension 5--Emphasis on Practical Problems--By Year Graduated From Mecca College of Education (Male Teachers) .......... 196 E-25. Analysis of Variance of Dimension 5--Emphasis on Practical Problems--By Year Graduated From Mecca College of Education (Female Teachers) ......... 197 E-26. Analysis of Variance of Dimension 6--Preparation for School Teaching--By Sex and Graduated With 40 or 60 Credits ....................... 198 E-27. Analysis of Variance of Dimension 6--Preparation for School Teaching--By Sex and Teaching at Which Level . . 199 E-28. Analysis of Variance of Dimension 6-—Preparation for School Teaching--By Sex and Percent of Mathematics Teaching Duty ..................... 200 E-29. Analysis of Variance of Dimension 6--Preparation for School Teaching-—By Year Graduated From Mecca College of Education (Male Teachers) .......... 201 ix E-30. E-31. E-32. E-33. E-34. E-35. E-36. E-37. E-38. E-39. E-40. E-41. E-42. E-43. Analysis of Variance of Dimension 6--Preparation for School Teaching--by Year Graduated From Mecca College of Education (Female Teachers) ......... Analysis of Variance of Dimension 7--Method of Teaching Mathematics-~By Sex and Graduated With 40 or 60 Credits ........................ Analysis of Variance of Dimension 7--Method of Teaching Mathematics--By Sex and Teaching at Which Level Analysis of Variance of Dimension 7--Method of Teaching Mathematics--By Sex and Percent of Mathematics Teaching Duty ..................... Analysis of Variance of Dimension 7--Method of Teaching Mathematics--By Year Graduated From Mecca College of Education (Male Teachers) ............... Analysis of Variance of Dimension 7--Method of Teaching Mathematics--By Year Graduated From Mecca College of Education (Female Teachers) .............. Analysis of Variance of Dimension 8--Student Teaching-- By Sex and Graduated With 40 or 60 Credits ....... Analysis of Variance of Dimension 8--Student Teaching-- By Sex and Teaching at Which Level ........... Analysis of Variance of Dimension 8--Student Teaching-- By Sex and Percent of Mathematics Teaching Duty Analysis of Variance of Dimension 8--Student Teaching-- By Year Graduated From Mecca College of Education (Male Teachers) .................... Analysis of Variance of Dimension 8--Student Teaching-- by Year Graduated From Mecca College of Education (Female Teachers) ................... Analysis of Variance of Dimension 9--Educationa1 Thought--By Sex and Graduated With 40 or 60 Credits Analysis of Variance of Dimension 9--Educational Thought--By Sex and Teaching at Which Level ...... Analysis of Variance of Dimension 9--Educationa1 Thought--By Sex and Percent of Mathematics Teaching Duty ..................... Page 202 203 204 205 206 207 208 209 210 211 212 213 E-44. E-45. E-46. E—47. E-48. E-49. E-50. E-51. E-52. E-53. E-54. E—55. E-56. Analysis of Variance of Dimension 9--Educational Thought--By Year Graduated From Mecca College of Education (Male Teachers) .............. Analysis of Variance of Dimension 9--Educationa1 Thought-~By Year Graduated From Mecca College of Education (Female Teachers) ............. Analysis of Variance of Dimension 10--Curriculum Design--By Sex and Graduated With 40 or 60 Credits . . . Analysis of Variance of Dimension 10--Curriculum Design--By Sex and Teaching at Which Level ....... Analysis of Variance of Dimension 10--Curriculum Design-~By Sex and Percent of Mathematics Teaching Duty .......................... Analysis of Variance of Dimension 10--Curricu1um Design-—By Year Graduated From Mecca College of Education (Male Teachers) ............... Analysis of Variance of Dimension 10--Curriculum Design--By Year Graduated From Mecca College of Education (Female Teachers) .............. Analysis of Variance of Dimension ll--Educationa1 Psychology--By Sex and Graduated With 40 or 60 Credits . Analysis of Variance of Dimension 11--Educational Psychology--By Sex and Teaching at Which Level ..... Analysis of Variance of Dimension ll--Educational Psychology--By Sex and Percent of Mathematics Teaching Duty ..................... Analysis of Variance of Dimension ll--Educational Psychology-~By Year Graduated From Mecca College of Education (Male Teachers) .............. Analysis of Variance of Dimension ll--Educationa1 Psychology--By Year Graduated From Mecca College of Education (Female Teachers) ............. Analysis of Variance of Dimension 12--Prob1ems of Teaching Mathematics--By Sex and Graduated With 40 or 60 Credits ..................... xi Page 216 217 218 219 220 221 222 223 224 226 E-57. Analysis of Variance of Dimension 12--Prob1ems of Teaching Mathematics--By Sex and Teaching at Which Level ...................... 229 E-58. Analysis of Variance of Dimension 12--Prob1ems of Teaching Mathematics-~By Sex and Percent of Mathematics Teaching Duty ............... 230 E-59. Analysis of Variance of Dimension 12--Prob1ems of Teaching Mathematics--By Year Graduated From Mecca College of Education (Male Teachers) .......... 231 E-60. Analysis of Variance of Dimension 12--Problems of Teaching Mathematics--By Year Graduated From Mecca College of Education (Female Teachers) ......... 232 xii CHAPTER I INTRODUCTION Saudi Arabia has one of the largest per capita investments in the world. In the fiscal year 1978-79, the government of Saudi Arabia allocated over 15 billion Saudi riyals (U.S.$4.3 billion), 11.6 percent of the total budget,1 for education, in addition to a little over $2 billion2 for the Ministry of Education. This allocation works out to roughly $1,000 per child, man, and woman of the population estimated between five and seven million people.3 This expenditure on education represents a steady increase in the annual educational budget from $3.1 million in 1952-534 to over $6 billion in 1978—79. Official statistics show that 1,329,4175 students, from the kinder- garten to the university level, were receiving free education under the Saudi system. That is, the Saudi Treasury spent $6,000 per learner in the 1978-79 fiscal year. By any standard, it is an impressive 1Kingdom of Saudi Arabia, Ministry of Education, Educational Statistics in the Kingdom of Saudi Arabia, 1978-79, p. 380. 21bid., Table 14-2. p. 380. 3Emile A. Kakhleh, The United States and Saudi Arabia: A Policy Analysis (Washingdon, D.C.: American Enterprise Institute for Public Policy Research, 1975), p. 5. 4Al—Nadwa [daily newspaper, Mecca], July 17, 1977. 5Kingdom of Saudi Arabia, Ministry of Education, Educational Statistics in the Kingdom of Saudi Arabia, op. cit., p. 51. 1 investment, which very few countries in the world can boast of match- ing. The Saudi government, in other words, treats education as one of the most important single national concerns. In this connection, it is interesting that In September 1957 a government scholarship program indicat- ing considerable official approval of foreign study was announced. Under its terms, the Ministry of Education was to select and send qualified students abroad to study the arts, sciences, and various professions. Upon the completion of their courses, the students were required either to work for the government for a period equal to that of the scholarship or to refund the amounts spent on them. The new program also provided for limited government assistance to Saudis studying abroad at their own expense. Until November 6, 1957, Saudi Arabia had no facilities for higher education, except for a small College of Islamic Law in Medina for training Islamic judges. On that date, however, the creation of a modern university, the University of Riyadh, was announced. Lipsky recalled: It consists so far only of a college of arts and sciences, but colleges of commerce and law are soon to be added, and these are to be followed by medical, agricultural, and engineer- ing schools. It is not known whether the level of instruction offered at this new institution actually represents higher edu- cation in the Western sense. The present curriculum of Saudi secondary schools provides inadequate preparation for university- 1evel courses in most fields. Despite the initial difficulties, the Ministry of Education has always endeavored to make Saudi education consistent with the best available in the world. In pursuit of this objective, four 6George A. Lipsky, Survey of World Cultures: For Saudi Arabia: Its People, Its Society and Its Culture, ed. Thomas Fitzsimmons (New Haven: Hraf Press, 1959), p. 282. 71bid., p. 280. additional universities--Islamic University of Medina in 1961, Univer- sity of Petroleum and Minerals in 1963, King Abdul-Aziz University in 1967-68, and King Faisal University in l979--have since been inaugurated.8 Recently, when King Khalid visited Mecca in 1980, he decreed that a university called Umm Al-Qura University be established at Mecca.9 By a subsequent decree, dated May 5, 1981, a budget of 432 million riyals (U.S.$123.4 million) for this new university was allocated, and since then the University has officially come into existence. Aims of the Study In the evolution of modern higher education in Saudi Arabia, the College of Education, Mecca, as one of the oldest colleges of education has, since its inauguration, been striving to improve its curricula and the quality of education for its alumni. In a society like the Saudi one, which is making an enormous effort to bring its population into the twentieth-century world of science and technology, Mecca College of Education is expected to provide at least adequately effective, if not excellent, teachers of science and mathematics. This study is an attempt to evaluate, with a view to providing a measure of the quality and adequacy of the College's programs, the mathematics curriculum given at the College of Education, Mecca, from the perspective of the teachers who graduated from the College in the years 1976-1980. It is hoped that this examination of the program 8Kingdom of Saudi Arabia, Ministry of Education, Educational Statistics, Vol. XII, pp. 20-21. 9Roya1 Decree No. 96, dated April 26, 1981. by criteria consistent with established practices of educational evaluation will benefit both the College of Education and the College's mathematics program. Under the largely centralized Saudi educational system, uni- versity education, including colleges of education, and the education for boys and girls, elementary through secondary, 'h; planned, coor- dinated, and executed through different central agencies, namely, the Ministry of Higher Education, the Ministry of Education, and the General Presidency of Schools for Girls. Administratively and organi- zationally, the Mecca College of Education is not directly involved in the planning and development of school curricula. The lack of intimate involvement of the College in the programs at intermediate and second- ary schools is further compounded by the fact that Mecca College of Education has its own departments of physics, mathematics, chemistry, biology, geography, English, physical education, curriculum and methods of teaching, art education, and education as integral parts of its management and control, and this invests the College with the respon- sibility of planning and implementing programs in these subjects for teachers who opt for teaching them at the intermediate and high school levels. In fact, this academic constitution of the College would appear to demand the closest possible relationships between the aca- demic subjects taught at intermediate and high schools and those taught at the College of Education. Until 1974-75, the department of mathematics used to function as a part of the physics department, but in 1975-76 an independent department of mathematics was created, invested with the full responsibility to plan and administer courses in mathematics for teachers who intended to teach the subject in intermediate and high schools. The department of mathematics, it is h0ped, may be better able to discharge its obligation to prepare teachers to teach mathe- matics effectively, consistent with the program objectives, if it could be provided with systematic feedback about the effectiveness of the program. The aim of this study is to obtain systematic feedback from the alumni of the College regarding its programs for preparing teachers of mathematics. Need for the Study Since the inception of the College of Education in 1950, no attempt has been made to evaluate its various programs. And the recent reorganization of the mathematics department into an indepen- dent part of the College, invested with the responsibility for design- ing and teaching programs for teachers of mathematics, makes the need for its programs to be consistent with enabling the teacher to be an effective teacher all the greater. It should, therefore, prove very useful to the department to evaluate its programs from the perspec- tive of whether it is accomplishing its intended objectives. Purposes of the Study The purposes of this study are: l. to gather systematic data on how well the program of mathematics at the College of Education, Mecca, appears to prepare teachers to teach, plan, and implement mathematics education; 2. to develop some initial means of involvement for graduate teachers of mathematics in the preparation of mathematics teachers at the College of Education, Mecca; and 3. to recommend remedies that may appear to be needed, and to point to what may appear to be the current strengths and weaknesses of the program. An exploratory factor analysis revealed the existence of clusters of items among the attitude questions. Scales were con- structed to answer the 12 research questions regarding the mathematics curriculum at the College of Education. Also, to test whether varying groups of subjects in the study responded differently to the question- naire, the following research hypotheses were analyzed with an analy- sis of covariance. Research Questions 1. Did the program enable student teachers to understand the objectives of teaching mathematics? 2. Did the program in mathematics at Mecca College of Educa- tion enable them to understand basic mathematics to teach mathematics? 3. Did the program prepare them for higher mathematics? 4. Did the program help them understand the relationships between the school and college curricula? 5. Did the program emphasize the practical, problem-solving nature of mathematics? 6. Did the program prepare the student teachers for teaching mathematics at school? 10. 11. 12. The Did the program provide an adequate theoretical introduc- tion to methods of teaching mathematics? Did the program provide adequate student-teaching practice? Did the program relate its teaching to the philosophical objectives of Saudi education? Did the program adequately prepare student teachers to design curricula in mathematics? Did courses in educational psychology at the College of Education help student teachers to teach mathematics better? Did the program acquaint student teachers with the problems of teaching mathematics? Study Hypotheses following eight hypotheses were tested in the study: There is no significant difference in the evaluation of the mathematics curriculum of the College of Education by male and female respondents. There is no significant difference in the evaluation of the mathematics curriculum given by the College of Edu- cation, Mecca, by respondents who graduated either with 40 or 60 credit hours in mathematics. There is no significant interaction effect between the sex of the respondent and the type of graduation. There is no significant difference in the evaluation of the mathematics curriculum of the Mecca College of Educa- tion by respondents who teach either at the junior or senior high level. 5. There is no significant interaction effect on the evalua- tion of the mathematics curriculum of the Mecca College of Education between sex of the respondent and the level at which the respondent teaches. 6. There is no significant difference in the evaluation of the mathematics curriculum of the College of Education by respondents with an 80 percent or less teaching responsi- bility in mathematics and those with a 100 percent teaching duty. 7. There is no significant interaction effect in the evalua- tion of the College of Education between the sex of the respondent and the percentage of mathematics teaching responsibility. 8. There is no significant difference in the evaluation of the mathematics curriculum by respondents who graduated in different years with mathematics as their specialty from the College of Education, Mecca. Limitations of the Study This study was delimited to the teachers of mathematics who graduated from the College of Education, Mecca, during the five aca- demic years 1975-76 through 1979-80. It is recognized that this study suffered from weaknesses inherent in a questionnaire survey. Another limitation of this study was that the 12 foreign student teachers who graduated with mathematics as their main specialty could not be con- tacted for their feedback, but the rest of the population--that is, 116 graduate teachers--did return the completed questionnaires. In this sense, this study was based on the feedback of the entire population of graduates involved in teaching Mathematics in Saudi Arabia. Procedure and Organization of the Study The investigator used a questionnaire (Appendix A) as the primary instrument for the survey. The questionnaire is divided into five parts, consisting of the following categories: Part I: General Information Questions 1-11 Part II: Adequacy of Professional Courses to . - Prepare Teachers of Mathematics Questions 12-26 Part III: Adequacy of the Courses in Mathemat- ics Given by the College of Educa- tion, Mecca, for Teaching Mathematics Questions 27-48 in Intermediate, Junior and Senior High Schools Part IV: Relatedness Between tge chooL Mathe- matics Curricu um Nee s an t e . Courses in Mathematics at the Quest1ons 49-52 College of Education Part V: Recommendations Questions 53-64 The questionnaire was administered to the teachers of mathemat- ics who had graduated from the College of Education, Mecca, during the academic years 1975-76 through 1979-80, with either 40 or 60 credit hours in mathematics. Information supplied by the administration of the College of Education, Mecca, indicated that 128 student teachers had graduated from the College with mathematics as their teaching specialty. A further analysis of the list indicated that of the 128 graduates, 12 were non-Saudi students who had since returned to their 10 countries. Considering the relatively small number of graduates, the investigator decided to administer the questionnaire to the entire population of 116 Saudi graduate teachers. Fully completed returned questionnaires indicated 100 percent participation of the population. Detailed information about the population, the procedure followed, and the questionnaire is contained in Chapter IV. As the main focus of this study was the mathematics program given by the College of Education, Mecca, Chapter 11 includes the relevant historical background on Saudi education in general and the College of Education in particular, with special emphasis on the College's mathematics program and the relationship with school edu- cation and the program of intermediate and high school mathematics. Related research and publications in a wide variety of scholarship and research works are reviewed in Chapter III. Presented in Chapter IV is a detailed discussion of the ques- tionnaire, the selection of the population, the procedure followed to gather the data, and the method of analyzing the data. The results of the survey and analysis of the data to test the formulated hypotheses are presented in Chapter V. Chapter VI concludes the study with a summary of suggestions and recommendations for further study. CHAPTER II EDUCATION IN SAUDI ARABIA The value of this study can be fully realized only in the context of the history, background, and commitment of Saudi educa- tion. The Ministry of Education of the Kingdom of Saudi Arabia has set forth a policy statement of the national educational objec- tives in the following terms: The educational policy is the broad lines on which rest the educational process in fulfilling the duty of acquaint- ing the individual with his God and religion and adjusting his conduct in accordance with the teaching of religion, in fulfillment of the needs of society and in achievement of the nation's objectives. It covers the various fields and stages of education, the programs and the curricula, the means of education, the administrative systems, the organs in charge of education and all other related sub- jects. Although Saudi education must forge ahead in the world of science and technology, it must never sever its continuity with the past traditions and the moral teachings of Islam--a feature that is a special characteristic not only of Saudi education but also of the entire country. Yet, as Lipsky pointed out, Until twenty-five years ago formal education in Saudi Arabia was entirely in the Islamic tradition of religious and classi- cal learning and was available only to a tiny segment of the 1The Educational Policy in the Saudi Arabian Kingdom (Riyadh: Ministry of Education, 1974), p. 5. 11 12 country's youth. Public education was nonexistent until the 1930's when, with Egyptian advice and personnel, a small gov- ernment school system was established. Whatever education existed prior to 1925 was traditional and conducted in the Kuttab or Koranic elementary schools, situated near or in the mosque. The curriculum of the kuttab is based on memorization of the Koran, with secondary emphasis on reading and writing. The prestige attached to religious learning is reflected in a strong pressure upon the villager and urban dweller to see that his sons acquire at least some formal knowledge of the Koran. When a pupil is able to recite a certain number of verses, his parents may give a feast in his honor, and a boy who has memor- ized the entire Koran--a rare feat--is publicly honored in some places. The limitation of this education was further compounded by the fact that the Arabs were not masters of their own destiny. As Salim Fahd Al-Hamdan pointed out: The long rule of the Turks in the Arabian peninsula left nothing to show that they had paid attention to spreading of knowledge. A few primary schools were established, but few attended because the population was suspicious about Turkish as the language of instruction. After the Turkish yoke was overthrown in 1925, a General Directorate of Education was established that very year.5 The year marks the 2George A. Lipsky, Survey of World Cultures: For Saudi Arabia: Its People, Its Society, Its Culture, ed. Thomas Fitzsimmons (New Haven: Hraf Press, 1959), p. 277. 3 4Saiim Fahd Al-Hamdan, "Educational System Charts of Saudi. Arabia From 1952 to 1974 With Projections to 1985" (M.S. dissertat1on, University of Kansas, 1977), p. 5. 5Saudi Arabia, Ministry of Education, Primary Education Depart- ment, Primary Education Yesterday and Today (Beirut: Muassasat Manturah Liltiba‘ah, 1969), p. 23. Ibid., p. 278. 13 beginning of the era of modern education in Saudi Arabia. Yet, From 1926 to 1951, over 82 percent of the total class hours were spent on religious and Arabic language subjects. The other 18 percent were spent on history, geography, arith- metic and geometry. Since the educational system was imitative and narrow, those who could afford it sent t eir sons to other Arab countries, mostly to Egypt and Lebanon. In 1953, the Ministry of Education was established to meet 7 Mohammad Ali Hibshi the responsibility of developing education. pointed out that "some profound and significant educational develop- ments took place in the period from 1925 til 1953, the year in which the General Directorate was replaced by the Ministry of Education."8 The main function of the Ministry of Education was, and has been, to plan, supervise, and coordinate education for kindergarten to secondary schools. Though a.Sharia College, a college of Islamic law had been in existence since 1949, no real institution of higher education was established until 1957. Six new universities--the University of Riyadh (1957); Islamic University, Medina (1961); the University of Petroleum and Minerals, Dhahran (1963); King Abdul-Aziz University, Jeddah, Mecca, and Medina (1967); the Islamic University of Imam Muhammad Ibn Saud, Riyadh (1974); and King Faisal University, 6Ai-Hamdan, op. cit., p. 7. 7Royal Decree No. 5/3/26/4950, dated 4/1/1373 H.J. 8Muhammad Ali Hibshi, "Educational Development: Some Basic Considerations,“ in Saudi Arabia and Its Place in the World, ed. Dar Al-Shoroug (Jeddah: Ministry of Information, Kingdom of Saudi Arabia, 1981). 14 Dammam (l975)9--were created under the Ministry of Education. By 1975, university education had become so important that a separate Ministry of Higher Education was created that year to coordinate higher education with the active cooperation of the existing univer- sities.10 In 1980, when King Khalid visited Mecca, he announced, in response to the demand by the population of the city, the creation of Umm Al-Qura University.H An allocation of 432 million riyals (U.S. $123 million) has already been made in the 1981 budget.12 The Mecca College of Education and the Sharia College of Mecca that became part of King Abdul-Aziz University on its inauguration as the state university in 1971 have since the opening of Umm Al-Qura University been transferred to this new university since its inauguration in 1981. Indeed, the College of Education, the main focus of this study, had its first commencement under the affiliation of the University of Umm Al-Qura in 1981.13 Yet education in Saudi Arabia has experienced pressures from two diametrically opposite directions. In this connection, the 9Kingdom of Saudi Arabia, Ministry of Education, Educational Statistics, Vol. 12 (1978-79), pp. 20-21. 10Kingdom of Saudi Arabia, Ministry of Education, Prggress of Education in Saudi Arabia: A Statistical Review (Riyadh: Ministry of Education, 1979), p. 6. 11 Royal Decree No. 96, dated April 26, 1981. 1ZOffice of Admissions and Registration, Umm Al-Qura Univer- sity, Commencement Issue (Mecca: 1980-81), p. 13. 13 Ibid. 15 Secretary General of King Abdul-Aziz University pointed out that "there are, for instance, those who accept Western technology and thoughts without any questioning, and those who reject them off- hand."]4 But Hibshi pointed out, Within this context, given the policy of the Saudi authorities of bringing about desirable developments gradually and in a peaceful manner, much time and patience are necessary to arrive at a formula conducive to development, and acceptable to the Ulema [Islamic religious scholars], who have insight into the real spirit of Islam, without incorporating any of the extreme views mentioned above. ‘ In deference to the wishes of the Ulema, a royal decree in April 1955 ordered all Saudi primary, secondary, and univer- sity students back home from abroad, except those studying engi- neering, law, and medicine.16 And within two years, when the authorities were able to satisfy those who objected to Saudi stu- dents' going abroad for higher education, a government scholarship program indicating considerable official approval of foreign study was announced. Under its terms, the Ministry of Education was to select and send qualified students abroad to study the arts, sciences and various professions. Upon the completion of their courses, the students were required either to work for the government for a period equal to that of the scholarship or to refund the amounts spent on them. The new program also provided for limited government assistance to Saudis studying abroad at their own expense.1 The trend has persisted since then, and in the 1970's, the universities of the world have seen the greatest influx of Saudi 14 15 16 Hibshi, op. cit., p. 128. Ibid. Lipsky, op. cit., p. 281. 171bid., p. 282. 16 students, specializing in subjects ranging from elementary education to nuclear physics. Although no reliable data are available on the exact number of Saudi students studying abroad, the Foreign Students Office of Michigan State University reported in the Fall 1980 Newsletter that the second highest number of foreign students registered for various courses at Michigan State University came from Saudi Arabia-- to acquire expertise in various areas of educational endeavors, basically to man the institutions of learning. Within Saudi Arabia itself, the expansion of education has been enormous. From 1960-61 to 1974-75, intermediate schools have multiplied from 57 for all-male schools to 647 schools for boys and girls--530 for boys and 117 for gir1s.18 For the same years, secon- dary schools increased from 19 for all-male schools to 156 for boys and 26 for girls.19 This expansion in education places the colleges of education in Saudi Arabia at the center of the educational scene, for schools become grounds for progress and preparation of tech- nologists, scientists, administrators, sociologists, economists, and so on, and the responsibility of the college of education, in this context--to prepare teachers to man the ever-increasing educa- tional complex--becomes all the greater. Since the main concern of this study is to evaluate the mathematics curriculum of the College of Education, Mecca, a detailed background and history of the College seems in order here. 18Al- Hamdan, op. cit., p. 116. 19 Ibid., p. 117. 17 The earliest institution of teacher education was founded in 20 Mecca in 1952 as the College of Teacher Training. It was renamed College of Education in 1962 and affiliated to King Abdul-Aziz Uni- versity in 1971.21 Mecca College of Education is a premiere teacher training institute in the country. It teaches courses leading to B.A. and 8.5. degrees in education. Students earning these degrees must have a minimum of 130 credit hours, which are broken down in the following fasion: Mandatory university courses 14 credits Mandatory college of education courses 12 credits Professional courses 32 credits Courses in the subjects of teaching 60 credits (A student can split these 60 hours into 40 for a major like mathematics and 20 for physics as his minor, if he chooses. Alternatively, he could take all 60 hours in mathematics alone.) Electives 12 credits Total 130 credits Besides these degrees, the College of Education awards a Special Diploma to those who earn 22 additional credits after meeting the requirements of 130 credit hours for the Bachelor's degree. Stu- dents pursuing their Master's degrees need only 20 credits after the completion of the Special Diploma requirement, or 42 credits after the Bachelor's degree. Such students qualify for a Master's in either 20College of Education, Mecca, College of Education in 25 Years, 1952-76 (Mecca: College of Education Press, 1976), p. 21. 21 King Abdul-Aziz University Catalog, 1979-80, p. 6. 18 Administration and Educational Planning, Curriculum and Teaching Methods, or Psychology.22 Since the College of Education started as an independent col— lege, it has had departments of subjects that a teacher needs to specialize in to teach at intermediate and high schools, in addition to the departments of traditional education subjects. The College of Education is unique in the sense that in addition to the usual depart- ments of education, the departments of geography, chemistry, physics, mathematics, biology, English, psychology, physical education, cur- riculum and methods of teaching, art education, and education form integral parts of the college. This process of having subject depart- ments under one college of education is, in all likelihood, to con- tinue. Until 1974-75, mathematics used to be a part of the Physics Department in the College of Education, but following that year it has been accorded an independent status and has since been charged with the responsibility of planning, developing, and implementing programs in mathematics for teaching of mathematics at intermediate and secondary schools of Saudi Arabia. The objectives of the Department of Mathematics, as defined in the schedules of the College of Education, are: l. to prepare teachers to teach mathematics, 2. to provide mathematics courses needed by other science graduate teachers. 3. to create specialization in mathematics to help interested teacher trainees proceed to qualify for teaching mathe- matics in colleges of education, 22Ibid.. pp. 100-132. 19 4. to conduct in-service refresher courses, and 5. to acquaint principals of elementary schools with the problems of teaching mathematics of grade-school children. 23 To qualify as teachers of mathematics for Saudi Arabian schools, student teachers are required to have either 40 credit hours or 60 in mathematics. Those who qualify with 60 hours of credit in mathematics are referred to as pure mathematics teachers, and those who have 40 hours in mathematics are required to choose a minor subject, which in the case of mathematics student teachers is generally physics. Each of these categories of trainees must have 32 hours distributed over the study of the main specialty in the manner shown below: Course # Course Name Credits 141 General Algebra 3 151 Logic and Set Theory 3 101 Calculus I 4 102 Calculus II 4 203 Calculus with Solid Geometry 4 211 Fundamentals of Analysis 4 241 Principles of Algebra 4 261 Principles of Geometry 3 490 Mathematics in Intermediate and High School 3 Total 32 credits Students wishing to qualify with 60 credits in mathematics are required additionally to have 28 hours of electives, which should include at least two of the following: 23College of Education, Mecca, op. cit., p. 143. Group I: Group II: Group III: Group IV: 20 Analysis Algebra Statistics and Probability Applied Mathematics Mathematics teachers with 40 credits must take 8 elective credits over and above the 32 required. to be in courses 300 and above. categories of graduates from the following offerings: Course # 101 , 102 141 151 170 171 203 211 221 231 241 261 272 290 304 312 313 321 24 Course Name Calculus I Calculus II General Algebra Logic and Set Theory Mathematics for Physicists I Mathematics for Physicists II Calculus With Solid Geometry III Introduction to Real Analysis Electronic Programing Principles of Statistics Principles of Algebra Principles of Geometry Mathematics for Physicists III Mathematics for Primary Schools Ordinary Differential Equations Real Analysis I Introduction to Complex Analysis Methods of Numerical Analysis and Programming 24 King Abdul-Aziz University Catalog, op. cit., p. 159. These additional 8 hours have Most electives are chosen by both Credits whwhmwwwwbpwwwwn-b co Course # 322 331 332 333 341 342 343 362 370 371 405 413 443 444 452 461 463 464 470 , 471 490 492 21 Course Name Numerical Analysis Introduction to Probability Statistics I Statistics II Introduction to Number Theory Linear Algebra I Abstract Algebra I Finite Geometry Dynamics Statistics Partial Differential Equations Real Analysis II Linear Algebra II Abstract Algebra II Set Theory Introduction to Topology Algebraic Geometry Differential Geometry Physical Mathematics I Physical Mathematics II Mathematics for Intermediate and Secondary School Selected Topics of Mathematics Credits (.40 wmwwwwwwhwwwwwwwwww 3 1-3 To comprehend the relationship between the College of Educa- tion curriculum in mathematics and the mathematics curricula for intermediate and high schools of Saudi Arabia, we should understand the organization and constitution of intermediate and secondary edu- cation of the country. The main central body responsible for the education of boys is the Ministry of Education: 22 The Ministry of Education has the over all responsibility for the educational policy, curriculum and organisation of boys educa- tion below university level. It administers boys schools at the pre-primary, the first and the second levels of general and voca- tional education including the teacher training at the second level. Recently a post-secondary technical education institute and two centers for the training of mathematics and science teachers also beyond secondary stage have also been set up under the Ministry of Education. Education of the physically or men- tally handicapped persons (both sexes) and the adult educagion are also the direct concern of the Ministry of Education. Besides, the Ministry of Education, since it replaced the Directorate General of Education in 1953, appoints teachers, develops curricula for various subjects and levels, allocates budgets, and provides for the training of teachers, among other things. When the Directorate General of Education was created in 1925, its main concern was the education of boys only, and very little of education for girls was included in its provisions. When the Direc- torate was elevated to the status of a ministry, the practice of concentrating exclusively on the education of boys by the Ministry of Education was carried forward. As late as 1960, many people held the view that modern edu- cation for women was "conducive to the degradation and immorality of women."26 Indeed, until the end of the 19505, women were allowed to take their primary, intermediate, or secondary examinations only externally, without the benefit of a formal education. Finally, the approval for education for women came “in 1959 when a royal speech 25Kingdom of Saudi Arabia, Ministry of Education, Progress of Education in Saudi Arabia, op. cit., p. 6. 26Hibshi, op. cit., p. 124. 23 was delivered stating that it had been decided, upon the wishes of the Ulema, to open school for girls under the control of a committee to be responsible to the Mufti [the leader of the Ulema, the Islamic scholars]. In 1960 this committee was replaced by the General Presi- dency of Schools for Girls to supervise the education of women at all 27 But by 1978-79, 394,478 girls were receiving free education levels." from kindergarten to secondary in 1,829 well—equipped and well-staffed schools.28 The General Presidency for Girls Education is responsible for the education of girls at all levels. The Presidency works in close co-operation with the Ministry of Education and adopts an identical programme of studies with only slight adaptations suited to the special interests of girls education. The voca- tional education for girls is at present limited to tailoring schools at intermediate level and teacher training schools at the secondary level. At the third level, the colleges of education for girls are supervised by the Presidency. Private schools for girls are also under its supervision. Despite the minor differences in the objectives of the Ministry of Education and the General Presidency of Schools for Girls, the syllabi and textbooks for all levels in academic subjects, such as physics, mathematics, chemistry, biology, social studies, geography, and history, are the same for boys and girls all through Saudi schools. Men and women graduates of mathematics from the College of Education, Mecca, are required to teach the same syllabi, whether they teach them in a girls' or boys' school. 27Ibid. 28Kingdom of Saudi Arabia, Ministry of Education, Educational Statistics in the Kingdom of Saudi Arabia, 1978/79, p. 45, 29Kingdom of Saudi Arabia, Ministry of Education, Progress of Education in Saudi Arabia, op. cit., p. 6. 24 As the main focal point of attention of this study is the mathematics curricula both at intermediate and high schools in Saudi Arabia and at the College of Education, it seems in order to notice that the Curriculum Department of the Ministry of Education, which is responsible for curricula for boys' and girls' schools, recommended, through the Ministerial Decree No. 20/10/29/666/2, in 1973, that the National Committee for the implementation of programs in schools in Saudi Arabia introduce an experimental program in modern mathematics with effect from 1973-74. As an initial step the program was intro- duced in two Saudi schools: Faisal Secondary School, Riyadh, and Al—Jazira Secondary, also in Riyadh. Later, in 1975, the High Power Political Committee, which supervises the overall social and academic programs in the country, approved that the work must begin toward the implementation of the program of mathematics in all schools in Saudi Arabia. Following that approval, modern mathematics was introduced in King Abdul-Aziz Secondary School, Riyadh, in 1976-77. In 1980-81, all secondary schools in the four major cities--Riyadh, Jeddah, Mecca, and Dammam--were teaching modern mathematics. The High Power Politi- cal Committee has further ordered that the full implementation of the program of modern mathematics be completed between the years 1981 and 1989, all through the country. Work to meet this deadline has already begun. A proposed program in modern mathematics for the seventh grade has already been issued by the General Directorate of Research and Curriculum of the Ministry of Education, Riyadh. 25 With these recent innovations in the curricula of mathe- matics, the respondents were required to teach the following curricula at various levels from the intermediate to the high school level: (Old): 7th Grade 8th Grade 9th Grade 10th Grade 11th Grade (New): (Old): (New): (Old): (New): (Old): (New): (Old): 3O 1. 2. N—‘ hum—a o o o o o o o o o o o o o o o o o c o o o (fihWN-fi o o o o o bWN-d o o o o 30 Algebra Geometry Groups and Relations Euclidian Geometry Numbers Analytical Geometry Algebra Geometry Groups and Relations Euclidian Geometry Numbers Analytical Geometry Arithmetical Measurements Arithmetic Algebra Geometry Groups and Relations Euclidian Geometry Numbers Analytical Geometry Statistical and Probability Measurements Algebra Geometry Rational and Real Numbers Analytical Geometry Equations Trigonometry Solid Geometry Algebra and Statistics Geometry Solid Geometry Analytical Geometry and Trigonometry Kingdom of Saudi Arabia, Ministry of Education, General Directory of Research and Curriculum (Riyadh: Ministry of Education, 1979). (New): 12th Grade (Old): (New): Looowoxcnth—a o o o o o o o o 0 (JUN—4 o o o 1 2. 3. 4 5 26 Matrices Groups Analytical Geometry Vector Analysis Trigonometry Complex Variables Powers and Logarithms Mathematical Deductions Statistics and Probability Algebra Calculus Analytical, Solid, and Trigonometric Geometry Analytical Geometry Functions Series Limits Differentiation and Integration In conclusion, this study seeks to evaluate the mathematics curriculum given by the College of Education, Mecca, with special reference to the curriculum in mathematics that Mecca College of Education graduate teachers are required to teach at intermediate and high schools in Saudi Arabia, from the perspective of whether the College curriculum prepares them adequately to teach mathematics effectively or not. CHAPTER III REVIEW OF THE LITERATURE The purposes of this study, as stated in Chapter I, were to examine the mathematics curricula of the College of Education, Mecca, with a view to understanding how well they prepare the gradu- ate teachers in mathematics to meet the challenges of their profes- sion; to develop some initial means of involvement of such graduates, at least in the mathematics curricula of the College; and finally to identify some strengths and weaknesses of the program of the College of Education in order that some recommendations may be made. In pursuit of these objectives, an extensive search for the related literature through the scholarly publications in the areas of evaluation, teacher education, mathematics education, and education in Saudi Arabia was made. Although the search turned up illumi- nating material in most of the areas of concentration of this study, very 1itt1e--indeed, none at all-~was found with regard to evalua- tion of curricula in Saudi institutions of higher education. The latter fact is understandable in light of the fact that modern higher education in Saudi Arabia is still young. It is, however, hoped that the process of scientific evaluation of Saudi higher education will be initiated, in a humble way, by this study. 27 28 The context in which this study ought to be viewed is defined in the Recommendations of the Second World Conference of Muslim Edu- cation, held on March 15, 1980, under the auspices of King Abdul-Aziz University and Quaid-i-Azam University, and sponsored by the Ministry of Education, Government of Pakistan. The curriculum recommended is classified into "perennial" and "acquired" categories of knowledge. The former comprises the knowledge of the Quran, the Hadith (the tradition of the Prophet), the life and character of the Prophet, his companions and their early followers, the Unity of God, fundamentals of Islamic jurisprudence, Quranic Arabic, Islamic metaphysics, comparative religion, and Islamic culture. The "acquired" category of knowledge, according to the document, con- sists of the humanities; social, natural, and applied sciences; and administrative disciplines.1 The Recommendations state that "the main job of educators and experts is to establish detailed links between Group-I (Perennial Knowledge) and Group-II (Acquired Knowledge) and then design the cur- riculum."2 Furthermore, "all the above branches of acquired sciences should be taught from the Islamic point of view. Islamic schools of Thought should be established in all branches of social studies."3 It appears that Saudi education is founded irrevocably on the basic tenets of Islam and Islamic culture, so much so that the social 1Recommendations of the Second World Conference on Muslim Edu- cation (Islamabad: Ministry of Education, Government of Pakistan, .1980, 9 pp. 6'7. 21bid., p. 7. 31bid. 29 sciences and the humanities are viewed in the context of the funda- mentals of Islam. To most people in the West, the cultural orienta- tion of Islam is not only unfamiliar but it is, if not totally, largely confusing. A paper given at the Annual Meeting of the American Educa- tional Research Association in 1980 by Paul Shaker pointed out that the need for multicultural education "arises from the persistent efforts of the government of Saudi Arabia to supplement the Arabian educational heritage with ideas and technology from America."4 Shaker concluded: There does seem to be a valid multicultural road to educational development, however, which profits all parties concerned and denigrates none of them. An attitude of mutual respect and sharing is not platitudinous; it is the most effective guide to action. As collaboration goes on we must press our analyses to truly symbolic levels. Transfer on less profound planes [is] of use, but should not be programmed to the exclusion of values, attitudes, and unifying concepts. This very theme was rehearsed in another paper given a year earlier, in 1979, at the annual meeting of the same association, held in San Francisco, California: Western educators have a great deal to offer countries such as Saudi Arabia, both in person and through the training of stu- dents abroad. There is a need for the developing countries to be understood educationally as they are, with allowances made for cultural differences and limitations in resources. The people of such countries are ready to adopt, as their own, reforms which are designed with care and implemented with sensibility.6 4Paul Shaker, "Curriculum Change in the Developing Country: The Case of Saudi Arabia" (paper presented at the Annual Meeting of the American Educational Research Association, Boston, Massachusetts, April 7-11, 1980), P. 2. 51bid., p. 17. 6A. El-Mahdi Abdel-Halim and Paul Shaker, "A Strategy for Pro- moting Educational Reform in Developing Countries" (paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, California, April 8-12, 1979), p. 18. 30 As a "trained student abroad," this researcher employed the techniques of evaluation with deep regard and respect for the funda- mental values of Saudi culture to assess the curriculum of one of the fundamental subjects of modern technology. A report published, under the auspices of UNESCO, by the State University of New York, Buffalo, Faculty of Educational Studies, stated that "there are concentrated efforts in Saudi Arabia to improve mathematics, science, and English language instruction, to upgrade the programs of the teacher training institutes, and to provide new schools for programs (such as commercial and agricultural education) which are in high demand."7 In an unpublished master's thesis entitled "Proposed Mathe- matics Curriculum for the Saudi Arabian Intermediate Schools," Al-Ajroush pointed out that the general feature of the mathematics curriculum at all levels of school education "is its narrow scope, consisting basic- ally of three major topics, arithmetic, algebra, and geometry; it con- tains too much of Euclidian geometry and traditional algebra with no mention of any concepts and principles of modern mathematics, such as sets, mapping, logic, structure of the number system and probability theory."8 7Taher A. Razik and Verna Willis, Comparative Analysis of Curriculum Change and Development in the Arab Countries: The Process (Buffalo: State University of New York, Faculty of Educational Studies, 1978), p. 246. 8Hamad Ali Al-Ajroush, "Proposed Mathematics Curriculum for the Saudi Arabian Intermediate Schools" (Master's thesis, The Uni- versity of Wisconsin, 1976), p. 10. 31 As pointed out in Chapter II, new curricula in mathematics have already been introduced in the Saudi intermediate and high school programs of mathematics since 1979. This emphasis on mathe- matics in the educational curricula is due to the importance of mathematics in the industry- and technology-oriented societies of the world: When one is concerned only with the effect of mathematics on science, the farthest one can go, cognitively, in subordinat- ing mathematics to science is suggested by the following simile. If science is viewed as an industrial establishment, then mathe- matics is an associated power plant which feeds a certain kind of indispensable energy into the establishment. The counterparts to mathematicians would be the designers, maintenance men, and administrators of the power plant. Of these, the majority need be interested only in the requirements of the power plant itself, and solely a minority need be aware of the actual workings of the establishment itself, let alone be expert in its activities. What has been hinted at in the preceding quotation regarding the wider implications of the study of mathematics was fully and expertly elaborated in a paper delivered at the Orono campus of the University of Maine in July 1973: There is a difference between the Art of Mathematics and the Craft of Mathematics. Only a few of us know the art of mathe- matics in much the same way as only a few individuals really know and possess the art of poetry. We know very little about how to teach the art but many of us can recognize it. This fact, how- ever, does not relieve the teacher of the responsibility for fostering the art. On the other hand the craft of mathematics can be learned to greater or less degree by all of us. The patrons of our schools demand that the schools teach the craft of mathematics because it has an immediate use in the store and the bank. This does not mean that the people want the mathe- matics program limited to the craft of mathematics any more than they want the literature program limited to the readin of the newspaper. The craftsmanship aspects of each subject [are] 9Salomon Bochner, The Role of Mathematics in the Rise of Science (Princeton: Princeton University Press, 1966), p. 47. 32 taken as a lower bound of what the schools must do. In this the schools should not fail.10 Despite the emphasis on the craft of mathematics, the art aspect of mathematics as enunciated in the following statement from the report of the National Advisory Committee on Mathematical Educa- tion in the United States, 1975, has not been overlooked in the objec- tives of mathematics programs in Saudi intermediate and high schools: The report . . . indicates an urgent need for research into means of assessing the development of mental attitudes, accurate thought, heuristic procedures in problem-solving, of all these attainments of intelligence which ought to be considered by mathematical peda- gogy as learning's final aims.n In one of the most remarkable works by three English head- masters, entitled Teachinngathematics, the authors, while lamenting the paucity of graduates in pure mathematics for teaching at schools, recommended the following training prerequisites for teacher gradu- ates in mathematics: 1. The colleges must recruit a continual and adequate supply of entrants who have had a sound mathematical education while at school. 2. The mathematical departments of the colleges must devise an imaginative course which will increase the mathematical con- tent of the students' knowledge. In some cases this will mean the introduction of new concepts of mathematics for the students, particularly for those who have learnt their mathe- matics in the rather arid traditional way. In any case, the course must include some modern mathematics. 10H. Van Engen, "Fostering Mathematical Maturity in the Middle School Classroom" (paper presented at the Orono Conference of Maine University, Orono, July 16-20, 1973), p. 36. 1]A. Z. Krygowska, "Mathematics Education at the First Level in Post-elementary and Secondary Schools," in New Trends in Mathe- matics Teaching, Vol. 4 (Paris: UNESCO, 1979), p. 38. 33 3. The mathematics departments in collaboration with the educa- tion department must devise interesting and realistic curric- ulum courses to show the students the most effective and up-to-date methods of teaching. It is essential that the students when they become teachers themselves are aware of the many developments that have been taking place and do not find refuge in using the methods by which they were taught themselves. 4. The colleges and the schools must come much closer together in the training of teachers. The art of teaching is learned in the classroom and it is in the classroom that exciting developments are taking place. It would seem to be a "sine qua non" that there should be a much greater exchange in teach- ing personnel between schogl and college and college and school than there is at present. As this study attempted to evaluate the mathematics curriculum of the College of Education, Mecca, from the perspective of graduate teachers of this College, it is interesting to note the following view expressed of the evaluation of curriculum: It is an illusion to think that one can evaluate a curriculum in any global sense. The curriculum does not exist globally; it exists only in the specifics of a particular instructional setting. Failure to appreciate what might be called the "situation—specific" nature of the curriculum may account for much of the current con- fusion about questions of evaluation. Attempts to ignore situa- tional variation in curriculums usually lead to the search for a "least common denominator" to be evaluated, which can have con- strictive effects on subsequent instruction. It does make sense, however, to talk about evaluating the activities and products of a given curriculum development project. This may seem like a small difference--between evaluating a cur- riculum and evaluating a project's work-~but it is an important distinction to make. When one attempts to evaluate a "curriculum" per se, one tends to reify it and to lose sight of its situation- specific character. One begins to talk of its effectiveness--as though it had such a quality--and to set up studies to compare the effectiveness of various curriculums. Such studies inevitably encounter difficulties because they assume that curriculum 12A. E. Howard, W. Farmer, and R. A. Blackman, Teaching Mathe- matics (London: Longmans, Green, & Co., Ltd., 1968), p. 39. 34 effectiveness is a quality that can be measured by, say, a set of tests and examinations. Paul L. Dressel in his work, Handbook of Academic Evaluation, among various approaches to curriculum evaluation suggested: Another approach to evaluation of the curriculum might con- sider its quality--the extent to which it is current in offerings, content, bibliography, and instructional techniques and method- ology. Adequacy of faculty preparation in relation to the courses taught is another criterion. 4 Furthermore, "In this process of evaluation, the opinions of various groups may be sought. Students completing, entering, or considering a 15 In program may have views worthy of collection and consideration." this connection, Mattson added: "The survey of different methods of evaluation involving graduates of programs indicates that the most practical means of gathering data is through feedback from the gradu- ates."16 The National Council for Accreditation of Teacher Education adopted the following professional-studies components for teacher education on May 6, 1977: Standard: The professional studies component of each curriculum for prospective teachers includes the study of the content to be taught to pupils, and the supplementary knowledge, from the sub- ject matter of the teaching specialty and from allied fields, 13Jeremy Kilpatrick, "Methods and Results of Evaluation With Respect to Mathematics Education," in New Trends in Mathematics Teaching, Vol. 4 (Paris: UNESCO, 1979), p. 169. 14Paul L. Dressel, Handbook of Academic Evaluation (San Francisco: Jossey-Bass, Inc., 1976), p. 314. 15 16R. Mattson, "An Evaluation of Teacher Educator Program at Montana State University by Graduates of That Program" (Ph.D. disser- tation, Montana State University, 1972), p. 33. Ibid., p. 315. 35 that is needed by the teacher for perspective and flexibility in teaching. Standard: The professional studies component of each curriculum includes the systematic study of teaching and learning theory with appropriate laboratory and clinical experience. Practicum: Standard: The professional studies component of each curriculum for prospective teachers includes direct, substantial, quality participation in teaching over an extended period of time in an elementary or secondary school. This practicum should be under the supervision of college personnel who are experienced in, and have continuing experience with, elementary or secondary teaching, and certified, experienced personnel from the cooperating school. Explicit criteria are established and applied for the selection oflsggool supervisors and for the assignment of college person- ne . During the last decade an enormous amount of research regard- ing teacher education has emerged. Myer and Reid concluded that because of the failure of the teacher education institutions, "few teachers regard their experience with the faculty of an education or t."18 Ruth Lambert, teachers' college with such nostalgia or respec on the other hand, suggested that the development of the basic skills and critical evaluation "will lead to the continual self-evaluation after the period of formal education is finished."19 In the 19605, six California professors concluded, with regard to the quality of teacher training in California, that "the preparation 17National Council for Accreditation of Teacher Education, Standards for Accreditation of Teacher Education (Washington, D.C.: NCATE, 1977), pp. 3-6. 18Douglas Myers and Fran Reid, Educatinngeachers: Critiques and Proposals (Ontario: The Ontario Institute for Studies in Educa- tion, 1974), p. 3. 19Ruth L. Lambert, "An Investigation of Attitudes of Selected Recent Graduates in Teacher Education Toward Their Education Prepara- tion for Teaching at the University of Arkansas at Pine Bluff" (Ph.D. dissertation, Michigan State University, 1977), p. 83. 36 of good teachers is the function of college or university as a whole."20 Furthermore, they asserted: "We believe uncompromisingly in the critical importance of preparation in subject matter to provide an essential part of the equipment of all teachers."21 Cornish arrived at the following strikingly similar recommen- dations for improving pre-service teacher education programs to the ones this investigator has made: Promote an effective student teaching program. Provide opportunities for classroom observation. Offer a broad liberal arts education. Obtain qualified instructors. Make adequate facilities available. Insure good student-faculty relationships. Maintain a balance in teaching between theory and its practical application. Provide some separate instruction for primary and inter- mediate grade teachers. 22 Offer a variety of courses in education. \0 CD \lmm'bWN-J o o o o o o o o 0 With regard to educational trends in South-East Asia, Paul Chang pointed out that "if the quality of teacher training in the region is to be raised, it is essential that universities should provide effective leadership."23 20Ernest L. Boyer, "Campus-Wide Perception of Teachers: An Exercise in Collaboration," The Journal of Teacher Education 21 (September 1965): 271-74. 21 Ibid. 22Robert J. Cornish, "Improving Undergraduate Elementary Training Programs," University of Kansas Bulletin of Education 17 (May 1963): 103. 23Paul Chang, "Educational Trends in South-East Asia With Special Reference to Problems of Improving the Quality of Education," International Review of Education Journal 17 (1971-72): 150-63. 37 Pas G. Ramos, a researcher at the University of the Philip- pines, recommended ways of making graduate teachers more effective by using continuous reassessment by the college of education: One such systematic appraisal of our college is the Self-Study Evaluation. Specifically, the Self-Study Evaluation project aims to find out how the College can make its faculty and pro- grams more relevant to, and consistent with, the significant developments in the New Society. During the last two decades, the Arab Organization for Educa- tion, Culture, and Science has been paying special attention to teacher preparation. The Conference on the Preparation of Arab Teachers, held in Cairo on January 17, 1972, recommended that teacher preparation should consist of the following essential components: i. general education dealing with the Arab world in particular and contemporary global issues in addition to other subjects; ii. major fields of specialization in a number of allied educa- tional disciplines; iii. education fields as theoretical studies in education such as educational psychology, counseling, educational administra- tion, teaching methodology» and supervised student teaching; and iv. practicum programs where the student teachers focus on the application of the theoretical preparation to practical problems in pedagogy.25 The Conference further suggested: The academic part of teacher education is not only intended to fill in the teacher in his major subject, but it should also be designed as to train him to continuously acquire 24Pas G. Ramos, "The College of Education and the New Educa- tion Reforms," Education Quarterly [College of Education, University of the Philippines] 20 (January-March 1974): 18-30. 25Arab Organization for Education, Culture, and Science, Department of Education, A Conference on Preparing Arab Teachers, From January 8 to 17, 1972 (Cairo: Al-Takadom Press, 1973), p. 23. 38 knowledge in his major field. A teacher in a rapidly chang- ing world should face children with up-to-date knowledge in his subject. A resolution to improve the teacher education programs in Arab countries, adopted by the cultural wing of the Arab League Sec- retariate, recommended: It is important to carry out a follow-up study of graduate teachers from colleges and institutions by observing them directly at work, by evaluating their cultural impact on the community at large. . . . The ultimate objective is to improve the existing standards of teaching by staffing the faculty with well-qualified teachers.27 Al-Roushad and Abdulatif, in a paper presented at the First International Conference on Islamic Education, stated: It is vitally important for the Education Colleges and the Ministry of Education to jointly follow up their university graduates. This follow-up activity can be conducted in various ways such as: l. to establish a sub-office to follow up the university graduates in every college. This sub-office will supply the graduates with the documentation and literature neces- sary for their professions. 2. to set up a seminar for graduates in each college annually: the graduates will select the agenda for each seminar by themselves. 3. every college of education should seek the help of its graduates in conducting various research studies, especially field researches. 26Ibid., p. 129. 27Arab League, General Secretariate, Cultural Department, Collection of the Arab League Council Resolutions on Cultural Affairs to be executed by the Arab countries, 1946-66). (Typewritten.) 28Mohammad Al-Roushad and Ahmad Abdulatif, "The Colleges of Education's Role in Teacher Preparation" (paper presented at the First International Conference on Islamic Education, March 31-April 7, 1977) (Jeddah: King Abdul-Aziz University Press, 1977), p. 15. 39 With regard to the evaluation of the teacher preparation pro- grams offered by teacher education institutions at various levels, the Conference recommended the following: A. There is a need for continuous review and evaluation of programs and techniques of preparing teachers in order to meet the demands of development in Arab societies and to improve the existing programs and techniques. B. Evaluation should include all aspects of educational pro- cess such as planning, curriculum development, preparation of textbooks, and the development of faculties for teacher preparation. For this kind of evaluation the staff should be specialized in its techniques. C. This Organization the Arab League will facilitate regular contacts among the representatives of Arab countries for study and exchange of experiences in regard to teacher preparation. 0. The follow-up of teacher gradutes from colleges and insti- tutions of education should be through visits, meetings, and questionnaires that should be answered by the graduates, institution directors, teacher educators in order to improve teacher education programs and to help improve the efficiency of graduate teachers. 9 Studies regarding the adequacy of professional courses in education in the United States indicate a sharply divided opinion. Some studies deplore the total ineffectiveness of the professional courses in content, organization, and instructional techniques, whereas others favor strongly their inclusion in the teacher preparation pro- grams. Lemons, a critic of education courses, concluded that "there is a distressing gap between what is taught in the education courses and the real world of teaching. There is unnecessary overlapping and duplication."30 29Arab Organization for Education, Culture, and Science, op. cit., p. 27 30Lawrence A. Lemons, "Education Courses," NEA Journal 54 (October 1965): 26-27. 40 Peter Renshow asserted that the "relationship between academic and professional studies is extremely tenuous."3] Based on his study of the effect of secondary education courses on student attitudes, Hansen concluded: Individual courses do not appear to produce immediate atti- tudinal change; courses that deal with specific areas, such as psychology, may not contribute to attigude change in areas unrelated to the specific course content. 2 Walter Borg, too, appeared to have reached similar conclusions, as is evident in the following remark: There appeared to be two important deficiencies in the typical methods course. One was that these courses tended to deal with generalities rather than identifying specific behaviors that teachers could employ to bring about specific outcomes. The second deficiency was that most of the courses were taught primarily using lecture and discussion techniques.33 Graff's study indicated that the "courses judged to be of little or no value were History of Education and Philosophy of Edu- cation."34 Goodlad came up with almost an identical conclusion: When the first course in education is a general "eclectic" introduction to teaching or a so-called "social foundations" course, it is almost universally disliked by students. . . . 3ITyrell Burgess et a1., Dear Lord James: A Critique of Teacher Education (England: Penguin Books, Ltd., 1971), p. 87. 32Thomas Charles Hansen, "An Evaluative Study of the Effect of Secondary Teacher Education Courses on Student Attitudes," Disser- tation Abstracts 37, 1-2 (1976): 234-A. 33Walter R. Borg, Moving Toward Effective Teacher Education-- One Man's Perspective (Logan: Utah State University Press, 1975), p. 7. 34Paui Graff, "Follow-Up Study of Graduates and Their Opinions of the Secondary Teacher Education Program of the University of Iowa, 1970-76" (Ph.D. dissertation, University of Iowa, 1976), p. 184. 41 It seems that the first course is a troublesome one, no mat- ter what its substance.35 Nash and others proposed a solution to the unpopularity and inadequacy of the foundational courses in the following recommenda- tion: Foundational studies will justify their place in teacher training programs when they are vigorously cross-disciplinary; when they are unifying in terms of fostering composite models of human behavior, needs, motivation, and learning; when they are as concerned with exploring, and helping people to develop workable theories as they have traditionally been with build- ing esoteric theories that too often are merely espoused but not practiced; when they can provide more vital and provoca- tive explanatory constructs, as well as a variety of experi- mental efforts to demonstrate the tactical implications of those constructs; when they become more "full-bodied," as concerned with the personal meaning of information as they are with intellectual inquiry and analysis; and when they abdicate their historical disengagement from the affairs of the socio-political/educational world and begin to advocate a larger, normative social vision.36 Ralph Preston surveyed the attitudes of 108 out of 175 gradu- ates from the school of education in an eastern university, regarding the education and academic courses, and reached an interesting conclu- sion based on the survey: Most students did not label all education courses as inferior, only a minority of education courses were judged to be infe- rior. Moreover, in answer to the question "Do you believe you could teach as well without any courses in Education as with them?" 82 percent responded with "No," 12 percent with "Yes," and 6 percent "undecided."3 35John I. Goodlad, "An Analysis of Professional Laboratory Experience in the Education of Teachers," The Journal of Teacher Education 16 (September 1965): 363-70. 36 Robert J. Nash and others, "The Foundations of Education: A Suicidal Syndrome?" Teacher College Record 92 (February 1977): 299-310. 37Ralph C. Preston, "Education Graduates View Education and Academic Courses," School and Society 92 (Summer 1964): 233-37. 42 Hardingham reported that “most of them [student teachers] consider formal college courses a necessity in the preparation pro- gram."38 Bruce Joyce and others concluded that "between 1973 and 1975 more professional courses were added than dropped and clinical experi- ence has been added steadily over the last several years."39 The following represents a typical evaluation of teacher education in Asia: 1. The contents of the science and the mathematics courses are mostly descriptive in nature and somewhat disconnected. Outdated materials are sometimes included. 2. There are unnecessary duplications in the contents of some professional courses. 3. In many courses, the content outlines consist of lists of topics taken directly from textbooks, and seem to have very little relationship to the main objectives--the courses of study. Most of the science curriculums give emphasis to development of the scientific attitude and the scientific methods in solving problems as part of the objectives; the general practice, however, seems to deviate from these important aims. 4. The curriculums are mostly prescribed and crowded with too many requirements. Individual planning with each student is almost non-existent. Each quarter a student is required to take 20-28 credits for undergraduate level and 15-18 credits for graduate level. Individual work or independent study is rather limited since students spend almost all of their time during a week in listening to lectures. 5. Facilities for the teaching-learning process are inadequate. Owing to limited budgets, textbooks, laboratory apparatus and teaching aids are not sufficient in most schools. 6. Thai textbooks are very limited in number. Most of good textbooks are in English and are not much used because of the language barrier. 38Robert J. Hardingham, "The Cooperating School in Teacher Education: Source of Theory or Practice?" Technical Report No. 13 (Iowa University, June 1977), p. 2. ERIC ED 147 101. 39Bruce R. Joyce and others, "Preservice Teacher Education" (Washington, D.C.: Office of Education, Department of Health, Edu- cation and Welfare, 1977), p. 21. ERIC ED 146 120. 43 7. The shortage of qualified instructors in specialized fields, especially in the sciences, mathematics, and languages is a serious problem. 8. In most institutions instruction is mainly by the lecture method. Facts and concepts are usually verbally explained. The inquiry method and active participation on the part of students are seldom used in general learning situations. 9. Generally speaking, students entering teacher training insti- tutions are not among the best ones. This usually is the main problem in upgrading the programs. 10. The upsurge of students in evening classes in various insti- tutions increases the teaching loads of instructors. It does not permit them enough time for thorough preparation of their lessons, trial of new techniques, or careful evalua- tion of their own work and students' achievement. 11. Continuity from one level to another seems to be lacking in many of the programs. In some programs integration between formal course work and practical work is to be desired.40 The problem with regard to teacher education in Arab countries is summed up in a paper given by Al-Roushad and Abdulatif at the Conference on Islamic Education held in Saudi Arabia in April 1977: It is noticeable that the programs of the colleges of education are so overloaded that the situation makes students suffer and complain. This situation is due to the constant competition among the subject teachers and teacher educators; each group thinks that their field of work is the only core of teacher preparation. We believe, therefore, that the time has come when a balance among the three essential cores of teacher prepa- ration must be initiated: (1) preparation in general education subjects; (2) preparation in a specialized field; and (3) pro- fessional preparation-training.4 Although these studies throw a flood of light on teacher preparation in general, none of the studies has examined a specific 40De Lamiama Saradatta and Poj Sapianchaiy, "Curriculum Evalua- tion in Teacher Education in Thailand" (paper presented at the Confer- ence on Curriculum Evaluation Teacher Education in S.E. Asia Organized by the Internal Council on Education for Teaching [ICET] and the Faculty of Education, University of Malaya [FEUM], August 3-7, 1970) (Malaysia: Malaya Publishing & Printing Co., 1970), pp. 87-88. 41A1-Roushad and Abdulatif, op. cit., p. 15. 44 curriculum in depth as does this study. The reason for this lack of scholarly interest in subject curricula is to be found in the fact that most colleges of education do not treat the teaching of such academic subjects as mathematics, physics, chemistry, biology, psy- chology, literature, etc., as one of their immediate and primary concerns. But the institution of the King Abdul-Aziz College of Education provides an excellent opportunity for a study of subject curricula, designed and executed by the College itself. CHAPTER IV PROCEDURE AND METHODOLOGY This survey research attempted to evaluate the mathematics cur- riculum given by the College of Education, Mecca, for teachers intend- ing to teach mathematics in the intermediate and high-school systems of Saudi Arabia from the perspective of teachers who were graduated from the College of Education with mathematics as their specialty. The study employed a combination of largely statistical and, in part, descriptive methods to analyze the data collected from the research questionnaire. Presented in this chapter, therefore, are the research questions and hypotheses, a description of the population, the sample used and the research questionnaire--its validity and reliability, the details of the procedure adopted to gather the data, and the techniques and procedures used for data analysis, the details of which are pre- sented at greater length in the following chapter. Based on the clusters of attitude questions, determined by an exploratory analysis and checked for reliability, scales were constructed to answer the following 12 research questions and test the following research hypotheses: Research Questions 1. Did the program enable student teachers to understand the objectives of teaching mathematics? 45 10. 11. 12. 46 Did the program in mathematics at Mecca College of Educa- tion enable them to understand basic mathematics to teach mathematics? Did the program prepare them for higher mathematics? Did the program help them understand the relationships between the school and college curricula? Did the program emphasize the practical, problem-solving nature of mathematics? Did the program prepare the student teachers for teaching mathematics at school? Did the program provide an adequate theoretical introduc- tion to methods of teaching mathematics? Did the program provide adequate student-teaching practice? Did the program relate its teaching to the philosophical objectives of Saudi education? Did the program adequately prepare student teachers to design curricula in mathematics? Did courses in educational psychology at the College of Education help student teachers to teach mathematics better? Did the program acquaint student teachers with the problems of teaching mathematics? Research Hypotheses The following eight null hypotheses were tested: 47 There is no significant difference in the evaluation of the mathematics curriculum of the College of Education by male and female respondents. There is no significant difference in the evaluation of the mathematics curriculum given by the College of Edu- cation, Mecca, by respondents who graduated either with 40 or 60 credit hours in mathematics. There is no significant interaction effect between the sex of the respondent and the type of graduation. There is no significant difference in the evaluation of the mathematics curriculum of the Mecca College of Educa- tion by respondents who teach either at the junior or senior high level. There is no significant interaction effect on the evalua- tion of the mathematics curriculum of the Mecca College of Education between sex of the respondent and the level at which the respondent teaches. There is no significant difference in the evaluation of the mathematics curriculum of the College of Education by respondents with an 80 percent or less teaching responsi- bility in mathematics and those with a 100 percent teaching duty. There is no significant interaction effect in the evalua- tion of the College of Education between the sex of the respondent and the percentage of mathematics teaching responsibility. 48 8. There is no significant difference in the evaluation of the mathematics curriculum by respondents who graduated in different years with mathematics as their specialty from the College of Education, Mecca. Population of the Study The population of this study comprised teachers who were graduated from the College of Education, Mecca, in the years 1975-76 to 1979-80 with mathematics as their specialty to teach mathematics in the intermediate and high-school systems in Saudi Arabia. The College of Education prepares two categories of mathe- matics teachers--those who have 40 credit hours in mathematics and 20 in a minor specialty, mostly physics, and those who take 60 hours in mathematics. For the purpose of this study, both categories of graduates were included in the population. The administration of the College of Education, Mecca, sup- plied the researcher with the numbers, names, and sex of the graduate population for each of the five years separately. It was found that 128 graduate teachers had completed their degree courses as mathemat- ics teachers either with 40 or 60 hours in mathematics. Furthermore, close inspection of the information collected from the administration revealed that of the total population of 128, 12 were non-Saudi stu- dents who had since gone back to their countries, presumably to teach. As the accessible population turned out to be relatively small, it was decided to administer the questionnaire to the entire population of 116 who could easily be reached. As Table l clarifies, all 49 .cwucogmms peach .coumsumsm pouch” opp mmp mm em up mp m_ m_ mm em Pouch mm mm m op o m m N m m om\mmmp mm mm N m m o m w m e mN\mump mm pm m m m m m 3 NF mp m~\-mp mm mm 1. t- t- t- t- 1. mm mm n~\ommp m_ up it -1 -t u- t- it mp m_ m~\mnmp .ammm .umsw .ammm .umsu .ammm .umsu .ammm .umsw .ammm .umsw quoh Pouch pouch Pouch Page». peace page» Page» npmuo» apogee m_esmd ope: mpmsmu ope: smm> .owmp gmzosgp mump .cowumuacu eo ommFFou move: we magmaumsm mowumsmspmztt.p m—nmh 50 respondents returned the completed questionnaires. It may well be assumed that this study was based on a 100 percent participation of the population. The Survey Instrument A research questionnaire was developed for the purpose of collecting research data. The development of the questionnaire involved several steps. First, a comprehensive review of the lit- erature related to educational evaluation was undertaken to acquire a sound background and knowledge in the construction of a question- naire relevant to the study. Second, based on the knowledge and background acquired, factors involved in the evaluation of the mathe- matics curriculum taught by the College of Education, Mecca, vis-a-vis effective mathematics teaching in intermediate and high schools of Saudi Arabia were identified to construct the questionnaire based on them. Third, the questionnaire was presented for review to the researcher's doctoral committee, and in light of their comments and suggestions, the questionnaire was revised and improved. Fourth, the approved and revised version was typed and made ready for adminis- tration to the population, and finally, the researcher had the question- naire translated into Arabic by a qualified translator. The accuracy of the translation was certified by A. Eldamatty. (See Appendix A.) The questionnaire is divided into five parts and has a total of 64 items, including Item 64 for subjective comments. The first part of the questionnaire contains 11 items concerning such variables as the respondent's sex, year of graduation, credit hours in 51 mathematics, the grade point average for the entire degree course as well as in mathematics, part- or full-time teaching responsibility in mathematics, the level at which the respondents were teaching, and the percentage of teaching responsibility devoted to mathematics. These variables formed bases for the eight hypotheses and the rela- tionship of the independent variables to the dependent ones. The second part of the questionnaire contains 15 items, intended to evaluate the adequacy of the professional courses that every graduate is required to take. It employs a scale of one to five, ranging from very positive to totally negative. In preparing this part of the questionnaire, care was exercised that every relevant course taken by the teachers was listed for graduates' evaluation. The third part consists of 22 items on the adequacy of the courses in mathematics given by the College of Education for teachers of mathematics at intermediate and high schools. Items 27 and 28 direct the respondents to evaluate concept-development and objectives- awareness-development capability of the mathematics curriculum of the College of Education. Items 29 through 36 seek to evaluate the individual items in the mathematics curriculum as they relate to their capability to enhance the teacher's ability to teach school mathematics. Items 37 through 41 relate to the objectives of the mathemat- ics curriculum, as stated by the Department of Mathematics of the College of Education, Mecca, and seek to elicit the respondents' views of whether those objectives are accomplished by the course. 52 Items 42 through 48 seek answers to the questions of whether research opportunities in curriculum planning, evaluation of courses, and so on, were or were not available. The fourth part of the questionnaire contains four items, 49 through 52, regarding the relationship between the College of Education mathematics curriculum and the curricula at intermediate and high schools. The fifth part, containing Items 53 through 64, presents recommendations that the respondents are directed to evaluate on a scale of one to five, ranging from very positive to totally negative. Also, this part includes Item 64, which makes it possible for the respondents to write in their subjective suggestions for the improve- ment of the mathematics curriculum of the College of Education. Validity of the Research Instrument Assuming that the validity of an instrument consists of its ability to measure what it set out to measure, the researcher took the following steps to insure the validity of the instrument. First, before and during the development of the questionnaire, the most reliable current publications on the validity of survey instruments were extensively consulted by the researcher. Second, members of the researcher's doctoral committee were constantly sought for advice all through the process of development of the instrument. Third, a tentative draft of the questionnaire was submitted to some English- speaking graduate students at Michigan State University for their comments. Fourth, the revised instrument, in light of the valuable 53 suggestions and comments emanating from step 3, was administered, at different times, to different groups of Saudi and non-Saudi students studying at Michigan State University. It was observed that the test respondents experienced no difficulty with regard to the language and meaning of the items. Fifth, the process was repeated with the Arabic translation of the questionnaire in Saudi Arabia, before the question- naires were distributed to the population. Sixth, based on the com- ments by the members of the researcher's doctoral committee and the graduate students to whom the questionnaire was submitted for review and on the observation of the results of the various administrations to ensure the validity of the instrument, the researcher revised the questionnaire thoroughly to meet the standards of clarity and accuracy. Whereas no statistical tests were performed to test the validity of the instrument, content validity was assumed to exist after these extensive review procedures. In the final version, the instrument was submitted to ten graduate students (five males and five females) at King Abdul- Aziz University for their approval. On their approval, the question- naire was administered to the population. Reliability of the Research Instrument Reliability is defined as obtaining the same result again if the instrument is administered to the same population on two different occasions. Validity and reliability are closely related: validity cannot rise above a certain point if the measure is inconsistent to some degree. To determine the reliability of the questionnaire by the method of internal consistency of items, the instrument was divided 54 into 11 subscales. The variables with a factor loading of i .40 and those that appeared to have a logical relation with the other variables of the set were used to compute Cronbach's Alpha and Standard Item Alpha of reliability, based on the Statistical Package for the Social Sciences reliability program. The following coefficients of reliability were obtained for the clusters of responses listed for each scale in Table 2. Table 2.--Subscales, clusters, and coefficients of reliability. Coefficient of Scale Clusters Reliability Understanding the objectives A28,A39,A40,A4l, .80 of teaching mathemat1cs A43,A45,A48,A49 Understanding basic mathe- A27,A29,A30,A3l, .80 matics to teach mathemat1cs A32,A33,A35 Preparation for higher A37,A38,A42, 72 mathemat1cs A44,A47 ’ College-school relations A53,A54,A56,A58 .67 Emphasis on practical problems A55,A60,A61 .64 Preparation for school teaching A36,A38,A50,A5l ,A52 .65 Methods of teaching mathematics A19,A25 .77 Student teaching A18,A20,A26 .59 Educational thought A12,A13,Al4 .64 Educational psychology ' A12,A16,A23 . .54 Problems of teaching mathematics A44,A45,A46 .65 Table 2 indicates that there was a high correlation among the responses of the population to questions that have close logical 55 relationships among one another. One can conclude, based on these results (H’ the internal reliability of items, that the research questionnaire has an acceptable level of reliability for the purposes of this study. Data Collection The registrar's office of the College of Education supplied the researcher with a list of teachers who had been graduated with mathematics as their main teaching specialty in the years 1975-76 through 1979-80. Then the Ministry of Education and the General Presidency of Schools for Girls, Saudi Arabia, were contacted for information regarding the current location of the male and female graduate teachers who had earned their degrees as mathematics teachers from the College of Education in the years 1976 through 1980. Male Graduate Teachers The researcher was able to contact each individual male teacher and deliver the questionnaire personally. In most cases, he was able to collect the completed questionnaire personally, and when, for reasons of logistics, the completed questionnaire could not be collected personally, the individual divisional offices concerned undertook to collect the teachers' sealed responses and deliver them to the researcher. Female Graduate Teachers In the case of female graduates, the General Presidency of Schools for Girls, which oversees the education of females from 56 the elementary to the university level, made available the services of one of its representative female assistants to help locate the 40 female graduates, deliver the questionnaires, and collect the completed sealed responses from the entire female population. Graduates Studying Abroad It was found that four members of the population had pro- ceeded abroad for higher degrees in education. The questionnaires were mailed to each one of them, after ascertaining their addresses. Within a short time, all of them returned the completed questionnaires to the researcher. Thus, 100 percent participation of the population was achieved for the purposes of this study. Data Analysis The responses were coded-and the results keypunched for com- puter processing. The Statistical Package for the Social Sciences (SPSS)1 was used for various computational procedures employed. Besides simple frequencies, an exploratory factor analysis was undertaken to determine the existence of any clusters of items among the attitude questions asked. Clusters found were used to construct scales to answer the 12 research questions regarding the quality of the mathematics program at the College of Education, Mecca. After a reliability check of the scales was performed, the scales were used to test the research hypotheses based on the analysis of covariance. 1Norman Nie, H. Hull, C. Hadulai, Jean G. Jenkins, Karin Steinbrenner, and Dale Bent, Statistical Package for the Social Sciences (New York: McGraw-Hill Book Co., 1975). 57 Summary This chapter contained a discussion of the procedure and methodology used to evaluate the curriculum of mathematics given by the College of Education, Mecca, for teachers of mathematics at intermediate and high schools of Saudi Arabia, from the perspective of the mathematics graduate of the College of Education. In addition, 12 research questions were identified, which the researcher sought to answer, and eight research hypotheses were stated, which the investi- gator attempted to test. Described in detail were the population for the study, the sample who responded to the questionnaire, which in itself was fully analytically described, how the respondents were located, and the procedures adopted to administer and analyze the data. CHAPTER V ANALYSIS AND INTERPRETATION OF THE DATA The purpose of this chapter is to analyze and interpret the data derived from the responses of teachers who graduated from the College of Education, Mecca, with mathematics as their teaching specialty, in the years 1975-76 through 1979-80. A simple frequency analysis of the responses of the population to the questions contained in the questionnaire (see Appendix A) and an exploratory factor analy- sis, with a factor loading of i .40 and higher, were used to test the following eight research hypotheses: 1. There is no significant difference in the evaluation of the mathematics curriculum of the College of Education by male and female respondents. There is no significant difference in the evaluation of the mathematics curriculum given by the College of Edu- cation, Mecca, by respondents who graduated either with 40 or 60 credit hours in mathematics. There is no significant interaction effect between the sex of the respondent and the type of graduation. There is no significant difference in the evaluation of the mathematics curriculum of the Mecca College of Educa- tion by respondents who teach either at the junior or senior high level. 58 59 There is no significant interaction effect on the evalua- tion of the mathematics curriculum of the Mecca College of Education between sex of the respondent and the level at which the respondent teaches. There is no significant difference in the evaluation of the mathematics curriculum of the College of Education by respondents with an 80 percent or less teaching responsi- bility in mathematics and those with a 100 percent teaching duty. There is no significant interaction effect in the evalua- tion of the College of Education between the sex of the respondent and the percentage of mathematics teaching responsibility. There is no significant difference in the evaluation of the mathematics curriculum by respondents who graduated in different years with mathematics as their specialty from the College of Education, Mecca. Factor analysis was used to determine groups of variables with a common factor to explore the following 12 research questions regarding the mathematics curriculum of the College of Education, Mecca: Did the program enable student teachers to understand the objectives of teaching mathematics? Did the program in mathematics at Mecca College of Educa- tion enable them to understand basic mathematics to teach mathematics? 60 3. Did the program prepare them for higher mathematics? 4. Did the program help them understand the relationships between the school and college curricula? 5. Did the program emphasize the practical, problem-solving nature of mathematics? 6. Did the program prepare the student teachers for teaching mathematics at school? 7. Did the program provide an adequate theoretical introduc- tion to methods of teaching mathematics? 8. Did the program provide adequate student-teaching practice? 9. Did the program relate its teaching to the philosophical objectives of Saudi education? 10. Did the program adequately prepare student teachers to design curricula in mathematics? 11. Did courses in educational psychology at the College of Education help student teachers to teach mathematics better? 12. Did the program acquaint student teachers with the problems of teaching mathematics? Tabulation and Analysis of the Survey Results In Appendix B, the frequencies of responses to all questions of the survey instrument are presented, with the exception of item 010, which reads "List the subject or subjects, other than mathe- matics, that you teach," since the entire population had no response to this question. A summary of the results, as listed in Appendix B, follows. 61 Personal Background See Table B-l.1, Appendix B, for background information on the respondents. Of the 116 respondents who returned the question- naire, 76 were men and 40 were women. There appears to be no significant pattern of enrollment of students for mathematics, as represented by the number of teachers graduating during the five academic years, 1975-76 through 1979-80, except that the enrollment of women teachers specializing in mathe- matics began to rise since 1977-78, when they first started enrolling, until 1979-80, when their number rose to 17 against the 16 men enrolled for the program, as Table 3 clarifies. Table 3.--Enrollment of males and females in mathematics department of Mecca College of Education, 1975-76 through 1979-80. Year Males Females 1975-76 16 -- 1976-77 23 -- 1977-78 . 18 13 1978-79 10 15 1979-80 16 17 Total 83 45 Table 3 further indicates that the Saudi teachers who gradu- ated from the College of Education, Mecca, with mathematics as their teaching specialty were 16 in 1975-76, 23 in 1976-77, 31 in 1977-78, 25 in 1978-79, and 33 in 1979-80. 62 A significant majority of the graduates, namely 74 out of 116, comprising 63.8 percent of the total number of respondents, graduated with 40 credits as compared with only 42 individuals, constituting 36.2 percent of the total, who graduated with 60 credits in mathemat- ics. This suggests that the majority of the teachers received aca- demic training to teach a subject other than mathematics. Academic Performance See Table B-l.2, Appendix B, for complete information on aca- demic performance of respondents. Frequency analysis of the overall GPA of the respondents indicated that 53.5 percent of the respondents had their GPA between 2.51 and 3.5, with the 2.01 to 2.5 range fol- lowing a close second, totalling 44.8 percent. Only two teacher graduates entered the profession with a grade point average between 3.51 and 4.0. Twelve graduates (10.3 percent) had only passing grades on their transcripts. However, the comparison with their grade point average in mathematics indicated that the graduates had a better average in their specialty than their overall average. Working,Situation Table B-l.3, Appendix 8, contains information on the respond- ents' working situation. Of the 116 respondents, 83 were teaching at the middle-school level, 28 at the high-school level, and only 1 at the junior-college level. Four respondents were studying for advanced degrees in the United States. In other words, 96.6 percent of those responding stated that they were working as full-time teachers, and the rest were studying abroad. 63 Of those currently teaching in Saudi Arabia, all but one were required to teach mathematics. Thirteen, or 11.2 percent, indicated that in addition to teaching, they had administrative responsibilities. A vast majority (75.9 percent) indicated a 100 percent responsibility in teaching mathematics, with some 21.4 percent indicating they had only 80 percent or less mathematics-teaching responsibility. Education Curriculum Table B-2, Appendix B, is a tabulation of the evaluation of education curricula at the College of Education, Mecca, by the respondents. On the whole, the evaluation was positive to mixed. The least positive evaluation of a mean of 3.2 on a scale of 1 (very positive) to 5 (very negative) was elicited in response to 021, which reads as "Education in Saudi Arabia," and the most positive ratings were registered with regard to the two courses in student teaching (020 and 026). Mathematics Curriculum In Table B-3, Appendix B, responses to questions Q27 through 048, dealing with the various aspects of the mathematics curriculum, are presented. The graduates, responding to these questions, were directed to indicate how well the curriculum of the College of Edu- cation prepared them to teach certain courses at the schools (Q29- Q36) and to function as effective teachers. Of the first two funda- mental questions, Q27 (the courses in mathematics were valuable in helping me understand the basics of mathematics) and 028 (to under- stand the objective of teaching mathematics in school), the former 64 was answered in a more positive manner than the latter, with mean ratings of 2.1 and 3.2, respectively. They considered themselves most prepared to teach algebra, its having the most positive rating (mean = 1.7), whereas they considered themselves least prepared for arithme- tic, its having the least positive rating (mean = 2.5). Ratings of global aspects of mathematics curriculum at the College of Education again were generally positive, with values ranging from 2.3 (competently trained in the methods of teaching mathematics) to 3.3 (insights into developing curricula at school). Finally, with respect to research and practical experience in curriculum planning, assessment of courses in mathematics, etc., the most positive rating of 2.7 was recorded in answer to the question, "The program provided me with enough research opportunity into the problems of teaching mathematics, whereas the least positive was in response to the question about ". . . enough opportunity . . . textbook writing," with a mean equal to 3.9. College-School Relationships Finally, responses to the questions concerning the relation- ship between what is being taught at the College of Education and how much of it is of practical use in the Saudi school setting are pre- sented in Table B-4, Appendix B. It is in this group of questions, Q49 through Q63, that the most negative ratings were encountered. In fact, the two most negative ratings were with regard to the relation- ship between the school and college curricula, in response to questions Q53 (College program ought to have a closer bearing on teaching mathe- matics at school), with a mean = 4.8, and 054 (There should be closer 65 contact between school and the department of mathematics), with a mean = 4.8. The most positive rating was in response to question Q49 (There is a high correlation between objectives of mathematics curriculum at school and the course objectives for mathematics at the College of Education), with a mean = 3.2. Open-Ended Responses Of the 116 graduate teachers, 88 chose to respond to the open-ended Question 64, eliciting their personal suggestions and recommendations. Their answers may be summarized as follows: 1. Thirty-one graduates suggested that more emphasis be given to mathematics courses and that education courses be reduced. 2. Seventeen teacher graduates complained that the College of Education does not have a lab for students to experiment in. They suggested the provision of one such laboratory. 3. Nineteen respondents suggested that the College of Educa- tion should teach courses relevant to intermediate and high-school curricula during the last two years of their schooling at the College of Education. 4. Thirty respondents complained of the nonavailability of books other than the textbooks in the College library. They sug- gested that the latest material in the subject of their specializa- tion be made available in the library. These same 30 graduates suggested that the prospective teachers at the College of Education 66 should have access to standard and current books on the subject in addition to the class notes. 5. Thirty-two respondents suggested that more emphasis be given to those courses of mathematics that have a close and imme- diate bearing on the subjects they have to teach at school. 6. Thirty-five respondents demanded better-qualified instructors. 7. Thirty-nine teachers repeated the charge that there is little relationship between the courses taught by the College and the curricula at school. 8. Twenty-three respondents recommended that work load in mathematics for graduating teachers be increased considerably. They made a specific mention of course 490 (Mathematics for Interme- diate and High School), which has a direct bearing on courses taught at the intermediate and high-school levels. 9. Forty-two respondents recommended the improvement of supervision of student teachers. 10. Forty-four participants in this study recommended the immediate establishment of a well-equipped media center to aid the practicing teachers. 11. A particularly pointed recommendation was made by 18 women teachers--that they should be taught by a "live" woman instruc- tor instead of being taught by a male instructor over a closed-circuit TV network. 67 Exploratory Factor Analysis and Reliability As a second step of data analysis, an exploratory factor analysis was undertaken to determine the existence of any groups of variables that might be converted into useful evaluation scales with regard to the mathematics program at the Mecca College of Education. The results of the factor analysis are presented in Appen- dix C. As may be noted from Table C-3, Appendix C, some 17 factors were extracted initially. A rotated factor matrix is presented in Table C-4 of the same appendix. Initially, variables with a factor loading of i .40 and higher, and/or the variables that appeared to have a logical rela- tionship with the other variables of the set, were selected and grouped together (see the starred factor loading in Table C-4). Next, Cronbach's Alpha and Standardized Item Alpha, using the Reliability Program of SPSS, were computed for each set of variables ("scale") selected from the factors in the previous step. Each scale with a reliability index of .50 or more was characterized as a dimen- sign_for further analysis. The results of the reliability analyses are presented in Appendix D. Each dimension, together with the results of the relia- bility analysis, is described as follows: Dimension 1 consists of the following variables (see starred factor loadings on Factor 1 in Appendix Table C-4 and Table D-l, Appendix D). 68 A28 Understand objectives of teaching math A39 Competent to critically assess programs A40 Able to construct adequate tests A41 Competent in methods of teaching math A43 Assessment of math courses A45 Problems of teaching math A48 Evaluation and grading A49 High correlation between college and school The scale resulting from this analysis was summarized and labeled as "Understanding the Objectives of Teaching Mathematics." With an alpha = .79795, the scale was considered sufficiently reliable for further analyses. Dimension 2 consists of variables with high factor loadings on Factor 2 and Factor 7 (see starred factor loadings in Table C-4 and Table D-2). These two factors were combined because they dealt inherently with basic mathematics. The following variables made up this dimension, which was summarized and labeled as "Understanding Basic Mathematics to Teach Mathematics": A27 Understand basic math to teach math A29 Algebra A30 Geometry A31 Trigonometry A32 Calculus A33 Arithmetic A35 Analytical Geometry .80242, this scale was also With a reliability coefficient of alpha considered reliable for further analysis. Dimension 3 consists of the following variables (see starred factor loadings on factor 3 in Table C-4 and Table 0-3). 69 A37 Prepared for higher studies in math A38 Insight to develop math curricula A42 Curriculum planning in math A44 Concept development in math A47 Math textbook writing As a result of the reliability analysis (alpha = .72138), Dimension 3 merited inclusion for future analyses and was summarized and labeled as "Preparation for Higher Mathematics." Dimension 4 deals with the relationship between the college program and its application to the intermediate and high schools. This dimension consists of the following variables (see starred fac- tor loadings on Factor 4 in Table C-4 and Table D-4). A53 College program closer to teaching in schools A54 More contacts between schools and college A56 More relevance for needs of schools A58 College to offer in-service refresher With alpha = .66551, the scale demonstrated an acceptable level of reliability and was considered for further analyses under the label "College-School Relations." Dimension 5 consists of only three variables (see starred factor loadings on Factor 5 in Table C-4 and Table 0-5). A55 More seminars between college and schools A60 Greater emphasis on practical problems A61 More experiments with new teaching methods This dimension deals with another aspect of college-school relation- ships, namely the degree of mutual cooperation. Again, with alpha = .63967, it was considered valuable for further analysis and was labeled as "Emphasis on Practical Problems." Dimension 6 consists of the following variables (see starred factor loadings on Factor 6 in Table C-4 and Table D-6). 70 A36 Modern mathematics A38 Insight to develop math curricula A50 Half material taught never used in school A51 College ignores difference in schools A52 College does not prepare adequately At first sight, there appeared to be a lack of correlation between the variables making up this factor, but on closer examination, it was summarized and labeled as "Preparation for School Teaching." A reliability alpha = .65407 was considered indeed sufficient for further analyses. Dimension 7 consists of only two variables (see starred fac- tor loadings on Factor 8 in Table C-4), both, 019 (Methods of teaching math [1]) and 025 (Methods of teaching math [2]), dealing with the methods of teaching mathematics. A reliability could not be com- puted, but a scale consisting of these two items was constructed in view of the high intercorrelation of r = .767 for the two items (see starred correlation in Table C-2). Dimension 8 consisted initially of three variables (see starred factor loading on Factor 9 in Table C-4 and Table D-7). A18 Education media A20 Student teaching [1] A26 Student teaching [2] However, a substantial increase in reliability of the scale, as well as an increased degree of coherence in the scale, i.e., a change of alpha from .58935 to .755, was detected if item A18 was deleted. It was decided to use only items A20 and A26 for a scale labeled "Student Teaching." Dimension 9 initially consisted of three items (see starred factor loadings on Factor 10 in Table C-4 and Table D-8). 71 A12 Introduction to education and psychology A13 Social and philosophical foundation of education A14 Development of educational thought However, deletion of the first of these items increased both the degree of reliability from .637 to .723 and the internal consistency of the scale. Hence the decision was made to reduce the scale to all but two items, labeling it as "Education Thought." Dimension 10 initially consisted of three items (see starred factor loadings on Factor 11 in Table C-4 and Table D-9). A17 Principles of curriculum A24 Curriculum design A62 Better preparation for test and evaluation From the results of the reliability analysis, it was noted that only by dropping item A62 would a reasonable level of reliability be estab- lished for this scale, and some measure of consistency of the items would be achieved, resulting in a scale labeled as "Curriculum Design." Dimension 11 consists of three items dealing with different aspects of educational psychology (see starred factor loadings on Factor 12 in Table C-4 and Table D-lO). A12 Introduction to education and psychology A16 Educational psychology (childhood and adolescence) A23 Introduction to counseling and mental hygiene The reliability for the scale resulting from the analysis was alpha = .54327, being sufficiently high to be included for further analysis. This factor was labeled "Educational Psychology.“ Factor 13 included three items (see starred factor loadings in Table C-4 and Table D-ll) with high factor loadings. The relia- bility for this group of items was close to zero; hence it was dropped from further consideration. 72 Dimension 12 consists of three variables (see starred fac- tor loadings on Factor 14 in Table C-4 and Table D-12): A44 Concept development in math A45 Problems of teaching A46 Mathematics in general They were summarized under the label "Problems of Teaching Mathematics," and with a reliability coefficient, alpha = .65382, this scale was treated as significant for further analysis. Finally, questions associated with the following three factors didn't demonstrate sufficient reliability to form a scale or dimension: Factor 15 consisted of three items with high factor loadings (see Table C-4 and Table D-l3). The reliability determined for this group of items was close to zero. Thus, the factor was dropped out of any further consideration. Factor 16 was based on three items with high factor loadings (see Table C-4 and Table D-l4). Even though the degree of reliability was moderately high (alpha = .50), the items did not show any internal coherence. The factor was dropped out of further consideration. Factor 17 was made up of three items with high factor loadings (see Table C-4 and Table D-l5). Again, as was the case with Factors 13 and 15, because of a very low degree of reliability, the items were excluded from any further analysis. In summary, it may be noted that the original 52 questions dealing with the different aspects of the mathematics curriculum of the College of Education at Mecca resulted in 12 usable scales, deal- ing with the following 12 dimensions of the program: 1. Understanding the Objectives of Teaching Mathematics 2. Understanding Basic Mathematics to Teach Mathematics 73 Preparation for Higher Mathematics College-School Relations Emphasis on Practical Problems 0301-4301.) Preparation for School Teaching 7. Methods of Teaching Mathematics Student Teaching 9. Educational Thought 10. Curriculum Design 11. Educational Psychology 12. Problems of Teaching Mathematics From the exploratory factor and the reliability analyses, 12 scales (see Appendix D) encompassing the 12 dimensions were con- structed in the following manner. Each scale was treated as consist- ing of the mean response over the items that contributed to the cor- responding dimension; for example, for Dimension 1, "Understand the Objectives of Teaching Mathematics," consisting of variables A28, A39, A40, A41, A43, A45, A48, and A49, the mean response of a given respondent was computed as (A28 + A39 + A40 + A41 + A43 + A45 + A48 + A49)/8. No adjustment had to be made for missing data, as all respondents answered all questions. Similar computations were made for the other 11 dimensions. In Table 4, means and standard deviations are presented for each of these 12 dimensions. The results presented in Table 4 may be summarized as follows: The two practical activities--method of teach- ing mathematics (007) and student teaching (008)--received the most positive ratings, whereas the college-school relationship (004) and the emphasis on practical problems (005) were rated most negatively. 74 "Preparation for Higher Mathematics" (003) was rated at the negative end of "uncertainty" (i.e., m = 3.35), and the remaining dimensions were evaluated between positive and uncertain. Table 4.--Mean§iand standard deviations of the 12 dimensions. Dimension Cases Mean DESngign 001 116 2.7985 .6884 002 116 2.0714 .6713 003 116 3.3517 .6738 004 116 4.7802 .3599 005 116 4.2678 .5904 006 116 3.3034 .7158 007 116 1.3276 .6760 008 116 1.2371 .5426 009 116 2.7672 .0288 010 116 2.1897 .8960 011 116 2.3132 .8527 012 116 2.8736 .8278 a1 = very positive to 5 = very negative. In Table 5, intercorrelations between the 12 dimensions repre- sented by the 12 factors evaluating the mathematics curriculum at Mecca College of Education are presented. From Table 5, it is clear that most correlations were not statistically significant. Of the statistically significant relationships found, even the most signifi- cant one between 001 and 012 (r = .58) represented a relatively low percentage (.582 = 34 percent) of variance from one variable to 75 ..o>o_ Po. a tee ca oeaoaeaemea up oem~.n a c Posop me. u ago ea oeaoeceemwa a? eemp.n a s .oo_ a e new: "oocz No. mo. mp.- as. co. am. mo.- NF.- mm. mm. mm. N_o AN. aw. 3F. mo. Nu. m... Fo.- om. mp. e_. __o mo. mo. NP. ac. oo.- mo.- mo. mo. mo. o_o me. _o. ao.- .o. mo.- so.- mp.- ao.- ace me. we.. P~.- a..- e_.- Nu. mo. moo No. m_.- mo.- oo.- mm. _o. Koo mo. Po. om. aw. em. cog am. we. _m.- mo.- moo mo. m~.- eo.- ace mp. ea. moo mm. Noe __o OPQ woo moo Koo coo moo eon moo Non _oo .Ampp n zv mwmxpecm souowm Ease umao_m>mc mmpmom NF cmmZHmn mcowpepmssou comcmma11.m open» 76 another. Thus, it led to the conclusion that on the whole, the 12 scales arrived at through the above process of exploratory factor and reliability analyses were dealing with relatively independent and different aspects of the curriculum under study. Testing of Hypotheses Each of the 12 factors encompassing the dimensions of the curriculum embodied in the questionnaire was used to test the eight hypotheses presented at the beginning of this chapter. In all cases, an analysis-of—covariance design was used. For example, the overall GPA and the mathematics GPA were used as covariates, to the extent that the relative academic success of the program might influence the attitudes of the respondents toward both the college curriculum and the respondents' present work setting. The independent vari- ables to be treated in the analyses were determined by the following hypotheses to be tested: 1. Sex of the respondent 2. Whether the respondent graduated from a 40- or 60-hour program 3. Interaction between the sex of the respondent and the type of program 4. Whether the respondent teaches at the junior- or senior- high-school level 5. Interaction between the sex of the respondent and the school level 6. Percentage of mathematics teaching duty 77 7. Interaction between the sex of the respondent and the percentage of mathematics teaching 8. The year the respondent graduated from Mecca College of Education, or the years he/she had been teaching. This hypothesis was dealt with separately for male and female teachers, as there were no women graduates until 1977-78, although men teachers have been enrolling in the mathe- matics program since 1952. An overview of the results is presented in Table 6, indicating that, in general, there was little difference between different groups of respondents in regard to their evaluation of the mathematics curric- ulum. AnaLysis of Variance The complete results for the analyses of covariance are pre- sented in Appendix E, whereas below only significant and near- significant results (p < .10) are mentioned in detail. Each of the 60 analyses of covariance presented in Appendix E consists of two sections: (a) the results of the covariance proper and (b) the table of cell means. The analysis of covariance itself gives the dependent variable (i.e., one of the 12 scales or dimensions of evaluating the mathe- matics curriculum at Mecca College of Education) and the independent variables (derived from the hypotheses to be tested, i.e., sex of the respondent, type of program the respondent graduated from, percentage 78 .mflucnumcp ”mg—u cw =o>pm m_ a o: aoeae "Seao.c.em.a so: a. <>cz< age .p v a code 1 1 1 ON. 1 1 1 1 KN. a N:— _v _v pv mm.— Fv pv _v —v m~.p a up. 1 1 1 1 1 1 aN. 1 a __o am._ —v —v .v —v —v —v m_.~ _v a mm. 1 1 cc. 1 ep. 1 cN. m_. a o_o m_.— _v _v oc.m —v mm.— pv e~.— mp.~ a an. 1 m_. 1 1 1 1 1 1 8 ea._ .v mm._ Po _v .v .v Po .v a mom 1 mo. cm. 1 mo. 1 ma. 1 1 a m a .v ae.~ we._ .v ma." .v we.m .v .v a o 1 cm. 1 1 me. mm. .o. 1 1 a Nan pv ~_.p _v —v am.~ we._ pm.“ pv pv a - - - - - - 1 2. - a .v Po .v .v _v .v .v mm._ pv a can 1 1 1 mm. 1 mm. 1 1 mp. a mac pv —v —v mm._ _v oo.— .v pv mo.~ a m.. mp. 1 am. 1 a.. 1 .N. 1 a ace .m._ No.— .v mm.p .v c~._ Fv mm._ —v m - - - a. - - - - 8. a .v .v _v e~._ .v .v _v .v ae.m a men - No. 1 4.. 1 P~. 1 aN. 1 a «on —v pm.~ —v —~.~ —v «9.. pv m_.— _v m GN. 1 no. mo. 1 1 1 1 1 ea .oo ~¢._ pv mo.m ¢—.m pv pv .v _v —v a usao> xgma> can: a x xom .guamp gun: a poonom x xum maze poogom Encmoga5.xom mash Eggnog; xom m mpmoguoa»: m m_mocuoaxz o mpmoguoaa: m mpmocuoa»: v mwmoguoq»: m m.muguon»: N m.mozuon>: p mvmozaoaxx .mmmmcuoaxz usu mc—ummu mo mu—ammc mo 3mv>gw>011.o o_nah 79 of teaching mathematics, and whether the respondent teaches at a middle or high school). In the case of the independent variable "year graduated from Mecca College of Education," a separate analysis was performed for male and female teachers because men teachers have been graduated since the 1975-76 school year, whereas women teachers have been graduated only since the end of the 1977-78 school year. The covariates for all analyses were the general GPA and the specific mathematics GPA. The kind of ANCOVA performed by the SPSS-program "ANOVA"] considered and adjusted for the covariates first, next for the indi- vidual factors, and finally for the interaction effects. The second section of Appendix E presents cell means and frequencies for the entire population, as well as broken down for the categories of the factors used in the ANCOVAs and the interaction effects. In the following discussion, each dimension is considered individually. Dimension 1: "Understanding the Objectives of Teaching Mathematics." The complete results of the ANCOVAs are presented in Tables E-l through E-5 in Appendix E. As noted in Table 4, the overall rating of this aspect was 2.8 on a scale of 1 (very positive) to 3 (uncertain) to 5 (very negative). In other words, the respond- ents as a whole were "uncertain" if the course made them aware of 1Nie et al., op. cit., pp. 410-33. 80 the objectives of teaching mathematics. It may be noted from Table 6, as well as from the results presented in Table E-3, that the only significant differences appeared to be between the respond- ents who taught either 80 or 100 percent mathematics: Those who had a 100 percent mathematics teaching duty evaluated their understanding of the objectives somewhat more negatively. With regard to the interaction effect between the sex of the respondent and the per- centage teaching duty, a statistically significant difference was noted. Men teachers as a group rated understanding of the objectives more positively, with a mean of 2.9, than women teachers with 80 percent teaching duty (m = 3.3), while women teachers with a 100 percent teaching duty gave a considerably more positive rating response with a mean of 2.6. Dimension 2: "Understanding Basic Mathematics to Teach Mathematics." The complete results of the ANCOVAs are presented in Tables E-6 through E-lO. As may be noted from Table 4, the overall rating of this dimension was moderately positive, with a mean of 2.07. With regard to different hypotheses to be tested, it may be added that no statistically significant differences were found between different groupings of respondents, except for a quasi-significant relationship with regard to the year of graduation for men students. In particular, the two classes graduating in 1978-79 and 1979-80 rated it somewhat more positively than the group graduating earlier (see Table E-9). 81 Dimension 3: "Preparation for Higher Mathematics.9 The complete results of the ANCOVAS are presented in Tables E-ll through E-15. As may be noted from Table 4, the overall rating of this dimen- sion was 3.35, or tending to be negative without being definitely negative. Relevant to the different hypotheses to be tested, only one quasi-significant difference was found between men and women teachers (see Table E-ll). Women teachers appeared to rate their preparation for higher mathematics more negatively than did men teachers. Dimension 4: "College-School Relationships." The complete results of the ANCOVAS are presented in Tables E-16 through E-20. As may be noted from Table 4, the overall group rating of this aspect as well as the one represented by Factor 5 was most negative, with a mean = 4.78. In other words, the need for an improved college-school relationship and cooperation was seen as most desirable by the group as a whole. No statistically significant differences were found in any of the analyses of covariance. Dimension 5: "Emphasis on Practical Problems." The complete results of the ANCOVAS are presented in Tables E-21 through E-25. The negative rating of this aSpect was much the same as that of Dimension 4, with a mean = 4.37. All groupings rated the current emphasis on practical problems equally negatively. Dimension 6: "Preparation for School Teaching." The complete ANCOVAS for this dimension are presented in Tables E-26 through E-30. The overall rating of the group was 3.3, which tended to be negative 82 without being definitely negative. Again, as was the case with the previous two factors, there were no statistically significant differ- ences in ratings between various groups of respondents. All rated themselves as being more or less prepared. Dimension 7: "Methods of Teaching Mathematics." The complete ANCOVAS for this dimension are presented in Tables E-3l through E-35. As may be noted from Table 4, the overall rating for this dimension by all respondents was 1.33, nearly "very positive." Statistically sig- nificant group differences were found with respect to the interaction of the sex of the respondent and whether the graduate had 40 or 60 credit hours in mathematics. As may be noted from Table E—31, women teachers who took a 40-hour course and men teachers who took the 60-hour program rated this dimension of the curriculum as practically "very good," whereas the other two groups, i.e., men teachers who had had the 40- hour program and women teachers with 60 hours in mathematics, rated Methods of Teaching Math somewhat less positively, but somewhere between positive and very positive. Another tendency, though not completely statistically significant, was found in the interaction between the sex of the respondent and the level at which the respond- ent was teaching (see Table E-32). Although the men teachers on the whole rated this dimension of the curriculum the same way as the whole group, female teachers teaching at the middle-school level rated the methods of teaching mathematics better than the group average, and those teaching at the senior-high level, below the group average. 83 Dimension 8: VStudent Teaching." Complete results of the ANCOVAS are presented in Tables E-36 through E-40. As may be noted from Table 4, the overall group rating of this dimension was again very positive, with a value of 1.24. In terms of the group differ- ences, the same results as the above may be noted in the interaction effect between the sex of the respondent and the 40- versus 60-hour program. As may be seen from Table E-36, the women teachers with the 40-hour program and the men teachers graduating with 60 hours in mathematics rated the student-teaching courses as better than did the other two groups of teachers. The same relationship may be noted in the interaction effect between sex and level of teaching (see Table E-37): Women junior-high-school teachers and men senior-high-school teachers rated the student-teaching experience as better than did men junior-high teachers and women senior-high teachers. Finally, a tendency, yet not firmly statistically significant, was found for the men teachers, graduating in different years from Mecca College of Education. Thas is, more recent graduates tended to rate the experi- ence more positively than earlier graduates (see Table E-39). Dimension 9: "Educational Thought." Complete results of the ANCOVAS regarding this aspect are presented in Tables E-41 through E-45. As may be noted from Table 4, the overall rating of this dimen- sion was 2.77. No statistically significant differences were found across different groups of respondents. Dimension 10: "Curriculum Design." Complete ANCOVAS are presented in Tables E-46 through E-50. As may be noted from Table 4, 84 the overall rating for this dimension was 2.19, a fairly high positive rating for the whole group. It may be seen from Table E-48 that there was a tendency for respondents with an 80 percent teaching responsi- bility in mathematics to evaluate this dimension somewhat more posi- tively than for respondents with a 100 percent teaching duty in mathematics. Dimension 11: "Educational Psychology." Complete ANCOVAS are presented in Tables E-51 through E-55. As may be noted from Table 4, the overall rating for this dimension was 2.31. No statistically significant differences were found in terms of various groupings of respondents. Dimension 12: "Problems of Teaching Mathematics." Complete ANCOVAS are presented in Tables E-56 through E-60. As may be noted from Table 4, the overall rating for this dimension was 2.87, a moderately positive rating. No statistically significant differences were found for different groupings of respondents. Summary of the Results With regard to the eight hypotheses proposed at the beginning of this chapter, the overview, as presented in Table 6, is summarized as follows: Hypothesis 1: No statistical 1y significant differences were found between men and women teachers in the way they evaluate the program. Only one tendency was found with regard to the Preparation for Higher Mathematics. That is, the women teachers tended to evaluate this aspect of the curriculum more negatively than did the men teachers. 85 Hypothesis 2: No statistically significant differences were found between graduates with 40 hours in mathematics and those with 60 hours with regard to this hypothesis. No statistically significant differences in the evaluation of any dimension of the program were found. Hypothesis 3: No statistically significant interaction effects were found between the sex of the respondent and his/her having gradu- ated with a 40- or 60-hour program. On one dimension--Methods of Mathematics Teaching--a statis- tically significant relationship was observed: women teachers who took a 40-hour course and men teachers who took the 60-hour program rated this dimension of the curriculum as practically "very good," whereas the other two groups, i.e., men teachers who had had the 40-hour pro- gram and women teachers with 60 hours in mathematics, rated Methods of Teaching Math somewhat less positively, but somewhere between positive and very positive. Hypothesis 4: No statistically significant differences were found between respondents teaching at the junior- and senior-high level. No statistically significant differences were found for any of the dimensions evaluated. Hypothesis 5: No statistically significant interaction effects of the sex of the respondent and his/her teaching at the junior- or senior-high-school levels were found. Only On two dimensions, 7 and 8, were statistically significant relationships observed: (a) the women teachers with the 40-hour program and the rmw1 teachers graduating with 60 hours in mathematics rated the 86 student-teaching courses as better than did the other two groups of teachers, and (b) men teachers on the whole rated this dimension of the curriculum the same way as the whole group, but female teachers teach- ing at the middle-school level tended to rate the methods of teaching mathematics better than the group average, and those teaching at the senior-high level, below the group average. Hypothesis 6: No statistically significant differences were found between respondents with a 100 percent teaching duty in mathemat- ics and respondents with an 80 percent or less teaching responsibility. No statistically significant differences in the evaluation of any dimension of the program were found. Hypothesis 7: No statistically significant effects of the sex of the respondent on the percentage of mathematics teaching responsibility were found. On only one dimension was a statistically significant relation- ship observed: men teachers as a group rated understanding of the objectives more positively, with a mean of 2.9, than women teachers with 80 percent teaching duty (m = 3.3), while women teachers with a 100 percent teaching duty gave a considerably more positive rating response with a mean of 2.6. Hypothesis 8: No statistically significant differences in response for the respondents who graduated in different years from the College of Education, Mecca, were found. No statistically significant differences in any of the dimen- sions evaluated were found regarding the women respondents, who were graduated between 1977-78 and 1979-80. 87 The men respondents who were graduated between 1975-76 and 1979-80 revealed a tendency toward differences in their responses with respect to Dimension 2, Understanding Basic Mathematics, and Dimension 8, Student Teaching. In either case, more recent gradu- ates tended to evaluate this aspect statistically more positively. The suggestions made by some respondents with regard to the open-ended Question 64 have been examined in the context of the con- clusions and recommendations in Chapter VI. CHAPTER VI CONCLUSIONS AND SUGGESTIONS The primary objective of this study has been to evaluate the mathematics curriculum given by the College of Education, Mecca, from the perspective of the teachers who graduated from the College in the years 1976 through 1980. Yet as a result of the survey, a number of corollary conclusions can be drawn from the data. These conclusions in the context of the purpose of the study are significantly relevant. Data collected on the enrollment figures reveal that during the academic years 1975-76 through 1979-80, 116 Saudi teachers were graduated to teach mathematics from the College of Education, Mecca. In terms of the need of the country to develop its industrial and technological potential, 116 graduates over five years is a poor number. An interesting trend the figures reveal is that more and more women teachers have since 1977-78 been enrolling to qualify to teach mathematics in Saudi intermediate and high schools. The trend is particularly significant as women's education started late in the country. This study cannot offer any explanation for the lack of interest in mathematics among the prospective Saudi teachers, but an investigation into the causes is worth the while of another study in 88 89 view of the importance of mathematics to modern science and tech- nology. Another significant conclusion from the enrollment and gradua- tion figures drawn is that a majority of mathematics teachers prefer the 40-hour program to the 60 hours in mathematics, possibly to qualify to teach an additional subject. No meaningful conclusion could be drawn from the academic performance of the graduates, except that it is lamentable that only 10.3% of the graduates could reach excellence in grades and that most graduates do better in mathematics than in the education courses. A striking fact that emerges out of the working situation is that of 116 graduates only 5 graduates appeared to have made headway toward higher degrees. Of these five, only one has been teaching at the junior-college level. If it is desired that there be a continuity between school and college education, a mobility of teachers of much greater magnitude from the high-school level to the university is also most desirable. Furthermore, it is encouraging to note that 96.6% of the Saudi graduates were still teaching mathematics as full-time teachers in Saudi schools. On the whole, the education curriculum has been rated posi- tively by the respondents. Among the most positively rated courses are Q15 (Developmental Psychology), Q16 (Educational Psychology), 018 (Educational Media), Q19 (Methods of Teaching Math [1]), Q20 (Student Teaching [1]), Q25 (Methods of Teaching Math [2]), and 026 (Student Teaching [2]). These courses have provided a good support to the beginning teachers in the initial years of their profession. These 90 courses Should be further strengthened and weaknesses, if any, be eliminated. On the other hand, the most negatively rated education pro- gram was Q21 (Education in Saudi Arabia). The response to this ques- tion is perhaps understandable. The history of ancient Saudi educa- tion may have little bearing on modern education in Saudi Arabia. Q12 (Introduction to Education and Psychology), 013 (Social and Philosophical Foundations of Education), 014 (Development of Edu- cational Thought), Q17 (Principles of Curriculum), Q22 (Educational Administration and Planning), Q23 (Introduction to Counseling and Mental Hygiene), and Q24 (Curriculum Design) were rated from fairly positive to definitely positive. A careful analysis of these rating results reveals that the courses that have a direct bearing on the classroom performance of the teachers have been rated very positively, and the programs that have a less immediate effect on the teacher's ability to teach tend to elicit fairly positive to definitely positive responses. The com- pelling conclusion is that the education courses should carry a greater measure of programs that are an immediate help to the student teachers than those the teachers would need when they have become well advanced in their careers. Responses to questions on the mathematics curriculum render themselves into two basic groupings: questions dealing with the com- ponents of mathematics and the global aspects of mathematics. The mathematics curriculum has been rated largely positively by the respondents. In other words, on the whole the teacher graduates were 91 satisfied with the content and emphasis of the mathematics program insofar as it prepares them to teach effectively. Among the most positively rated contents of the mathematics curriculum were 029 (Algebra), Q32 (Calculus), Q35 (Analytical Geom- etry), and Q36 (Modern Mathematics). Courses in these subjects, it appears, have been designed and executed with care and imagination. On the other hand, 027 (Understand Basic Math to Teach Math), Q30 (Geometry), A31 (Trigonometry), Q33 (Arithmetic), and Q34 (Statis- tics) have been rated fairly positive to definitely positive. The most negatively rated component of the mathematics curricu- lum was Q28 (Understand the Objectives of Teaching Math), with a mean = 3.233 on a scale of 1 (very positive) to 5 (very negative). The con- tent courses are, on the whole, satisfactory from the standpoint of their enabling the teachers to teach well; yet programs in the basics of mathematics, Geometry, Trigonometry, Arithmetic, and Statistics need strengthening, and the strength of the very positively rated con- tent subjects needs to be constantly reinforced. Such abstract con- tents as understanding the objectives of teaching mathematics need more emphasis in the content curriculum. The second part of the mathematics curriculum dealing with the global aspects of mathematics has been rated from fairly positive to generally positive. Respondents were fairly positive about the curriculum's ability to prepare them for higher studies in mathematics, to make them competent to assess programs critically, to assess mathe- matics courses, to do research in mathematics in general, and to prepare 92 them to evaluate the work of the pupils and grade them. Respondents felt negative with regard to Q38 (Insight to Develop Math Curricula), Q42 (Curriculum Planning in Math), Q44 (Concept Development in Math), and Q47 (Math Textbook Writing). It appears that the pro- grams in the mathematics curriculum that deal with the actual, imme- diate classroom needs are generally rated positively. In other words, most respondents show very positive feelings about those segments of the curriculum that have a direct bearing on their function as teach- ers in class. The relationship between the college and school curricula in mathematics was rated highly negatively, if Q53, Q54, Q56, and Q58 are read together. Based on the responses to Questions 49 through 63, the follow- ing conclusions can be drawn: 1. There is little relationship between the courses in mathe- matics at the College of Education, Mecca, and curricula in mathematics in intermediate and high schools. 2. The mathematics curriculum does not account for the spe- cific needs of the intermediate and high school mathematics. 3. The mathematics curriculum of the College does not pre- pare prospective teachers of mathematics as adequately as it ought to. 4. There is a very poor relationship between the College pro- gram and what it takes to teach in schools in Saudi Arabia. 5. Contacts with regard to the common objective, that is, to teach school mathematics effectively and consistently with the 93 objectives, are very poor between schools and the College of Edu- cation. 6. Seminars on topics of common interest between the inter- mediate and high schools and the College of Education are almost unheard of. 7. Even though the College mathematics courses have been rated positively, there appears to be a need to have a closer rele- vance to the needs of the schools. 8. Teachers already teaching are not allowed sufficient say in the supervision of practice teaching. 9. The College of Education does not offer adequate in-service programs for its past graduates. 10. Present programs of the College of Education need improve- ment urgently and immediately. 11. The mathematics curriculum does not give due emphasis to practical problem-solving aspects of mathematics in the mathematics program of the College. 12. The College programs do not encourage innovation and experimentation in the teaching of mathematics. 13. The College of Education mathematics curriculum prepares teachers of mathematics poorly in the techniques of evaluating and grading. 14. Little emphasis is given to abstract mathematical concepts. 15. Based on the complete results of the ANCOVAS, it may be concluded that the teacher graduates were fairly well satisfied with understanding the objectives of teaching mathematics (Dimension 1). 94 Even so, this part of the mathematics curriculum could be improved to increase its effectiveness even further. 16. The rating of Dimension 2 (Understanding Mathematics to Teach Mathematics), through the complete ANCOVA results, is moderately positive with a mean = 2.7. It can be concluded that although this aspect (if the curriculum is rated positive, there is plenty of scope for improvement. 17. The ANCOVAS of the results of Dimension 3 (Preparation for Higher Mathematics) indicate that the respondents rate Dimension 3 more negatively, with a mean = 3.35. Furthermore, the results support the conclusion that the mathematics curriculum does not prepare the student sufficiently well to proceed for higher studies in mathe- matics. This conclusion is further supported by the fact that only five graduate respondents have continued their studies beyond their first degree programs at the College of Education. 18. Dimension 4 (College-School Relations) is one of the most negatively rated dimensions of this study. It is clear that the respondents believe that there is hardly any correlation between the courses in mathematics given by the College of Education and the cur- ricula of mathematics executed at the intermediate and high-school levels of Saudi schools. This conclusion is further supported by the fact that administratively the College of Education and intermediate and high-school education are controlled and managed by two different ministries, creating an administrative distance between the two seg- ments of Saudi education. 95 19. Dimension 5 (Emphasis on Practical Problem Solving), like Dimension 4, is one of the most negatively rated dimensions, with a mean = 4.37 on a scale of 1 (very positive) to 5 (very negative). All respondents believe that the emphasis on the problem-solving aspect of the mathematics curriculum is minimal, and the improvement of this aspect the respondents indicated is most desirable. I20. With a mean = 3.3, Dimension 6 (Preparation for School Teaching) is rated at the negative end of "uncertainty." Most respondents appear to say that they consider themselves to be somewhat prepared. 21. One of the most positive ratings is accorded to Dimension 7 (Methods of Teaching Math) by the graduate mathematics teachers of the College of Education, with a rating mean = 1.33. In the rating of this dimension, differences across the sex of the respondents and the type of program in mathematics (40 or 60 credits) were reflected in the Opinions of the population. Women graduate teachers with 40 credit hours in mathematics and men graduates with 60 credit hours rated this dimension of the curriculum as very positive, whereas men graduates with 40 hours in mathematics and women respondents with 60 hours rated this dimen- sion between positive and very positive. A somewhat significant inter- action effect is observed with regard to the sex of the respondents. Women teachers teaching at the middle-school level rated methods of teaching mathematics better than the group average, and those women teachers teaching at the senior-high level, below the population average. It appears that the women teachers who are called upon to teach at a high level feel handicapped in acquiring the necessary 96 confidence because of the indirect closed-circuit TV system of learn- ing. It may be concluded that, on the whole, the methods of teaching mathematics of the curriculum of the College of Education accomplish their objectives very well. 22. Student teaching, which this study identifies as Dimen- sion 8, has received one of the most positive endorsements from the population. Differences across the sex of the respondents and the type of mathematics are identical to those noted in conclusion 21. The conclusion that student teaching is one of the strongest features of the curriculum of the College of Education becomes one of the most logical. 23. The respondent population has expressed an uncertain to a negative reservation about Educational Thought (Dimension 9), giving rise to the conclusion that educational thought in the present form and design contributes less than optimally to the enhancement of the teachers' efficiency and effectiveness in the classroom. 24. Dimension 10 (Curriculum Design) receives a quasi- positive rating from the whole population. Respondents with an 80% teaching responsibility in mathematics evaluate this dimension some- what more positively than do respondents with a 100% teaching duty in mathematics. The respondents, in other words, indicate that the mathematics curriculum of the College of Education could prepare them even better in the techniques of curriculum designing than the cur- riculum does at present. 25. Educational Psychology (Dimension 11) is rated as quasi- positive, with a mean rating of 2.31. Although the attitude of the 97 graduate teachers toward this dimension is positive, it is clearly written in the dimension of the mean of this component of the curricu- lum that its positive contribution toward better preparation of the teacher could be improved. 26. Dimension 12, concerning problems of teaching mathematics, has been assessed as fairly positive in preparing teachers to deal with the problems of teaching mathematics, but it is far from totally satisfactory. Improvement of this aspect of the curriculum would appear to be desirable. Suggestions Based on the conclusions derived from the simple frequency analyses and factorial analyses, the following suggestions can be made for the improvement and further investigation of the mathematics cur- riculum of the College of Education: 1. Efforts should be made to attract more and better stu- dents to qualify as mathematics teachers by offering attractive stipends and salaries comparable to what they get in industry and private enterprise as pure mathematics graduates. 2. The trend of women teachers' going in for mathematics should be encouraged and reinforced because under the Saudi system only women teachers can teach in girls' schools. 3. Women respondents suggested that provision should be made for "live" women instructors for them, instead of the current practice of providing male instruction on a closed-circuit TV. 4. On the whole, education curricula are satisfactory, but they could be made more effective as an aid to better teaching. 98 5. Courses such as "Saudi Education" that have little relevance to teaching should be reduced or altered , or form part of an allied subject matter. 6. The courses that have a direct bearing on student teachers' ability to teach should be reinforced and enhanced. 7. The courses in mathematics have proven very successful in preparing graduate teachers to teach their specialty. They should generally be reinforced and kept up to date in content and their rela- tionship with the school curricula. Special attention Should be paid to the content and teaching of the basics of mathematics, geometry, trigonometry, and arithmetic. 9. Courses dealing with developing insight into mathematics curricula at school, curriculum planning, concept developing in mathe- matics, and mathematics textbook writing should be carefully examined and researched to determine why they generally fail to accomplish their objectives. 9. There is an urgent need to have a closer relationship between the college curricula in mathematics and the curricula in mathematics taught at the intermediate and high-school levels in Saudi Arabia. This aspect is in an immediate need of research investigation, as the relationship was very poorly rated by the respondents. 10. Specific parts of the mathematics curriculum of the Col- lege should deal separately with the courses at the two levels, namely intermediate and high school. 11. There should be more contacts, through seminars and con- ferences, between the intermediate and high-school teachers of mathe- matics and the college teachers teaching the courses in mathematics. 99 12. School teachers should be more deeply involved in the supervision of student teaching than has been possible so far. For instance, in the evaluation of the student teacher, during his/her assignment to a school for practice, a significant weight should be attached to the regular teacher's observation and assessment. 13. The mathematics curriculum of the College of Education should make an adequate allowance for the practical problem-solving aspect of the programs at school. 14. Fundamental mathematical concepts should be given an adequate weight in the program and emphasis of the mathematics cur- riculum. 15. It was found that the courses in mathematics do not moti- vate prospective teachers sufficiently strongly to pursue higher studies in the subject. This weakness of the curriculum should be investigated and remedies found. 16. The methods of teaching mathematics have received one of the most positive endorsements. Efforts should be made to maintain the high level of their effectiveness by regular feedback and research. 17. Student teaching, as one of the most effective programs of the mathematics department, should, like the methods of teaching mathematics, be maintained not only at the current levels of effici- ency but also should be improved and reinforced. 18. Curriculum designing should be given greater empha- sis in the programs of the mathematics department of the College of Education as, it is hoped, more and more teachers, by reason of 100 their efficiency and commitment to their profession, would get involved in the mathematics curriculum at schools in Saudi Arabia. It is hoped that these conclusions and suggestions will inspire future researchers to pursue similar investigations with regard to other specialties provided by the College of Education, Mecca, and to examine what effect the administrative division between the College of Education and schools in Saudi Arabia has on the effective use of the College's resources in the preparation of teachers of mathematics, how well focused the College mathematics curriculum is with regard to the curricula at intermediate and high schools in Saudi Arabia, what specific kinds of contact between the College and its alumni would best serve the interest of continuing education of mathematics teach- ers, and such other problems as content evaluation of mathematics by experts. APPENDICES 101 APPENDIX A ARABIC AND ENGLISH VERSIONS OF THE COVER LETTER AND QUESTIONNAIRE 102 103 MICHIGAN STATE UNIVERSITY COLLEGE OF ARTS AND LETTERS EAST LANSING ' MICHIGAN ° 4882-1 DEPARTMENT OF LINGL’ISTICS AND ORIENTAL AND AFRICAN LANGUAGES WELLS HALL May 2, 1981 To whom it may concern: We hereby certify that Mr. Abdulwahab Zefar has translated into the Arabic language the English version of the questionnaire used as a tool in his research for his doctoral dissertation entitled "An Evaluation of Mathe- matics Curriculum Given at the College of Education, Mecca, From the Perspective of the Teachers Who Graduated From the College in the Years 1975-1980." We hereby verify that the translation is honest, accurate, and valid. The cover letter as well as the questionnaire was translated into Arabic in the same format, except that it follows the standard writing style for the Arabic language. ' We do wish him the best of luck. 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MWJWIowgJJI 1J...J.1. o->1 1_,.-J5. t319...... 6J5...“ (1..—51.9. (,4... L...31..11.1.:1 .- 'VW'JW‘J m4"— oL..L.JJ|'-...3 L,.s1._....1J.1J1 41,41 3.___...1J.1.,_Ls JSJ—‘L g1 ”.11...." —oY _oA 0‘1 —'11 -"11 :11 114 L,J11..,,_~..11..:.1LsJLL,:..11.1_.1._>J:...i.. 1.1.1.1041 {1.141.541 _15 CAL... J.J1..:.u_o..L.. L91 .15....u.J1J U1.L.J1 ¢L>J.3.J1 . 1.J5._1115.._. L..J.J171_.JS.L'>L..L.JJ1‘..JUJ 1.1.1.11 115 Dear Mathematics Teacher: Efforts are being made to improve the quality and quantity of educational services in the Kingdom of Saudi Arabia. Teachers are considered to be the cornerstone of the educational process, and it is more so in the area of teaching mathematics, which has gone through technical and up-to-date changes in light of technological development and progress. The success of mathematics teachers in achieving the objectives of mathematics programs offered in schools is contingent on the way they were trained and prepared by their colleges. This study is an attempt to assess the program and curricula used in preparing teachers of mathematics, as well as their needs. Your participation, cooperation, and honesty in responding to the questionnaire are highly appreciated and are a reflection of your awareness of the importance of this study. The questionnaire consists of five parts: l. General information 2. Adequacy of professional courses for teaching mathematics 3 Adequacy of courses in mathematics for teaching math in schools 4. Correlation between the high school objectives for a math curriculum and the design of the curriculum at the College of Education 5. Recommendations Please make sure you read and understand the instructions pro- vided for each part, which will help you in completing the question— naire. Thank you for your participation and cooperation. Abdulwahab Zafar 116 QUESTIONNAIRE PART I GENERAL INFORMATION Questions l-ll DIRECTIONS: Please answer the following questions by putting an X in the blank space against the answer that most appropriately describes your response: 1. 10. 11. What is your sex? Male Female When did you graduate from the College of Education, Mecca? 1975-76____ 1976-77____ 1977-78;___ 1978-79_(_ 11979-80____ Did you graduate with 60 or 40 credits in Mathematics? 60 credit hours 40 credit hours What was your overall Grade Point Average? 4.0 3.5 3.0 2.5 2.0 What was your Grade Point Average in Mathematics? 4.0 3.5 3.0 2.5 2.0 Are you working as a full-time teacher? Yes No Are you required to teach Mathematics in your present job assignment? Yes No At what level are you teaching now? What percentage of your teaching assignment is devoted to teaching Mathematics? 100%___ 80%____ 60%___ 50%____ Less than 50%____ None___ List the subject or subjects other than Mathematics you teach. l. 2. 3. Are you involved in any administrative duties in addition to teaching? Yes No 117 PART II ADEQUACY OF PROFESSIONAL COURSES TO PREPARE AS A TEACHER OF MATHEMATICS Questions l2-26 DIRECTIONS: Please record your assessment of the following profes- sional courses by circling the number that appears in the column headed by a word or phrase that bears the nearest approximation to your opinion to indicate how well the particular course has prepared you as a teacher of Mathematics in schools: m 3 Q) l— v- (U .D > 0) f5 3 3 C OJ r- F- 0) 0|- I'— (U (U '— C'U «H > > .D 44 +3 it! S- °r- 0 >5 3 (D .J 2 S- f" U Q) to C ‘4— '4- > > D O 0 l2. Introduction to Education and Psychology 1 2 3 4 5 l3. Social and Philosophical Foundations of Education I 2 3 4 5 l4. Development of Educational Thought I 2 3 4 5 l5. Developmental Psychology (Childhood and Adolescent) l 2 3 4 5 l6. Educational Psychology 1 2 3 4 5 l7. Principles of Curriculum 1 2 3 4 5 l8. Educational Media l 2 3 4 5 l9. Methods of Teaching Mathematics (1) l 2 3 4 5 20. Student Teaching (l) l 2 3 4 5 21. Education in Saudi Arabia 1 2 3 4 5 22. Educational Administration and Planning l 2 3 4 5 23. Introduction to Counseling and Mental Hygiene 1 2 3 4 5 24. Curriculum Design l 2 3 4 5 25. Methods of Teaching Mathematics (2) l 2 3 4 5 26. Student Teaching (2) l 2 3 4 5 118 PART III ADEQUACY OF THE COURSES IN MATHEMATICS GIVEN BY THE COLLEGE OF EDUCATION, MECCA, FOR TEACHING MATHEMATICS HYINTERMEDIATE, JUNIOR HIGH, AND SENIOR HIGH SCHOOLS Questions 27-48 DIRECTIONS: Please indicate your assessment of the courses in Mathe- matics given at the College of Education, Mecca, by circling the number in the column headed by a word or phrase that bears the nearest approxi- mation to your opinion as to how well the courses prepared you to teach Mathematics in Saudi intermediate, junior high, and senior high schools. a) Q) L d) m 0! rd L U) 01 'I- < o C >. w- m >. l_' G O.) F- CD +4 L 05 C m L U) C O G) CD CD 0 L L U U) L 44 c» : .,.. a m < D Q (I) 27. The courses in Mathematics I took were valuable in helping me to understand the basics of Mathematics to teach Mathematics at school. I 2 3 4 5 28. The courses in Mathematics at the College of Education, Mecca, were so designed as to make me adequately aware of the objectives of teaching Mathematics at school. l 2 3 4 5 Courses in the following Mathematics subjects I took at the College of Education were such as to make me a highly competent teacher of these at school: 29. Algebra 30. Geometry 3l. Trigonometry 32. Calculus 33. Arithmetic 34. Statistics 35. Analytical Geometry 36. Modern Mathematics d—l—l—l—l—J-J—J NNNNNNNN wwwwwwww b-D-h-b-h-h-h-D 0101010101010101 119 Q) 0) L OJ CD 0) (U L m U? 'r- < D C >. -P m >. F- (U Q) r— U') +2 L CD C Q) L 03 C O Q) 0) CO 0 L L U m L H , 0" C -r- +2 U) < D D W 37. Courses in Mathematics I took at the College of Education prepared me sufficiently well to enable me to pursue higher studies in Mathematics. 1 2 3 4 5 38. Courses in Mathematics I took at the College of Education created insights in me to develop curricula in Mathematics at various levels of Saudi schools. 1 2 3 4 5 39. The Mathematics courses developed competence in me to critically assess programs or cur- ricula in schools. l 2 3 4 5 40. Courses in Mathematics have enabled me to build competent tests to examine the attain- ment of my students in Mathematics. l 2 3 4 5 41. I was competently trained in the methods of teaching Mathematics. 1 2 3 4 5 The program in Mathematics at the College of Education provided me with enough research opportunities into: 42. Curriculum planning in Mathematics 1 2 3 4 5 43. Assessment of courses in Mathematics 1 2 3 4 5 44. Concept developing in Mathematics 1 2 3 4 5 45. Problems of teaching Mathematics 1 2 3 4 5 46. Mathematics in general l 2 3 4 5 47. Mathematics textbook writing 1 2 3 4 5 48. Evaluation and grading l 2 3 4 5 120 PART IV RELATEDNESS BETWEEN THE SCHOOL MATHEMATICS CURRICULUM NEEDS AND THE COURSES IN MATHEMATICS AT THE COLLEGE OF EDUCATION Questions 49-52 DIRECTIONS: Please indicate your assessment of the relatedness between the school Mathematics curriculum needs and the courses in Mathematics at the College of Education, Mecca, by circling the number in the column headed by a word or phrase that bears the near- est approximation to your opinion. Uncertain Strongly Agree Disagree Agree Strongly Disagree 49. There is a high correlation between the objectives of the Mathematics curriculum at school and the course objectives for Mathematics at the College of Education, Mecca. l 2 3 4 50. Courses in Mathematics at the College of Education, Mecca, include 50% of the material- that is never made use of by the teacher of Mathematics in the classroom. 1 2 3 4 51. The curriculum of Mathematics at the College of Education does not take into account the differences in teaching Mathematics at inter- mediate and high school levels. 1 2 3 4 52. The courses in Mathematics at the College of Education do not prepare teachers adequately to teach Modern Mathematics. 1 2 3 4 121 PART V RECOMMENDATIONS Questions 53-64 DIRECTIONS: Please indicate the degree of your agreement with the following recommendations regarding the program for Mathematics at the College of Education by circling the number in the column headed by a word or phrase that very nearly approximates the degree of your response. Strongly Agree Agree Uncertain Disagree Strongly Disagree 53. The program in Mathematics at the College of Education ought to have a closer bearing on teaching Mathematics at school. 1 2 3 4 54. A closer contact between schools in the country and the Department of Mathematics of the College of Education must be main- tained to coordinate their programs. l 2 3 4 55. There should be more seminars between the students and faculty of the Department of Mathematics of the College of Education and the teachers of Mathematics at school. l 2 3 4 56. Courses in Mathematics at the College of Education need greater relevance in terms of the needs of teaching Mathematics at school. l 2 3 4 57. Student teaching for Mathematics should be supervised largely by school teachers. I 2 3 4 58. The College of Education should conduct in-service refresher courses at least once every two years. 1 2 3 4 59. The present program in Mathematics for teachers of Mathematics needs no improvement. 1 2 3 4 122 4) cu L Q) 0) OJ to L m O) 't- < D C >. -~ w >. F- I'U OJ F- 05 «P L U) C Q) L CD C O (I) (D f6 0 L L U m L +4 05 C ‘l— +3 V) < D D U) 60. The program in Mathematics for prospective teachers of Mathematics should place greater emphasis on practical problems of teaching the subject at school than on mathematical abstractions. l 2 3 4 5 61. Prospective Mathematics teachers should be given greater freedom to experiment with new teaching methods. 1 2 3 4 5 62. Student teachers of Mathematics should be better prepared in the techniques of testing and evaluating. l 2 3 4 5 63. Courses in Mathematics at the College of Education should emphasize the study of abstract Mathematics. 1 2 3 4 5 64. What other suggestions, in addition to the above, would you like to make in order to improve the Mathematics curriculum at the College of Education, Mecca? APPENDIX B FREQUENCIES 123 124 Table B-l.l.--Personal background. Relative Adjusted Absolute Category Frequency Frequency Frequency (Percent) (Percent) Question A01: Sex Male 76 65.5 65.5 Female 40 34.5 34.5 Total 116 100.0 100.0 Question A02: Year Graduated From Mecca College of Education Year 1975/76 15 12.9 12.9 Year 1976/77 22 19.0 19.0 Year l977/78 29 25.0 25.0 Year 1978/79 22 19.0 19.0 Year 1979/80 28 24.1 24.1 Total 116 100.0 100.0 Question A03: Graduated With 40 or 60 Credits 40 credits 74 63.8 63.8 60 credits 42 36.2 36.2 Total 116 100.0 100.0 125 Table B-1.2.--Academic performance. Relative Adjusted Category éazolgxg Frequenc Frequency q y (Percent (Percent) Question A04: Overall GPA 1.51-2.00 12 10.3 10.3 2.01-2.50 40 34.5 34.5 2.51-3.00 38 32.8 32.8 3.01-3.50 24 20.7 20.7 3.51-4.00 2 1.7 1.7 Total 116 100.0 100.0 Question A05: Mathematics GPA 1.51-2.00 9 7.8 7.8 2.01-2.50 38 32.8 32.8 2.51-3.00 32 27.6 27.6 3.01-3.50 32 27.6 27.6 3.51-4.00 5 4.3 4.3 Total 116 100.0 100.0 126 Table B-l.3.--Working situation. Relative Adjusted Category Etiolgzi Frequency Frequency q y (Percent) (Percent) Question A06: Working as a Full-Time Teacher? No 1 .9 .9 Yes 112 96.6 99.1 No response 3 2.6 -- Total 116 100.0 100.0 Question A07: Required to Teach Mathematics? No 2 1.7 1.8 Yes 111 95.7 98.2 No response 3 2.6 -- Total 116 100.0 100.0 Question A08: Teaching at Which Level? Middle school 83 71.6 74.1 High school 28 24.1 25.0 Junior college 1 .9 .9 No response 4 3.4 -- Total 116 100.0 100.0 Question A09: Percent of Mathematics Teaching Duty None 1 .9 .9 60 percent 3 2.6 2.7 70 percent 1 .9 .9 80 percent 19 16.4 17.0 100 percent 88 75.9 78.6 No response 4 3.4 -- Total 116 100.0 100.0 Question A11: Administrative Duties No 99 85.3 88.4 Yes 13 11.2 11.6 No response 4 3.4 -- Total 116 100.0 100.0 127 Table B-2.--Education curriculum. Relative Adjusted Category 2:30:33: Frequency Frequency q y (Percent) (Percent) Question A12: Introduction to Education and Psychology Very positive 23 19.8 19.8 Positive 58 50.4 50.4 +/- 4 3.4 3.4 Negative 25 21.6 21.6 Very negative 6 5.2 5.2 Total 116 100.0 100.0 Mean 2.422 Standard deviation Question A13: Social and Philosophical Foundations of Education Very positive 7 6.0 6.0 Positive 65 56.0 56.0 +/- 8 6.9 6.9 Negative 26 22.4 22.4 Very negative 10 8.6 8.6 Total 116 100.0 100.0 Mean 2.716 Standard deviation 1.141 Question A14: Development of Educational Thought Very positive 10 8.6 8.6 Positive 53 45.7 45.7 +/- 11 9.5 9.5 Negative 32 27.6 27.6 Very negative 10 8.6 8.6 Total 116 100.0 100.0 Mean 2.819 Standard deviation Question A15: Developmental Psychology Very positive 62 53.4 53.4 Positive 38 32.8 32.8 +/- 4 3.4 3.4 Negative 11 9.5 9.5 Very negative 1 .9 .9 Total 116 100.0 100.0 Mean 1.716 Standard deviation 128 Table B-2.--Continued. Relative Adjusted Category éezolgfig Frequency Frequency q y (Percent) (Percent) Question A16: Educational Psychology (Childhood and Adolescence) Very positive 41 35.3 35.3 Positive 55 47.4 47.4 +/- 4 3.4 3.4 Negative 14 12.1 12.1 Very negative 2 1.7 1.7 Total 116 100.0 100.0 Mean 1.974 Standard deviation 1.017 Question A17: Principles of Curriculum Very positive 41 35.3 35.3 Positive 52 44.8 44.8 +/- 9 7.8 7.8 Negative 10 8.6 8.6 Very negative 4 3.4 3.4 Total 116 100.0 100.0 Mean 2.000 Standard deviation 1.047 Question A18: Educational Media Very positive 76 65.5 65.5 Positive 30 25.9 25.9 +/- 1 .9 .9 Negative 7 6.0 6.0 Very negative 2 1.7 1.7 Total 116 100.0 100.0 Mean 1.526 Standard deviation .918 Question A19: Methods of Teaching Math (1) Very positive 89 76.7 76.7 Positive 20 17.2 17.2 +/- 3 2.6 2.6 Negative 4 3.4 3.4 Total 116 100.0 100.0 Mean 1.328 Standard deviation .695 129 Table B-2.--Continued. Relative Adjusted Category égzolgzg Frequency Frequency q y (Percent) (Percent) Question A20: Student Teaching (1) Very positive 97 83.6 83.6 Positive 15 12.9 12.9 Negative 3 2.6 2.6 Very negative 1 .9 .9 Total 116 100.0 100.0 Mean 1.241 Standard deviation .668 Question A21: Education in Saudi Arabia Very positive 7 6.0 6.0 Positive 30 25.9 25.9 +/- 29 25.0 25.0 Negative 43 37.1 37.1 Very negative 7 6.0 6.0 Total 116 100.0 100.0 Mean 3.112 Standard deviation 1.053 Question A22: Educational Administration and Planning Very positive Positive +/- Negative Very negative Total Mean 2.405 24 20.7 20.7 54 46.6 46.6 12 10.3 10.3 19 16.4 16.4 7 6.0 6.0 116 100.0 100.0 Standard deviation 1.165 Question A23: Introduction to Counseling and Mental Hygiene Very positive Positive +/- Negative Very negative Total Mean 2.543 27 23.3 23.3 46 39.7 39.7 8 6.9 6.9 23 19.8 19.8 12 10.3 10.3 116 100.0 100.0 Standard deviation 1.321 130 Table B-2.--Continued. Relative Adjusted Category égzolgfig Frequency Frequency q y (Percent) (Percent) Question A24: Curriculum Design Very positive 21 18.1 18.1 Positive 57 49.1 49.1 +/- 15 12.9 12.9 Negative 19 16.4 16.4 Very negative 4 3.4 3.4 Total 116 100.0 100.0 Mean 2.379 Standard deviation 1.069 Question A25: Methods of Teaching Math (2) Very positive 89 76.7 76.7 Positive 22 19.0 19.0 +/- 1 .9 .9 Negative 2 1.7 1.7 Very negative 2 1.7 1.7 Total 116 100.0 100.0 Mean 1.328 Standard deviation .743 Question A26: Student Teaching (2) Very positive 93 80.2 80.2 Positive 21 18.1 18.1 Negative 2 1.7 1.7 Total 116 100.0 100.0 Mean 1.233 Standard deviation .533 131 Table B-3.--Mathematics curriculum. Relative Adjusted Category éezolgfig Frequency Frequenc q y (Percent) (Percent Question A27: Understand basic math to teach math Very positive 27 23.3 23.3 Positive 70 60.3 60.3 Negative 17 14.7 14.7 Very negative 2 1.7 1.7 Total 116 100.0 100.0 Mean 2.112 Standard deviation .985 Question A28: Understand objectives of teaching math Very positive 2 1.7 1.7 Positive 30 25.9 25.9 +/- 30 25.9 25.9 Negative 47 40.5 40.5 Very negative 7 6.0 6.0 Total 116 100.0 100.0 Mean 3.233 Standard deviation .963 Question A29: Algebra Very positive 57 49.1 49.1 Positive 47 40.5 40.5 +/- 3 2.6 2.6 Negative 8 6.9 6.9 Very negative 1 .9 .9 Total 116 100.0 100.0 Mean 1.698 Standard deviation .887 Question A30: Geometry Very positive 31 26.7 26.7 Positive 55 47.4 47.4 +/- 5 4.3 4.3 Negative 21 18.1 18.1 Very negative 4 3.4 3.4 Total 116 100.0 100.0 Mean 2.241 Standard deviation 1.139 132 Table B-3.--Continued. Relative Adjusted Category égzolgfig Frequency Frequency q y (Percent) (Percent) Question A31: Trigonometry Very positive 14 12.1 12.1 Positive 60 51.7 51.7 +/- 26 22.4 22.4 Negative 15 12.9 12.9 Very negative 1 .9 .9 Total 116 100.0 100.0 Mean 2.388 Standard deviation .892 Question A32: Ca1cu1us Very positive 58 50.0 50.0 Positive 42 36.2 36.2 +/- 8 6.9 6.9 Negative 7 6.0 6.0 Very negative 1 .9 .9 Total 116 100.0 100.0 Mean 1.716 Standard deviation .902 Question A33: Arithmetic Very positive 30 25.9 25.9 Positive 37 31.9 31.9 +/- 20 17.2 17.2 Negative 24 20.7 20.7 Very negative 5 4.3 4.3 Total 116 100.0 100.0 Mean 2.457 Standard deviation 1.204 Question A34: Statistics Very positive 32 27.6 27.6 Positive 39 33.6 33.6 +/- 20 17.2 17.2 Negative 21 18.1 18.1 Very negative 4 3.4 3.4 Total 116 100.0 100.0 Mean 2.362 Standard deviation 1.168 133 Table B-3.--Continued. Relative Adjusted Category égzolgfifi Frequency Frequency q y (Percent) (Percent) Question A35: Analytical Geometry Very positive 44 37.9 37.9 Positive 49 42.2 42.2 +/- 15 12.9 12.9 Negative 8 6.9 6.9 Total 116 100.0 100.0 Mean 1.888 Standard deviation .882 Question A36: Modern Mathematics Very positive 52 44.8 44.8 Positive 48 41.4 41.4 +/- 4 3.4 3.4 Negative 7 6.0 6.0 Very negative 5 4.3 4.3 Total 116 100.0 100.0 Mean 1.836 Standard deviation 1.046 Question A37: Prepared for Higher Studies in Math Very positive 3 2.6 2.6 Positive 40 34.5 34.5 +/- 45 38.8 38.8 Negative 16 13.8 13.8 Very negative 12 10.3 10.3 Total 116 100.0 100.0 Mean 2.948 Standard deviation 1.003 Question A38: Insight to Develop Math Curricula Very positive 2 1.7 1.7 Positive 28 24.1 24.1 +/- 32 27.6 27.6 Negative 42 36.2 36.2 Very negative 12 10.3 10.3 Total 116 100.0 100.0 Mean 3.293 Standard deviation 1.004 134 Table B-3.--Continued. Relative Adjusted Category 932012;: Frequency Frequency q y (Percent) (Percent) Question A39: Competent to Critically Assess Programs Very positive 8 6.9 6.9 Positive 41 35.3 35.3 +/- 21 18.1 18.1 Negative 42 36.2 36.2 Very negative 4 3.4 3.4 Total 116 100.0 100.0 Mean 2.940 Standard deviation Question A40: Able to Construct Adequate Tests Very positive 27 23.3 23.3 Positive 49 42.2 42.2 +/- 14 12.1 12.1 Negative 24 20.7 20.7 Very negative 2 1.7 1.7 Total 116 100.0 100.0 Mean 2.353 Standard deviation Question A41: Competent in Methods of Teaching Math Very positive 30 25.9 25.9 Positive 54 46.6 46.6 +/- 9 7.8 7.8 Negative 19 16.4 16.4 Very negative 4 3.4 3.4 Total 116 100.0 100.0 Mean 2.250 Standard deviation 1.118 Question A42: Curriculum Planning in Math Very positive 3 2.6 2.6 Positive 21 18.1 18.1 +/- 21 18.1 18.1 Negative 60 51.7 51.7 Very negative 11 9.5 9.5 Total 116 100.0 100.0 Mean 3.474 Standard deviation 135 Table B-3.--Continued. Relative Adjusted Absolute Category Frequency Frequenc Frequency (Percent) (Percent) Question A43: ASsessment of Math Courses Very positive 5 4.3 4.3 Positive 49 42.2 42.2 +/- 22 19.0 19.0 Negative 36 31.0 31.0 Very negative 4 3.4 3.4 Total 116 100.0 100.0 Mean 2.871 Standard deviation 1.018 Question A44: Concept Development in Math Very positive 4 3.4 3.4 Positive 36 31.0 31.0 +/- 27 23.3 23.3 Negative 42 36.2 36.2 Very negative 7 6.0 6.0 Total 116 100.0 100.0 Mean 3.103 Standard deviation 1.025 Question A45: Problems of Teaching Math Very positive 13 11.2 11.2 Positive 47 40.5 40.5 +/- 25 21.6 21.6 Negative 25 21.6 21.6 Very negative 6 5.2 5.2 Total 116 100.0 100.0 Mean 2.690 Standard deviation 1.091 Question A46: Mathematics in General Very positive 9 7.8 7.8 Positive 48 41.4 41.4 +/- 21 18.1 18.1 Negative 30 25.9 25.9 Very negative 8 6.9 6.9 Total 116 100.0 100.0 Mean 2.828 Standard deviation 1.113 136 Tab1e B-3.—-Continued. Relative Adjusted Absolute Category Frequency Frequency Frequency (Percent) (Percent) Question A47: Math Textbook Writing Very positive 1 .9 .9 Positive 6 5.2 5.2 +/- 24 20.7 20.7 Negative 53 45.7 45.7 Very negative 32 27.6 27.6 Total 116 100.0 100.0 Mean 3.940 Standard deviation .878 Question A48: Evaluation and Grading Very positive 7 6.0 6.0 Positive 49 42.2 42.2 +/— 23 19.8 19.8 Negative 33 28.4 28.4 Very negative 4 3.4 3.4 Total 116 100.0 100.0 Mean 2.810 Standard deviation 1.029 137 Table B-4.--College-school relations. Relative Adjusted Category Absolute Frequenc Frequenc Frequency (Percent (Percent Question A49: High correlation between college and school Very positive 7 6.0 6.0 Positive 32 27.6 27.6 +/- 16 13.8 13.8 Negative 48 41.4 41.4 Very negative 13 11.2 11.2 Total 116 100.0 100.0 Mean 3.241 Standard deviation 1.154 Question A50: Half Materia1 Taught Never Used in School Very positive 8 6.9 6.9 Positive 11 9.5 9.5 +/- 9 7.8 7.8 Negative 52 44.8 44.8 Very negative 36 31.0 31.0 Total 116 100.0 100.0 Mean 3.836 Standard deviation 1.172 Question A51: College Ignores Differences in Schools Very positive 4 3.4 3.4 Positive 11 9.5 9.5 +/- 8 6.9 6.9 Negative 53 45.7 45.7 Very negative 40 34.5 34.5 Total 116 100.0 100.0 Mean 3.983 Standard deviation 1.055 Question A52: College Does Not Prepare Adequately Very positive 5 4.3 4.3 Positive 29 25.0 25.0 +/- 6 5.2 5.2 Negative 47 40.5 40.5 Very negative 29 25.0 25.0 Total 116 100.0 100.0 Mean 3.569 Standard deviation 1.232 138 Table B—4.--Continued. Relative Adjusted Category Absolute Frequenc Frequency requency (Percent (Percent) Question A53: College Program Closer to Teaching in Schools Very positive 1 .9 .9 Negative 15 12.9 12.9 Very negative 100 86.2 86.2 Total 116 100.0 100.0 Mean 4.836 Standard deviation .492 Question A54: More Contacts Between Schools and College +/- 1 .9 .9 Negative 18 15.5 15.5 Very negative 97 83.6 83.6 Total 116 100.0 100.0 Mean 4.828 Standard deviation .402 Question A55: More Seminars Between College and Schools Positive 3 2.6 2.6 +/- 7 6.0 6.0 Negative 34 29.3 29.3 Very negative 72 62.1 62.1 Total 116 100.0 100.0 Mean 4.509 Standard deviation .728 Question A56: More Relevance for Needs of Schools +/— 2 1.7 1.7 Negative 20 17.2 17.2 Very negative 94 81.0 81.0 Total 116 100.0 100.0 Mean 4.793 Standard deviation .448 139 Table B-4.--Continued. Relative Adjusted Category Absolute Frequency Frequenc Frequency (Percent) (Percent Question A57: Student Teaching Be Supervised by Teachers Very positive 1 .9 .9 Positive 4 3.4 3.4 +/- 4 3.4 3.4 Negative 36 31.0 31.0 Very negative 71 61.2 61.2 Total 116 100.0 100.0 Mean 4.483 Standard deviation .797 Question A58: College to Offer In-Service Refresher Positive 3 2.6 2.6 +/- 3 2.6 2.6 Negative 24 20.7 20.7 Very negative 86 74.1 74.1 Total 116 100.0 100.0 Mean 4.664 Standard deviation .659 Question A59: Present Program Needs Improvement Positive 5 4.3 4.3 +/- 6 5.2 5.2 Negative 62 53.4 53.4 Very negative 43 37.1 37.1 Total 116 100.0 100.0 Mean 4.233 Standard deviation .738 Question A60: Greater Emphasis on Practical Problems Very positive 1 .9 .9 Positive 9 7.8 7.8 +/- 10 8.6 8.6 Negative 50 43.1 43.1 Very negative 46 39.7 39.7 Total 116 100.0 100.0 Mean 4.129 Standard deviation .928 140 Table B-4.--Continued. Relative Adjusted Category Absolute Frequenc Frequenc Frequency (Percent (Percent Question A61: More Experiments With New Teaching Methods Positive 1 .9 .9 +/- 6 5.2 5.2 Negative 47 40.5 40.5 Very negative 62 53.4 53.4 Total 116 100.0 100.0 Mean 4.466 Standard deviation .638 Question A62: Better Preparation for Testing and Evaluation Very positive 1 .9 .9 Positive 2 1.7 1.7 +/- 5 4.3 4.3 Negative 52 44.8 44.8 Very negative 56 48.3 48.3 Total 116 100.0 100.0 Mean 4.379 'Standard deviation .730 Question A63: More Emphasis on Abstract Math Very positive 5 4.3 4.3 Positive 19 16.4 16.4 +/- 9 7.8 7.8 Negative 66 56.9 56.9 Very negative 17 14.7 14.7 Total 116 100.0 100.0 Mean 3.612 Standard deviation 1.061 APPENDIX C EXPLORATORY FACTOR ANALYSIS 141 142 Table C-1.--Means and standard deviations of variables entering the factor analysis. Variable Mean 3:312:13n Cases A12 2.4224 1.1806 116 A13 2.7155 1.1406 116 A14 2.8190 1.1839 116 A15 1.7155 .9763 116 A16 1.9741 1.0169 116 A17 2.0000 1.0467 116 A18 1.5259 .9180 116 A19 1.3276 .6950 116 A20 1.2414 .6675 116 A21 3.1121 1.0531 116 A22 2.4052 1.1645 116 A23 2.5431 1.3213 116 A24 2.3793 1.0686 116 A25 1.3276 .7434 116 A26 1.2328 .5334 116 A27 2.1121 .9849 116 A28 3.2328 .9633 116 A29 1.6983 .8868 116 A30 2.2414 1.1392 116 A31 2.3879 .8922 116 A32 1.7155 .9022 116 A33 2.4569 1.2043 116 A34 2.3621 1.1677 116 A35 1.8879 .8824 116 A36 1.8362 1.0463 116 Tab1e C-1.--Continued. 143 Variable Mean gzgggiggn Cases A37 2.9483 1.0030 116 A38 3.2931 1.0045 116 A39 2.9397 1.0656 116 A40 2.3534 1.1054 116 A41 2.2500 1.1180 116 A42 3.4741 .9821 116 A43 2.8707 1.0175 116 A44 3.1034 1.0247 116 A45 2.6897 1.0908 116 A46 2.8276 1.1134 116 A47 3.9397 .8776 116 A48 2.8103 1.0293 116 A49 3.2414 1.1544 116 A50 3.8362 1.1717 116 A51 3.9828 1.0549 116 A52 3.5690 1.2316 116 A53 4.8362 .4924 116 A54 4.8276 .4016 116 A55 4.5086 .7283 116 A56 4.7931 .4475 116 A57 4.4828 .7965 116 A58 4.6638 .6586 116 A59 4.2328 .7385 116 A60 4.1293 .9281 116 A61 4.4655 .6384 116 A62 4.3793 .7302 116 A63 2.3879 1.0613 116 Tab1e C-2.--Corre1ation coefficients. 144 A12 A13 A14 A15 A16 A17 A18 A19 A20 A12 1.00000 .35476 .19204 .17306 .36407 .26034 .13023 -.O1115 .15637 A13 .35476 1.00000 .56682 .19219 .11355 .08012 .03615 -.10080 .01103 A14 .19204 .56682 1.00000 .10552 .10442 .08420 -.09566 -.00128 -.O7626 A15 .17306 .19219 1.0552 1.00000 .33411 .18720 .01313 .06165 .09294 A16 .36407 .11355 .10442 .33411 1.00000 .20423 .20098 -.02482 .12457 A17 .26034 .08012 .08420 .18720 .20423 .00000 .20813 .13148 .01245 A18 .13023 .03615 -.O9566 .01313 .20098 .20813 1.00000 .25917 .24514 A19 -.01115 -.10080 -.00128 .06165 -.02482 .13148 .24917 1.00000 .40912 A20 .15637 .01103 -.O7626 .09294 .12457 .01245 .24514 .40912 1.00000 A21 .19938 .06297 .13497 .19197 .12453 .10255 -.O9746 .10385 .17147 A22 .20964 .17918 .11043 .14051 .04564 .19974 .01045 .04946 .00733 A23 .20283 .13225 .04116 .31629 .32117 .23891 .39334 -.00604 -.01190 A24 .11313 .03223 .06850 .02932 .00911 .43536 .12288 .05370 .06558 A25 .10847 -.O1220 .07785 .04565 .16084 .11175 .24231 .76664* .32993 A26 .11868 .03832 .10862 .06147 .07532 .01558 .28062 .44932 .62239 A27 .04120 -.12619 -.O7940 -.05699 .08974 -.00844 .04966 .11105 -.OO182 A28 .06571 -.21621 -.06947 .06177 .08609 -.11211 -.14944 .06695 .00357 A29 -.O6823 -.18876 -.16843 .00043 .14555 .23419 .27135 .23230 .13879 A30 -.13466 -.05377 .04558 .09355 .11803 .16773 .11038 .10793 .07137 A31 .01644 -.O6151 -.10581 .00800 .16450 .01862 .04603 .11581 .17722 A32 .08114 -.10468 -.02421 -.02357 .27624 .07366 .01421 .12217 .02838 A33 -.03295 -.13245 -.20983 .14110 .02393 .02759 .05607 .15207 .22940 A34 .05209 -.O3951 -.02765 .03775 .00795 .12806 .09664 .13117 .05424 A35 -.12110 -.O3195 -.06121 .16455 .15179 .00941 .10558 .21635 .09061 A36 .00722 .08449 -.O4521 .00506 .08589 .01588 .00898 .11030 .04465 A37 .15813 -.O4338 .08724 .10029 .08393 .09111 .11479 .08689 -.07211 A38 .12199 -.O7079 -.07198 .01483 .21179 0 .15201 -.12627 -.19721 A39 .04117 -.13587 -.11902 .05858 .04670 —.10915 -.O1172 -.O6701 -.05269 A40 .02453 -.05060 .08254 -.O3494 .02367 -.01503 -.O7335 -.06147 -.11663 A41 .18939 .02898 -.03777 .08166 .10516 .07430 -.O6989 .09512 .10486 A42 .26073 -.O3379 .05203 .00586 .09075 .08459 .03933 -.10213 -.21589 A43 .08930 .00549 .03815 -.01985 .01355 -.O9797 .01757 -.09943 .07196 A44 -.06518 -.20523 -.16361' -.10071 -.03079 -.03243 .11729 -.02358 -.O7496 A45 .04191 -.07158 -.05062 .13684 .06326 .07616 .05150 .05498 .07989 A46 .00958 -.04581 -.OO409 .03448 .09587 -.05969 .06395 -.O6122 -.02542 A47 .08356 -.02599 .03961 -.05066 .13464 .10412 .12607 -.10987 -.24210 A48 .08797 .04253 .01439 .04834 -.05457 -.O4843 -.08679 -.11904 -.05936 A49 .09680 .05261 .06406 -.00798 .10166 .02159 -.17826 -.08858 -.09884 A50 .13216 .04942 -.OO902 .04253 .15697 .06381 -.16983 -.17913 -.12690 A51 .06176 -.07638 -.10696 -.00480 .25088 .10238 -.05341 .04335 -.O4344 A52 .03062 .02956 -.OO627 .15024 .19931 .19560 .14837 .02417 -.00985 A53 .09012 .04017 .03819 -.02542 -.O6063 0 .03830 .03110 -.01095 A54 .13658 -.O3207 .08008 -.03747 -.16004 0 -.03497 .07949 -.10289 A55 .10192 .01868 .16823 -.21055 -.12299 -.O9126 -.24746 -.16025 -.09376 A56 .13518 -.O9927 .01075 -.11598 -.12650 -.12993 .03430 -.11568 -.15156 A57 -.02455 -.02937 -.02639 .14396 .06922 .12515 -.O7668 -.19390 -.12294 A58 -.01706 -.16315 -.06758 -.05537 .03884 -.20181 -.09335 -.08024 -.09071 A59 .10567 -.O4459 .01878 -.22095 -.O4981 -.06750 -.00254 -.08208 .06144 A60 .13701 -.13745 .02149 -.15098 -.O6092 .06266 -.06009 -.07972 -.05082 A61 .04834 -.O4345 .02043 -.16238 -.O6167 -.16918 -.12459 -.15071 -.18437 A62 -.O4626 -.O4681 -.02046 -.06688 -.13892 -.27306 -.31313 -.16131 -.26085 A63 -.00006 .15660 .09098 .22492 -.05508 .03914 -.16656 .02662 -.03513 Tab1e C-2.--Continued. 145 A21 A22 A23 A24 A25 A26 A27 A28 A29 A12 .19938 .20964 .20283 .11313 .10847 .11868 .04120 .06571 -.06823 A13 .06297 .17918 .13225 .03223 -.01220 .03832 -.12619 -.21621 -.18876 A14 .13497 .11043 .04116 .06850 .07785 .10862 -.07940 -.O6947 -.16843 A15 .19197 .14051 .31629 .02932 .04565 .06147 -.05699 .06177 .00043 A16 .12453 .04564 .32117 .00911 .16084 .07532 .08974 .08609 .14555 A17 .10255 .19974 .23891 .43536 .11175 .01558 -.OO844 -.11211 .23419 A18 -.09746 .01045 .39334 .12288 .24231 .28062 .04966 -.14944 .27135 A19 .10385 .04946 -.OO604 .05370 .76664 .44932 .11105 .06695 .23230 A20 .17147 .00733 —.01190 .06558 .32993 .62239 -.00182 .03357 .13879 A21 1.00000 .24627 .04337 .30189 .13041 .16989 -.13797 .05978 -.08452 A22 .24627 1.00000 .34175 .37156 .14669 .02884 -.06268 .00047 -.OO690 A23 .04337 .34175 1.00000 .16692 -.01450 .09052 .15329 .09794 .12622 A24 .30189 .37156 .16692 1.00000 .07210 .04209 -.01596 -.11186 -.08006 A25 .13041 .14669 -.01450 .07210 1.00000 .48589 .22260 .07474 .34909 A26 .16989 .02884 .09052 .04209 .48589 1.00000 .14856 .11366 .26007 A27 -.13797 -.O6268 .15329 -.01596 .22260 .14856 1.00000 .28390 .25809 A28 .05978 .00047 .09794 -.11186 .07474 .11366 .28390 1.00000 .10328 A29 -.08452 -.OO69O .12622 -.08006 .34909 .26007 .25809 .10328 1.00000 A30 -.11697 -.09403 .12012 -.06158 .17279 .15002 .20045 .08306 .55474 A31 .11066 -.01869 .07789 -.04623 .30494 .19234 .35583 .14697 .43497 A32 -.O3022 .01962 .05779 .06780 .32166 .15687 .35914 .16689 .33738 A33 -.05444 -.05254 .14326 -.07503 .16161 .15790 .29371 .20736 .41518 A34 .09400 -.07045 .10252 .11896 .11261 .18464 .28956 .21819 -.00275 A35 .00428 .02765 .20927 .01781 .29507 .18524 .45484 .20486 .37868 A36 -.05422 .06208 .08377 -.03728 .14785 .08449 .22894 .31424 .25555 A37 .22781 .17444 .08699 .09149 .10456 .03895 .09395 .10257 .01163 A38 .07554 .03883 .14108 -.02347 -.01325 -.07975 .15989 .16253 .11967 A39 .03707 -.O7823 .10377 .00500 -.00776 -.00567 .20536 .31877 .16461 A40 .04038 .06342 .11748 .05483 .03777 .00674 .20293 .34672 .24280 A41 .21233 .16864 .07211 .15285 .23540 .16405 .21915 .23616 .22584 A42 .14155 .18791 .09468 .23315 .03553 .00329 .09742 .22241 .00594 A43 -.O107O .16936 .10443 -.01048 -.02398 .10401 .17946 .24389 .03348 A44 .16643 .09573 .08659 .09886 .06928 .08284 .19520 .23086 .13033 A45 .06839 .18200 .05763 .19140 .15864 .12524 .04075 .22658 .17204 A46 .00179 -.O6637 .08194 .07007 .06883 .02424 .12087 .19990 .04373 A47 -.04907 -.12902 .03601 -.16083 .04389 -.06262 .09844 .11961 -.04594 A48 -.01231 .17349 .08279 .10551 -.12266 -.02977 .11551 .17646 .01298 A49 .11346 .16595 .09574 .16481 -.10308 -.13441 .16722 .21491 -.O4716 A50 .13480 .10004 .05234 .00838 -.O4768 -.14718 .19689 .24978 .05245 A51 .10351 -.14292 -.03066 -.08672 .16251 .00719 .16928 -.05592 .19889 A52 .09120 -.13181 .09701 -.05309 .01310 .04816 .13336 .07064 .16650 A53 -.03137 .13189 .09781 .03647 .07658 -.05223 .00232 -.23056 .06506 A54 .10775 -.01667 -.08418 -.00838 -.01306 -.09518 -.12659 .01472 -.12291 A55 -.02962 .00097 -.31667 .01811 -.00526 -.10595 -.OO742 -.09585 -.13731 A56 .08652 -.15476 .01521 .07461 -.23883 -.12436 -.06531 -.06885 -.24629 A57 .02824 .04041 -.04473 -.00247 -.16660 -.18491 -.20258 -.06839 -.O7513 A58 .16762 -.13829 -.05814 -.08904 -.16382 -.O9709 -.11568 -.O1264 -.36872 A59 .05562 .13206 .07429 .12957 -.07674 -.02836 .04752 .04542 -.02461 A60 -.O4165 -.07303 -.25630 .12547 -.09974 -.21942 .00303 -.15067 -.20574 A61 -.02654 -.10386 -.24049 -.04440 -.08593 -.26993 -.O6987 -.12117 -.13374 A62 -.10100 -.11073 -.17933 -.24173 -.18285 -.34031 -.16846 .03410 -.27831 A63 .06968 .06872 .01588 -.18454 -.08532 -.02264 -.O4195 .02148 -.05934 146 Tab1e C-2.--Continued. A30 A31 A32 A33 A34 A35 A36 A37 A38 A12 -.13466 .01644 .08114 -.03295 .05209 -.12110 .00722 .15813 .12199 A13 -.05377 -.06151 -.10468 -.13245 -.03951 -.03195 .08449 -.04338 -.07079 A14 .04558 -.10581 -.02421 -.20983 -.02765 -.06121 -.04521 .08724 -.07198 A15 .09355 .00800 -.02357 .14110 .03775 .16455 .00506 .10029 .01483 A16 .11803 .16450 .27624 .02393 .00795 .15179 .08589 .08393 .21179 A17 .16773 -.01862 .07366 .02759 .12806 .00941 .01588 .09111 0 A18 .11038 .04603 .01421 .05607 .09664 .10558 .00898 .11479 .15201 A19 .10793 .11581 .12217 .15207 .13117 .21635 .11030 .08689 -.12627 A20 .07137 .17722 .02838 .22940 .05424 .09061 .04465 -.O7211 -.19721 A21 -.11697 .11066 -.03022 -.05444 .09400 .00428 -.05422 .22781 .07554 A22 -.09403 -.01869 .01962 -.05254 -.07045 .02765 .06208 .17444 .03883 A23 .12012 .07789 .05779 .14326 .10252 .20927 .08377 .08699 .14108 A24 -.06158 -.04623 .06780 -.07503 .11896 .01781 -.03728 .09149 -.02347 A25 .17279 .30494 .32166 .16161 .11261 .29507 .14785 .10456 -.01325 A26 .15002 .19234 .15687 .15790 .18464 .18524 .08449 .03895 -.07975 A27 .20045 .35583 .35914 .29371 .28956 .45484 .22894 .09395 .15989 A28 .08306 .14697 .16689 .20736 .21819 .20486 .31424 .10257 .16253 A29 .55474 .43497 .33738 .41518 -.00275 .37868 .25555 .01163 .11967 A30 1.00000 .36906 .22814 .37528 .06447 .42507 .23774 .09474 .08202 A31 .36906 1.00000 .35434 .41630 .13945 .47542 .32017 .01290 .13400 A32 .22814 .35434 1.00000 .28873 .13164 .47296 .31868 .16617 .18875 A33 .37528 .41630 .28873 1.00000 .19053 .47411 .21174 .08453 .02491 A34 .06447 .13945 .13164 .19053 1.00000 .23383 .19844 .20918 .08667 A35 .42507 .47542 .47296 .47411 .23383 1.00000 .26251 .12112 .15511 A36 .23774 .32017 .31868 .21174 .19844 .26251 1.00000 .10786 .21156 A37 .09474 .01290 .16617 .08453 .20918 .12112 .10786 1.00000 .36042 A38 .08202 .13400 .18875 .02491 .08667 .15511 .21156 .36042 1.00000 A39 .13388 .19862 .22620 .31983 .07362 .28868 .31084 .13537 .42848 A40 .14954 .17718 .19761 .18465 .04821 .21927 .26102 .14997 .34446 A41 .17068 .26806 .33835 .26963 .04330 .15204 .33266 .12019 .09679 A42 .01340 .06613 .06523 .03581 .15989 .06185 .10162 .21049 .39559 A43 -.01785 .06532 .13955 .11250 -.01880 .08057 .15963 .04451 .11398 A44 .06781 .23154 .13557 .16571 .25185 .17642 .22681 .19984 .26596 A45 .15178 .08011 .17458 .11550 .04803 .12617 .31318 .07263 .09961 A46 .21821 .12044 .22776 .13709 .12201 .28110 .22189 .19440 .22441 A47 .04079 -.02537 .07697 .02631 .12333 .09225 .03649 .36193 .50356 A48 .06905 -.O7069 .17549 .22485 .09381 .15831 .10818 .09149 .12993 A49 .10078 -.01572 .09990 .12014 .07653 .12069 .31381 .25121 .33592 A50 -.03527 .14449 .08715 .01036 .09457 .09984 .21200 .08152 .41794 A51 .05415 .26587 .21408 -.06220 -.10078 .14738 -.O3410 .13887 .17715 A52 .05001 .10601 .09215 -.01850 .13969 .01918 .35636 .06626 .33495 A53 .04009 -.09162 -.00793 -.00468 .05867 .05745 .01499 .14115 .09790 A54 -.06029 -.19998 -.18452 -.10539 .06010 -.17767 -.02640 .23670 -.08919 A55 -.13879 -.05203 -.00285 -.21770 -.08551 -.30294 .06464 .08395 .02029 A56 -.13997 -.34167 -.16857 -.06509 .01148 -.16932 -.24013 .11155 .13607 A57 -.12953 -.25357 -.18233 -.25913 .03482 -.25639 -.02950 .00976 .09331 A58 -.19222 -.30883 -.11845 -.22124 .03528 -.27486 -.24465 .07875 .05824 A59 .16004 .08613 .06109 .16293 .15353 -.07972 .03852 .20423 .08307 A60 -.31763 -.22912 -.17376 -.17002 -.13987 -.26883 -.21082 .04461 .06159 A61 -.27544 -.O9082 -.08512 -.23383 -.O9977 -.24620 -.05410 .05152 -.06547 A62 -.32011 -.24119 -.13837 -.21858 -.20328 -.10890 -.13424 -.04422 .02494 A63 .13045 -.02256 -.09261 -.15348 -.00907 .00040 .09687 -.10352 -.21361 147 Tab1e C-2.--Continued. A39 A40 A41 A42 A43 A44 A45 A46 A47 A12 .04117 .02453 .18939 .26073 .08930 -.06518 .04191 .00958 .08356 A13 -.13587 -.05060 .02898 -.03379 .00549 -.20523 -.07158 -.04581 -.02599 A14 -.11902 .08254 -.03777 .05203 .03815 -.16361 -.05062 -.00409 .03961 A15 .05858 -.03494 .08166 .00586 -.01985 -.10071 .13684 .03448 -.05066 A16 .04670 .02367 .10516 .09075 .01355 -.03079 .06326 .09587 .13464 A17 -.10915 -.01503 .07430 .08459 -.09797 -.03243 .07616 -.05969 -.10412 A18 —.01172 -.07335 —.06989 .03933 .01757 .11729 .05150 .06395 .12607 A19 —.O6701 -.06147 .09512 -.10213 -.09943 -.02358 .05498 -.06122 -.10987 A20 -.05269 -.11663 .10486 -.21589 .07196 -.07496 .07989 -.02542 -.24210 A21 .03707 .04038 .21233 .14155 -.01070 .16643 .06839 .00179 -.04907 A22 -.07823 .06342 .16864 .18791 .16936 .09573 .18200 -.06637 -.12902 A23 .10377 .11748 .07211 .09468 .10443 .08659 .05763 .08194 .03601 A24 .00500 .05483 .15285 .23315 -.01048 .09886 .19140 .07007 -.16083 A25 -.00776 .03777 .23540 .03553 -.02398 .06928 .15864 .06883 .04389 A26 -.00567 .00674 .16405 .00329 .10401 .08284 .12524 .02424 -.06262 A27 .20536 .20293 .21915 .09742 .17946 .19520 .04075 .12087 .09844 A28 .31877 .34672 .23616 .22241 .24389 .23086 .22658 .19990 .11961 A29 .16461 .24280 .22584 .00594 .03348 .13033 .17204 .04373 -.04594 A30 .13388 .14954 .17068 .01340 -.01785 .06781 .15178 .21821 .04079 A31 .19862 .17718 .26806 .06613 .06532 .23154 .08011 .12044 —.02537 A32 .22620 .19761 .33835 .06523 .13955 .13557 .17458 .22776 .07697 A33 .31983 .18465 .26963 .03581 .11250 .16571 .11550 .13709 .02631 A34 .07362 .04821 .04330 .15989 -.01880 .25185 .04803 .12201 .12333 A35 .28868 .21927 .15204 .06185 .08057 .17642 .12617 .28110 .09226 A36 .31084 .26102 .33266 .10162 .15963 .22681 .31318 .22189 .03649 A37 .13537 .14997 .12019 .21049 .04451 .19984 .07263 .19440 .36193 A38 .52848 .34446 .09679 .39559 .11398 .26596 .09961 .22441 .50356 A39 1.00000 .50552 .34123 .40980 .34563 .30838 .22315 .21837 .30292 A40 .50552 1.00000 .37820 .18872 .25747 .12098 .37304 .21953 .16560 A41 .34123 .37820 1.00000 .19204 .19683 .20493 .34939 .13273 .04209 A42 .40980 .18872 .19204 1.00000 .32294 .42606 .19537 .13108 .41685 A43 .34563 .25747 .19683 .32294 1.00000 .34653 .48063 .12599 .20541 A44 .30838 .12098 .20493 .42606 .34653 1.00000 .37905 .38923 .31641 A45 .22315 .37304 .34939 .19537 .48063 .37905 1.00000 .39233 .03477 A46 .21837 .21953 .13273 .31308 .12599 .38923 .39233 1.00000 .29183 A47 .30292 .16560 .04209 .41685 .20541 .31641 .03477 .29183 1.00000 A48 .35419 .34223 .33627 .25318 .42475 .16717 .40409 .14575 .17975 A49 .35834 .36190 .35036 .37372 .38217 .10368 .30863 .18151 .32350 A50 .34721 .30021 .19084 .33255 .07690 .08080 -.01290 .15814 .15942 A51 .09963 .13951 .07742 -.00883 -.08311 .09015 .00287 .04187 .04583 A52 .24504 .18953 .16103 .09854 .03840 .17343 .06785 .12923 .12053 A53 .03071 .07533 -.05133 .10803 .02678 -.01783 .08262 .07493 .03729 A54 .03643 .04052 —.05809 -.01140 -.11886 -.14644 -.08350 -.00872 -.00510 A55 .15195 .12041 .15219 .17052 .06606 .01045 -.01850 -.O9467 .03483 A56 .08300 .06122 -.17378 .12620 -.04017 -.00981 -.04361 -.03731 .14505 A57 -.03709 -.03746 -.04882 .04945 -.04033 -.04041 .00380 -.13805 .12911 A58 -.01677 -.06229 -.08561 .02005 -.10436 -.16704 -.17070 -.18646 .02477 A59 .05116 .16466 .18168 .15824 .02883 .04834 -.02829 -.01422 .04869 A60 -.00963 .02287 -.19903 .13249 -.06501 .00410 -.14898 -.14654 .07372 A61 -.17567 -.03803 -.09138 .00324 -.01362 -.02109 -.06546 .10168 .01954 A62 .05203 .06947 -.13848 .02592 -.01534 -.13425 -.10203 -.01512 .03603 A63 -.16365 -.13271 .08610 -.18633 .03880 -.12517 .06734 .00558 -.16136 Tab1e C-2.--Continued. 148 A48 A49 A50 A51 A52 A53 A54 A55 A56 A12 .08797 .09680 .13216 .06176 .03062 .09012 .13658 .10192 .03518 A13 .04253 .05261 .04942 -.O7638 .02956 .04017 -.O3207 .01868 -.09927 A14 ' .01439 .06406 -.00902 -.10696 -.OO627 .03819 .08008 .16823 .01075 A15 .05834 -.00798 .04253 -.OO480 .15024 -.02542 -.O3747 -.21055 -.11598 A16 -.05457 .10166 .15697 .25088 .19931 -.06063 -.16004 -.12299 -.12650 A17 -.O4843 .02159 .06381 .10238 .19560 O O -.O9126 -.12993 A18 -.08679 -.17826 -.16983 -.05341 .14837 .03830 -.03497 -.24746 .03430 A19 -.11904 -.08858 -.17913 .14335 .02417 .03110 .07949 -.16025 -.11568 A20 -.05936 -.09884 -.12690 -.O4344 -.OO985 -.01095 -.10289 -.09376 -.15156 A21 -.O1231 .11346 .13480 .10351 .09120 -.03137 .10775 -.02962 .08652 A22 .17349 .16595 .10004 -.14292 -.13181 .13189 -.01667 .00097 -.15476 A23 .08279 .09574 .05234 -.03066 .09701 .09781 -.08418 -.31667 .01521 A24 .10551 .15381 .00838 -.08672 -.05309 .03647 -.OO838 .01811 .07461 A25 -.12266 -.10308 -.04768 .16251 .01310 .07658 -.01306 -.00526 -.23883 A26 -.02977 -.13441 -.14718 .00719 .04816 -.05223 - 09518 -.10595 -.12436 A27 .11551 .16722 .19689 .16928 .13336 .00232 -.12659 -.OO742 -.O6531 A28 .17646 .21491 .24978 -.05592 .07064 -.23056 .01472 -.09585 -.O6885 A29 .01298 -.O4716 .05245 .19889 .16650 .06506 - 12291 -.13731 -.24629 A30 .06905 .10078 -.03527 .05415 .05001 .04009 -.06029 -.13879 -.13997 A31 -.O7069 -.01572 .14449 .26587 .10601 -.O9162 -.19998 -.05203 -.34167 A32 .17549 .09990 .08715 .21408 .09215 -.OO793 - 18452 -.00285 -.16857 A33 .22485 .12014 .01036 -.06220 -.01850 -.00468 - 10539 -.21770 -.06509 A34 .09381 .07653 .09457 -.10078 .13969 .05867 06010 -.08551 .01148 A35 .15831 .12069 .09984 .14738 .01918 .05745 - 17767 -.30294 -.16932 A36 .10181 .31381 .21200 -.03410 .35636 .01499 -.02640 .06464 -.24013 A37 .09149 .25121 .08152 .13887 .06626 .14115 .23670 .08395 .11155 A38 .12993 .33592 .41794 .17715 .33495 .09790 -.08919 .02029 .13607 A39 .35419 .35834 .34721 .09963 .24504 .03071 .03643 .15195 .08300 A40 .34223 .36190 .30021 .13951 .18953 .07533 .04052 .12041 .06122 A41 .33627 .35036 .19084 .07742 .16103 -.05133 -.05809 .15219 -.17378 A42 .25318 .37372 .33255 -.OO883 .09854 .10803 -.01140 .17052 .12620 A43 .42475 .38217 .07690 -.08311 .03840 .02678 -.11886 .06606 -.O4017 A44 .16717 .10368 .18080 .09015 .17343 -.O1783 -.14644 .01045 -.00981 A45 .40409 .30863 -.01290 .00287 .06785 .08262 -.08350 -.01850 -.O4361 A46 .14575 .18151 .15814 .04187 .12923 .07493 -.00872 -.O9467 -.03731 A47 .17975 .32350 .15942 .04583 .12053 .03729 -.00510 .03483 .14505 A48 1.00000 .39017 .01007 —.14720 —.07877 .05827 -.10082 .00220 .04622 A49 .39017 1.00000 .36379 -.13937 .05547 .03956 -.05950 .03888 .08068 A50 .01007 .36379 1.00000 .25800 .37244 -.03183 -.O4205 .10867 -.01544 A51 -.14720 -.13937 .25800 1.00000 .38242 .19539 .11607 .10207 .08447 A52 -.O7877 .05547 .37244 .38242 1.00000 .18366 .14729 .09143 -.00544 A53 .05827 .03956 -.O3183 .19539 .18366 1.00000 .47148 .28281 .35782 A54 -.10082 -.05950 -.O4205 .11607 .14729 .47148 1.00000 .36187 .42870 A55 .00220 .03888 .10867 .10207 .09143 .28281 .36187 1.00000 .13892 A56 .04622 .08068 -.01544 .08447 -.00544 .35782 .42870 .13892 1.00000 A57 .16568 .13696 .20658 .04104 .21395 .07033 .07217 .12768 .08748 A58 -.05640 .05048 -.O7198 -.00842 -.O1941 .15046 .33778 .17832 .44046 A59 .15011 .28034 .04444 -.13992 .02522 .01010 .16579 .13367 .12066 A60 .00769 -.02939 .04363 .21546 .07961 .27505 .22362 .46792 .33712 A61 -.11592 -.21282 -.01343 .12824 -.00801 .07869 .18010 .32798 .09656 A62 .09656 -.06830 .12407 .04243 -.1067O .12592 .16564 .15733 .21563 A63 -.O1963 -.05580 -.05335 -.08718 -.01067 -.17684 -.08652 —.20124 -.26892 Tab1e C-2.--Continued. 149 A57 A58 A59 A60 A61 A62 A63 A12 -.02455 -.01706 .10567 .03701 .04834 -.04626 -.00006 A13 -.02937 -.16315 -.04459 -.13745 -.04345 -.04681 .15660 A14 -.02639 -.06758 .01878 .02149 .02043 -.02046 .09098 A15 .04396 -.05537 -.22095 -.15098 -.16238 -.06688 .22492 A16 .06922 .03884 -.04981 -.06092 -.06167 -.13892 -.05508 A17 .12515 -.20181 -.06750 .06266 -.16918 -.27306 .03914 A18 -.07668 -.09335 -.00254 -.06009 -.12459 -.31313 -.16656 A19 -.19390 -.08024 -.08208 -.O7972 -.15071 -.16131 .02662 A20 -.12294 -.O9071 .06144 -.05082 -.18437 -.26085 -.03513 A21 .02824 .16762 .05562 -.O4165 -.02654 -.10100 .06968 A22 .04041 -.13829 .13206 -.O7303 -.10386 -.10073 .06872 A23 -.04473 -.05814 .07429 -.25630 -.24049 -.17933 .01588 A24 -.00247 -.08904 .12957 .12547 -.04440 -.24173 -.18454 A25 -.16660 -.16382 -.O7674 -.O9974 -.08593 -.18285 -.08532 A26 -.18491 -.O9709 -.02836 -.21942 -.26993 -.34031 -.02264 A27 -.20258 -.11568 .04752 .00303 -.O6987 -.16846 -.04195 A28 -.O6839 -.01264 .04542 -.15067 -.12117 .03410 .02148 A29 -.O7513 -.36872 -.02461 -.20574 -.13374 -.27831 -.05934 A30 -.12953 -.19222 .16004 -.31763 -.27544 —.32011 .13045 A31 -.25357 -.30883 .08613 -.22912 -.09082 -.24119 -.02256 A32 -.18233 -.11845 .06109 -.17376 -.08512 -.13837 -.O9261 A33 -.25913 -.22124 .16293 -.17002 -.23383 -.21858 -.15348 A34 .03482 .03528 .15353 -.13987 -.09977 -.20328 -.00907 A35 -.25639 -.27486 -.07972 -.26883 -.24620 -.10890 .00040 A36 -.02950 -.24465 .03852 -.21082 -.05410 -.13424 .09687 A37 .00976 .07875 .20423 .04461 .05152 -.04422 -.10352 A38 .09331 .05824 .08307 .06159 -.O6547 .02494 -.21361 A39 -.03709 -.01677 .05116 -.OO963 -.17567 .05203 -.16365 A40 -.O3746 -.06229 .16466 .02287 -.03803 .06947 -.13271 A41 -.O4882 -.08561 .18168 -.19903 -.O9138 -.13848 .08610 A42 .04945 .02005 .15824 .13249 .03324 .02592 -.18633 A43 -.O4033 -.10436 .02883 -.O6501 «.01362 -.01534 .03880 A44 -.04041 -.16704 .04834 .00410 -.02109 -.13425 -.12517 A45 .00380 -.17070 -.02829 -.14898 -.06546 -.10203 .06734 A46 -.13085 -.18646 -.O1422 -.14654 .10168 -.01512 .00558 A47 .12911 .02477 .04869 .07372 .01954 .03603 -.16136 A48 .16568 -.05640 .15011 .00769 -.11592 .09656 -.01963 A49 .13696 .05048 .28034 -.02939 -.21282 -.06830 -.05580 A50 .20658 -.07198 .04444 .04363 -.O1343 .12407 -.05335 A51 .04104 -.00842 -.13992 .21546 .12824 .04243 -.08718 A52 .21395 -.01941 .02522 .07961 -.00801 -.10670 -.01067 A53 .07033 .15046 .01010 .27505 .07869 .12592 -.17684 A54 .07217 .33778 .16579 .22362 .18010 .16564 -.08652 A55 .12768 .17832 .13367 .46792 .32798 .15733 -.20124 A56 .08748 .44046 .12066 .33712 .09656 .21563 -.26892 A57 1.00000 .12974 -.00051 .17359 .16983 .16085 .02341 A58 .12974 1.00000 .10865 .10019 .06526 .24940 -.07303 A59 -.00051 .10865 1.00000 .05720 -.02894 -.O8453 -.327OO A60 .17359 .10019 .05720 1.00000 .33783 .20929 -.37799 A61 .16983 .06526 -.02894 .33783 1.00000 .32680 .01350 A62 .16085 .24940 -.08453 .20929 .32680 1.00000 .05533 A63 .02341 -.O7303 -.32700 -.37799 .01350 .05533 1.00000 150 Table C-3.--Factor matrix using principal factor with iterations. Factor Factor Factor Factor Factor Factor Factor Factor Factor 1 2 3 4 5 6 7 8 9 A12 .13641 .11322 .52445 -.OO492 -.10282 .10352 .12403 -.01788 .03779 A13 -.06462 -.O7538 .45691 -.31655 -.23186 .23476 .21722 .16948 .32809 A14 -.O6596 .02638 .38386 -.14214 -.06881 .23337 .21115 .12883 .26438 A15 .15963 -.13860 .29307 -.19735 -.25900 -.00621 .20605 -.OO104 -.05187 A16 .29302 -.O4428 .29747 .02762 -.45309 -.03833 .09059 -.O9794 -.03884 A17 .16616 -.15151 .47077 .02872 -.22268 -.08238 -.37753 .15041 -.07341 A18 .21478 -.25381 .25480 .23936 -.06077 -.47903 -.O7894 -.12542 .28217 A19 .24021 -.46722 .17380 .39490 .27188 .09919 .17510 -.17404 .02101 A20 .18029 -.45132 .19272 .17600 .27661 .07357 .11267 -.13432 -.10536 A21 .12143 .06680 .44491 .02193 .07716 .12797 .11653 -.20243 -.42323 A22 .15995 .02307 .50466 -.26989 .16689 .06524 -.20387 .07359 -.03378 A23 .32327 -.07195 .33950 -.17492 -.20426 -.38839 .06007 .14357 .02382 A24 .12648 .04663 .51075 -.O4527 .25051 -.11461 -.44120 .07374 -.17288 A25 .41593 -.39764 .20786 .43643 .17385 .25779 .08474 -.22489 .14889 A26 .33989 -.42641 .20676 .20106 .25378 .03633 .20030 -.21529 .02307 A27 .47379 .00093 -.19273 .14970 -.03161 .01330 .01869 .06753 -.03511 A28 .40897 .15361 -.17433 -.11251 .09420 .07095 .21708 -.14183 -.20952 A29 .53945 -.3OS62 -.17520 .23232 -.12482 .02285 -.23325 .20799 .08716 A30 .47467 -.24400 -.16748 .03246 -.O9035 -.08064 .03323 .39712 .10424 A31 .55245 -.23714 -.20949 .13870 -.12585 .18066 -.08948 .05850 -.13119 A32 .53320 -.05547 -.10905 .11496 -.O4302 .13160 -.02667 .07498 .01094 A33 .52852 -.17357 -.23940 .04576 .15501 -.14539 .06650 .27388 -.08900 A34 .29914 .01806 .06714 .09641 .07759 -.18382 .14734 -.04210 -.16089 A35 .63242 -.20817 -.21159 .04747 -.08565 -.O7631 .13089 .16259 .05587 A36 .51702 .05750 -.O9759 -.O6517 -.05545 .25505 .01558 .05760 .02628 A37 .26510 .27364 .21799 .18010 .01952 -.11623 .14731 -.00471 .01523 A38 .40783 .49202 -.00168 .11247 -.29314 -.21023 .04426 -.13360 .00031 A39 .52672 .44390 -.17753 .01116 .01567 -.00477 .09855 .01427 -.05612 A40 .45583 .36877 -.07990 -.02272 .05834 .15743 .02328 .17670 .00689 A41 .41962 .10871 .08793 -.O9893 .15162 .32042 -.00960 .07313 -.15631 A42 .34207 .49917 .17921 -.02448 .06861 -.10136 -.09121 -.16143 .02513 A43 .35348 .26823 -.O1665 -.26950 .25568 .07100 -.01378 -.15258 .21961 A44 .46088 .26125 -.10384 .01839 .13815 -.13732 -.24111 -.39275 .05854 A45 .47369 .14729 .06741 -.22892 .30742 .15023 -.15068 -.13509 .24851 A46 .38453 .16794 -.10303 -.O4673 -.O1978 -.O3281 .03201 -.12934 .22727 A47 .25658 .46420 -.O6013 .06185 -.13270 -.28304 .18714 -.26728 .28777 A48 .31722 .33088 -.00259 -.33132 .30037 -.O1077 .01485 .12556 .13045 A49 .39017 .47075 .09904 -.29455 .13295 -.01141 .08195 .12820 -.10530 A50 .29210 .40946 .01441 -.02572 -.34999 .17800 -.04679 -.O7075 -.27053 A51 .13843 .10125 -.02622 .45163 -.38852 .22383 -.10359 -.04382 -.04187 A52 .27567 .21091 .09961 .27552 -.43525 .12655 -.03332 -.05555 -.O7635 A53 -.01588 .25108 .19018 .38273 .06252 .01021 .04638 .29935 .27767 A54 -.21980 .29058 .20231 .43854 .13747 .09291 .26990 .29542 .01576 A55 -.16694 .43374 .06320 .29567 .14942 .43047 -.11745 .12166 .08676 A56 -.24428 .43694 .09170 .29818 .15738 -.29549 .19539 .14038 .01008 A57 —.17425 .28979 .11991 -.03791 -.16489 .02176 -.10637 -.05787 -.O6632 A58 -.33036 .29408 .06193 .19045 .10341 -.13927 .37113 -.00303 -.26208 A59 .12151 .22052 .08585 .06562 .27211 -.13083 -.00630 .30520 -.20174 A60 -.31207 .40529 .09123 .42237 .06578 .06014 -.29946 -.OOO62 .07011 A61 -.30639 .24878 -.06876 .17622 -.O4482 .26073 -.13485 —.12910 .15985 A62 -.34235 .36006 -.20442 -.01094 -.O3479 .18303 .17516 -.O4949 .06371 A63 .04925 -.24262 -.01529 -.39788 -.16888 .26078 .18927 .07633 .01088 Tab1e C-3.--Continued. 151 Factor Factor Factor Factor Factor Factor Factor Factor 10 11 12 13 14 15 16 17 A12 -.19298 4.13426 .10639 .13996 -.01449 .21448 -.08525 .15809 A13 -.27333 -.01882 -.13612 .13320 .12219 -.16457 .08799 -.04557 A14 -.23895 .10788 -.10988 -.00852 -.03162 -.09650 .17167 -.04104 A15 .25124 -.00573 .17733 .03996 .02199 -.00121 .11238 .21023 A16 -.08102 -.18529 .24866 .05367 -.21429 .27123 .02505 -.05980 A17 .15015 .04560 -.06908 -.18143 .02599 .14605 .18768 .14357 A18 .03199 -.19974 -.09281 .03507 .03541 .02357 -.14840 -.09S90 A19 .10805 .07491 .00831 -.34645 .15010 -.02665 .00695 -.01134 A20 -.02160 -.37558 -.00438 .15774 .00089 -.03897 .08799 .04280 A21 .07416 .19200 .04912 .15979 -.21873 -.25568 .05705 .05306 A22 .01197 .17602 .16807 -.08787 .09319 -.10647 -.39823 .01411 A23 .11273 -.03462 .14610 .12325 .16948 .04109 -.26656 -.07609 A24 -.00049 .20237 .04825 .02787 .04163 -.01298 .21487 -.20103 A25 -.08838 .12873 .11089 -.30780 .00804 .00575 -.06765 -.03444 A26 -.05907 -.20864 -.09181 .08679 .00550 -.09036 .06900 -.01094 A27 -.17125 .07566 .05469 .05940 .25540 .20900 .04213 -.04446 A28 .05017 -.01010 -.00412 -.01615 .12612 .15197 -.05796 .04899 A29 .11829 -.12749 .00768 -.12506 -.13142 -.07060 -.13218 .13823 A30 .08557 .06400 -.17268 -.08156 -.32041 -.06210 .06798 .09466 A31 -.20989 .08138 .01594 .22782 -.07263 -.09445 -.11778 .06036 A32 —.14104 .09385 .18410 .00179 -.08568 .23706 .04639 -.19549 A33 -.04695 -.06013 .09664 .11063 .04847 -.01020 .06139 .27038 A34 -.01026 .22795 -.31098 .09283 .23360 .25037 .14026 .07246 A35 -.02414 .29533 .25278 .04775 .16338 -.07975 .14910 -.03795 A36 .08802 -.02092 -.30706 -.01831 .14146 .09922 -.11522 -.13161 A37 -.02962 .26380 -.05328 -.06574 -.17189 .05803 -.06069 .06855 A38 -.08775 -.04396 .00690 -.15868 -.05029 -.l7103 -.07539 -.10570 A39 .02786 -.19013 .07828 -.02025 .09759 -.20387 .04208 .03616 A40 .06587 -.10139 .07824 -.06141 .00996 -.09356 .01469 -.13715 A41 .02077 -.09664 -.00090 -.01951 -.12807 .07006 -.04710 -.01188 A42 -.15369 .06442 .00091 -.04272 .02940 -.04858 -.03788 .18947 A43 .03759 -.20340 .07141 .10661 .05475 .01631 -.05177 .05452 A44 .05519 .19484 -.15879 .25897 -.00277 -.09601 -.06178 .10858 A45 .43392 -.07258 .04084 .08628 -.16171 .07681 .08346 —.12314 A46 .12210 .22570 -.06179 .18773 -.11819 .05109 .09853 -.13119 A47 -.20346 .07831 -.09036 -.19131 -.16193 .00595 .05354 .13783 A48 .07840 -.12490 .16271 -.05923 .03182 .08700 .13790 .11070 A49 -.06795 -.06901 -.06622 -.25251 -.04045 .00754 .09817 -.09871 A50 -.07866 -.01725 -.03857 -.07415 .18827 -.12638 -.02336 -.00737 A51 .10563 .01961 .21464 .11807 -.09399 -.07336 .06578 -.05019 A52 .26883 -.20742 -.33550 .06559 .14569 -.04771 .04692 -.09043 A53 .23540 .05561 .06984 .09295 .10603 -.07956 -.06847 .00518 A54 .27850 .12878 -.14765 .07917 .01322 .03916 -.13232 .09205 A55 -.15512 -.08399 -.11416 .04333 -.03405 .04890 -.04533 .05269 A56 .13722 -.01443 .10502 .11288 .00639 -.08079 .12417 —.07440 A57 .19304 -.12523 -.10417 -.20654 -.01780 .09249 .03467 .11014 A58 .10908 -.05226 .07646 -.01758 -.13664 .11458 -.04117 -.14392 A59 -.27303 -.06920 -.20495 .04169 -.15568 .08541 -.16241 -.04385 A60 -.11537 o.11146 .15018 -.00402 .14475 .02782 .20028 .13634 A61 -.01744 .15028 .03509 .15002 -.06173 .20931 -.10333 .04885 A62 .09778 .07192 .28614 -.06969 .11184 .01139 -.08130 .02754 A63 .29832 .16365 -.10243 -.02814 -.01580 .06074 -.04218 .10302 152 Table C-4.--Varimax rotated factor matrix after rotation with Kaiser normalization. Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Factor 6 Factor 7 Factor 8 A12 .10521 -.03186 .10612 .06960 .13371 .00891 -.06889 .00065 A13 -.02467 -.02857 -.05764 -.03921 -.06201 .05161 -.04166 -.09749 A14 .00934 -.04820 .03223 .04447 .04981 -.05213 ~.02033 .06488 A15 .08036 -.03411 -.05659 .02868 -.27216 .03342 .09940 -.01849 A16 -.00706 .09486 .11916 .10510 -.11480 .15993 .03933 .02205 A17 -.06529 -.13849 -.02600 -.03076 -.05670 .13344 .28959 .08859 A18 -.21499 -.02504 .24342 .10579 -.28511 .03253 .09250 .12676 A19 -.06938 .09216 -.06439 .06646 -.10727 -.03120 .06483 .78026* A20 .03476 .05761 -.22207 -.05746 -.05044 -.04844 .03566 .22647 A21 .01817 -.04805 .06897 .05252 -.04231 .07277 -.09000 .06993 A22 .18783 -.05030 -.01669 -.01840 -.09131 -.07979 -.03575 .13009 A23 .04753 .12564 .07444 .12623 -.49852 .07921 .01897 -.11625 A24 .10034 .02207 -.02172 .03350 -.03122 -.05803 -.12312 .02856 A25 -.03152 .25908 .07746 -.03994 .08548 -.00009 .12370 .83249* A26 .02981 .13053 -.02970 -.05984 -.12276 -.01334 .06041 .36747 A27 .15816 .51753* .07348 -.05038 .02136 .15845 .02969 .10091 A28 .38176* .16648 .07134 -.11578 -.08145 .13515 -.05795 .08062 A29 .06659 .27594(*) .00374 -.06757 -.05082 .18793 .63665(*) .20355 A30 .08342 .22913(*) .02266 .01087 -.23339 .00425 .71365(*) .05779 A31 -.00320 .57575* .03186 -.23372 .06515 .20224 .34546 .03674 A32 .20539 .49398* .01897 -.11119 .02940 .07660 .13503 .21598 A33 .26405 .46777(*) .02574 .01847 -.15193 -.09584 .38481(*) -.04803 A34 .01562 .15802 .12896 .05476 -.10460 .08233 -.00843 .05837 A35 .14989 .72169* .09256 .00078 -.29130 .03074 .20956 .15699 A36 .31575 .16108 -.05600 -.12176 -.01867 .41051* .19761 .13823 A37 .06785 .04067 .38528* .23093 .00226 -.00161 .00902 .14749 A38 .19015 .08219 .60568* .05631 -.13620 .41311* -.01141 -.01561 A39 .54117* .22767 .32759 .09413 -.06070 .32354 .04287 -.07533 A40 .53046* .20239 .10287 .12100 -.00594 .26753 .08621 .02305 A41 .49804* .13542 -.06497 -.11187 .07237 .16332 .19147 .14452 A42 .33291 .01668 .54312* .02045 .13082 .08574 -.05227 -.05272 A43 .57114* .02299 .15458 -.07649 .06251 -.02984 -.06775 -.07806 A44 .18618 .16200 .45060* -.11201 .12015 .12329 .02444 -.10482 A45 .62141* -.05162 -.03633 .00243 .00040 -.00358 .11123 .08887 A46 .18923 .21103 .22337 .02071 -.03228 .05860 .06692 -.02834 A47 .14142 -.04311 .77627* .02040 .00629 .00960 .01924 .01945 A48 .68105* .02077 .10025 .04301 -.03077 -.17010 .02112 -.10421 A49 .61335* -.04920 .24239 -.03388 -.15233 .11873 -.00045 -.01313 A50 .20177 .10383 .23055 -.11299 .05427 .56448* -.08154 -.08237 A51 —.15147 .24383 .06061 .17131 .24660 .39383* .08072 .06725 A52 .00935 -.07820 .07450 .13835 .02467 .76083* .11496 -.01460 A53 .03368 .03965 .03717 .65543* .13957 .08375 .06472 .05155 A54 -.07451 -.16991 -.07079 .72603* .19909 .06591 .04453 .08182 A55 .12646 -.10066 .00636 .24066 .64235* .14110 -.04312 .00702 A56 .01541 -.09521 .18164 .63002* -.01374 -.06463 -.24267 -.16415 A57 .06584 -.42111 .07061 .03916 .09946 .18243 -.01725 -.06678 A58 -.04970 -.23758 -.00130 .38489* -.06559 -.06073 -.31217 -.01048 A59 .14211 .02407 .08453 .12399 .03760 -.05742 .10883 -.11494 A60 -.03984 -.08401 .16591 .30482 .54789* .00424 -.22273 -.07548 A61 -.14983 -.07798 .00044 .09713 .52784* -.02550 -.14927 -.04954 A62 .08032 -.07498 -.00633 .19703 .20269 -.03907 -.31360 -.04755 A63 -.00002 -.17935 -.29681 -.21807 -.l4966 -.00973 .11012 .04304 153 Tab1e C-4.--Continued. Factor 9 Factor10 Factorll Factor12 Factor13 Factor14 Factorls Factor16 Factorl7 A12 .16951 .28784 .05488 .51021* .08860 -.09218 .02384 .23405* .10984 A13 .06906 .84176* .00320 .10040 -.03040 -.02686 -.07501 .13610 -.03412 A14 -.02993 .67616* .05106 .05743 .07318 .00656 .00754 -.02035 -.01031 A15 .03054 .13509 .03444 .31721 .19279 -.06104 -.40446* .07423 .08526 A16 .05855 .05730 .05651 .73153* .03750 .03883 -.04816 -.03811 -.07503 A17 -.01831 .05062 .61320* .25109 -.01992 -.08902 -.14252 .11277 .13777 A18 .43154* -.07092 .16402 .17982 -.34830* .16607 .03571 .16077 -.02323 A19 .28765 -.05927 .05224 -.07040 .02679 -.05940 -.09842 .01153 .11287 A20 .67937* -.01864 .00670 .09925 .10205 -.07806 .01061 -.O4863 .01537 A21 .14197 .04712 .15517 .09651 .75011* .04028 -.00657 .10589 .02559 A22 -.08046 .13423 .26040 .05051 .16591 -.01566 .05839 .69040* -.07591 A23 .07079 .03286 .12740 .32556 -.11793 .04071 -.03105 .41709* .06011 A24 .04189 .04181 .76879* -.01674 .18595 .09458 .14421 .16545 .02283 A25 .24612 .03732 .04456 .09410 .04316 .04676 -.04518 .08966 -.01979 A26 .63668* .07943 -.02328 .04242 .09410 .05711 .01034 -.02848 .07704 A27 .00635 -.09074 .00918 .08363 -.16154 -.01200 .05309 -.02422 .25133 A28 -.01230 -.17688 -.21490 .05114 .10565 .01882 .00880 .01503 .29640* A29 .14321 -.22252 .03955 .05978 -.15036 .00579 -.03720 .08932 -.13501 A30 -.00876 .03727 -.00298 .00365 -.01602 .10988 .08058 -.13494 .02327 A31 .15796 -.07069 -.09071 .05022 .15273 .05876 .07200 .10644 .00872 A32 -.06549 -.05650 .06190 .26478 -.04074 .16807 .12901 -.07694 .01364 A33 .21400 -.17696 -.04104 -.01833 -.01052 -.16276 -.01002 -.01134 .17329 A34 .08361 -.02434 .11515 -.01111 .03282 .07203 .06121 -.04809 .62692* A35 -.04990 -.00832 .03492 -.00460 -.00343 .06484 -.19524 -.03626 .08481 A36 -.01476 .07044 -.09471 -.03364 -.09989 .21831 .10524 .09735 .23648* A37 -.10482 .03911 .05036 .14715 .19208 .11726 .13545 .06686 .17356 A38 -.12233 -.06651 -.02050 .12416 .01044 .02652 .10799 -.00689 -.11135 A39 .04150 -.11564 -.10740 -.05438 .04909 -.07050 .00368 -.04445 -.03711 A40 -.09714 .00113 -.00599 —.00854 .02473 .04948 .11366 -.01216 -.10122 A41 .05583 .01018 .02088 .14539 .21806* .07440 .16091 .09749 .05330 A42 -.01241 .00345 .13413 .04720 .09953 -.01119 .04473 .19625 .11167 A43 .17195 .01183 -.08461 -.00422 -.08967 .18204 -.06105 .16210 -.00720 A44 .17583 -.24399 .07953 -.18763 .11709 .40888* -.06861 .18925 .18041 A45 .12293 -.08480 .14632 .02233 .01933 .54530* -.14191 .06652 -.05228 A46 -.04767 .02011 -.00634 .01026 .01681 .49525* -.07449 -.07002 .09431 A47 -.10319 .05565 -.14541 .08811 -.09433 .10342 .01342 -.14662 .08057 A48 -.04240 .02189 .07324 .00917 -.06906 .00447 -.04S78 .02189 .04872 A49 -.18847 .11905 .11007 .02123 .08324 -.04525 .25476 -.03945 .08577 A50 -.19728 .01802 .01518 .06287 .16176 -.15644 -.00742 .07168 .04702 A51 -.04753 -.12801 .03717 .23818 .13693 .06026 -.17303 -.12170 -.23638 A52 .10172 -.00330 .04287 .11807 -.02497 .10659 -.07894 -.07689 .11733 A53 -.01189 .07819 .07082 -.02140 -.10295 .05112 -.04518 .11843 -.07146 A54 -.07505 .04508 -.10877 -.03060 .12871 -.01373 .10862 .04567 .18305 A55 -.04859 .13668 -.02675 -.05434 .01378 -.06454 .23418 -.00208 -.05614 A56 -.01182 -.08278 .04861 -.04226 .04436 -.04746 .09503 -.18053 -.04372 A57 -.17717 -.06399 .08918 .09303 -.01839 -.09218 -.07854 -.03560 .03260 A58 -.10391 -.16019 -.18247 .14708 .20373 -.08233 .23210 -.20067 .02884 A59 .05244 -.00556 .05674 .00618 .06648 -.10195 .60472* .07592 .13295 A60 .00557 -.09002 .27673 -.02395 -.12341 -.25078 -.03475 -.11548 -.12307 A61 -.19436 -.03182 -.10023 .05866 -.03620 .17116 -.03977 .03654 -.01967 A62 -.36394 -.05838 -.29837 -.04237 -.00667 -.09885 -.18018 -.02720 -.13520 A63 -.18861 .16457 -.22435 .01380 .13836 .16066 -.33025* .07823 .15809 APPENDIX D RELIABILITY ANALYSES OF SCALES 154 155 Table D-1.--Re1iabi1ity analysis for scale: Dimension 1-~Understanding the Objectives of Teaching Mathematics. A28: Understand objectives of teaching math A39: Competent to critically assess programs A40: Able to construct adequate tests A41: Competent in methods of teaching math A43: Assessment of math courses A45: Problems of teaching math A48: Evaluation and grading A49: High correlation between college and school Means Std. Dev. Cases A28 3.233 .963 116 A39 2.940 1.066 116 A40 2.353 1.105 116 A41 2.250 1.118 116 A43 2.871 1.018 116 A45 2.690 1.091 116 A48 2.810 1.029 116 A49 3.241 1.154 116 Correlation Matrix: A28 A39 A40 A41 A43 A45 A48 A49 A28 .00000 A39 .31877 1.00000 A40 .34672 .50552 1.00000 A41 .23616 .34123 .37820 1.00000 A43 .24389 .34563 .25747 .19683 1.00000 A45 .22658 .22315 .37304 .34939 .48063 1.00000 A48 .17464 .35419 .34223 .33627 .42475 .40409 1.00000 A49 .21491 .35834 .36190 .35036 .38217 .30862 .39017 1.00000 N of Cases = 116 Statistics for Mean Variance Std. Dev. Variables 5“” 22.388 30.326 5.5 8 Item Means Mean Min. Max. Range Min./Max. Variance 2.798 2.3 3.2 1.0 1.4 .132 Tab1e D-1.--Continued. 156 Scale Scale Item-Total Mean Variance Corrected Squared .AIPha Statistics if Item if Item Item-Total MUItIPIT 1f Item Deleted Deleted Correlation Correlation Deleted A28 19.155 25.715 .377 .171 .794 A39 19.448 23.606 .539 .363 .770 A40 20.034 23.060 .569 .384 .765 A41 20.138 23.842 .479 .266 .780 A43 19.517 24.182 .511 .365 .775 A45 19.698 23.639 .518 .359 .774 A48 19.578 23.863 .537 .320 .771 A49 19.147 23.204 .521 .289 .774 A value of 99.0 is printed if a coefficient cannot be computed. Reliability coefficients AIpha = .79795 8 items Standardized item alpha = .79726 157 Table D-2.-—Re1iabi1ity analysis for scale: Dimension 2--Understanding Basic Mathematics to Teach Mathematics. A27: Understand basic math to teach math A29: Algebra A30: Geometry A31: Trigonometry A32: Ca1cu1us A33: Arithmetic A35: Analytical geometry Means Std. Dev. Cases A27 2.112 .985 116 A29 1.698 .887 116 A30 2.241 1.139 116 A31 2.388 .892 116 A32 1.716 .902 116 A33 2.457 1.204 116 A35 1.888 .882 116 Correlation Matrix: A27 A29 A30 A31 A32 A33 A35 A27 1.00000 A29 .25809 1.00000 A30 .20045 .55474 1.00000 A31 .35583 .43497 .36906 1.00000 A32 .35914 .33738 .22814 .35434 1.00000 A33 .29371 .41518 .37528 .41630 .28873 1.00000 A35 .45484 .37868 .42507 .47542 .47296 .47411 1.00000 N of cases = 116 Statistics for Mean Variance Std. Dev. Variables 5““? 14.500 22.078 4.7 7 Item Means Mean Min. Max. Range, Min./Max. Variance 2.071 1.7 2.5 1.4 .096 Tab1e D-2.--Continued. 158 Scale Scale _ . Corrected Squared Alpha étg$112§2; iYeIEem ¥2rizgge Item-Total Multiple if Item Correlation Correlation Deleted Deleted Deleted A27 12.388 17.457 .444 .256 .793 A29 12.802 17.013 .585 .410 .769 A30 12.259 16.106 .511 .375 .783 A31 12.112 17.005 .581 .345 .770 A32 12.784 17.666 .474 .283 .787 A33 12.043 15.485 .543 .318 .778 A35 12.612 16.553 .661 .464 .757 A value of 99.0 is Reliability coefficients Alpha = .80242 printed if a coefficient cannot be computed. 7 items Standardized item alpha = .80918 159 Table D-3.--Re1iabi1ity analysis for scale: Dimension 3--Preparation for Higher Mathematics. A37: Prepared for higher studies in math A38: Insight to develop math curricula A42: Curriculum planning in math A44: Concept development in math A47: Math textbook writing Means Std. Dev. Cases A37 2.948 1.003 116 A38 3.293 1.004 116 A42 3.474 .982 116 A44 3.103 1.025 116 A47 3.940 .878 116 Correlation Matrix: A37 A38 A42 A44 A47 A37 1.00000 A38 .36042 1.00000 A42 .21049 .39559 1.00000 A44 .19984 .26596 .42606 1.00000 A47 .36193 .50356 .41685 .31641 1.00000 N of cases = 116 Statistics for Mean Variance Std. Dev. Variables sca‘e 16.749 11.350 3.4 5 Item Means Mean Min. Max. Range Min.[Max. Variance 3.352 2.9 3.9 1.0 1.3 .147 Scale Scale Item-Total Mean Variance Corrected Squared _Alpha Statistics if Item if Item Item'T°t?‘ ”"It‘p‘? ‘1 A‘pha Deleted Deleted Correlat1on Correlation Deleted A37 13.810 8.155 .382 .178 .713 A38 13.466 7.399 .538 .328 .650 A42 13.284 7.614 .511 .301 .662 A44 13.655 7.915 .414 .211 .702 A47 12.819 7.767 .575 .349 .642 A value of 99.0 is printed if a coefficient cannot be computed. Reliability coefficients 5 items Alpha = .72138 Standardized item alpha = .72542 160 Table D-4.--Reliabi1ity analysis for scale: Dimension 4--C011ege-Sch001 Relations. A53: College program closer to teaching in schools A54: More contacts between schools and college A56: More relevance for needs of schools A58: College to offer in-service refresher Means Std. Dev. Cases A53 4.836 .492 116 A54 4.828 .402 116 A56 4.793 .448 116 A58 4.664 .659 116 Correlation Matrix: A53 A54 A56 A58 A53 1.00000 A54 .47148 1.00000 A56 .35782 .42870 1.00000 A58 .15046 .33778 .44046 1.00000 N of cases a 116 Statistics for Mean Variance Std. Dev. Variables 5“” 19.121 2.072 1.4 4 Item Means Mean Min. Max. Range Min./Max. Variance 4.780 4.7 4.8 .2 1.0 .006 Sca1e Sca1e Item-Total Mean Variance Corrected Squared Alpha . . . . Item-Total Multiple if Item Stat1st1cs 1f Item 0:16:23 Correlation Correlation Deleted Deleted A53 14.284 1.388 .381 .257 .640 A54 14.293 1.392 .548 .328 .555 A56 14.328 1.300 .560 .315 .534 A58 14.457 1.102 .388 .227 .678 A value of 99.0 is printed if a coefficient cannot be computed. Reliability coefficients 4 items Alpha = .66551 Standardized item alpha = .69639 161 Table D-5.--Re1iabi1ity analysis for scale: Dimension 5--Emphasis on Practical Problems. A55: More seminars between college and schools A60: Greater emphasis on practical problems A61: More experiments with new teaching methods Means Std. Dev. Cases A55 4.509 .728 116 A60 4.129 .928 116 A61 4.466 .638 116 Correlation Matrix: A55 A60 A61 A55 1.00000 A60 .46792 1.00000 A61 .32798 .33783 1.00000 N of cases = 116 Statistics for Mean Variance Std. Dev. Variables sca‘e 13.103 3.137 1.8 3 Item Means Mean Min. Max. Range Min./Max. Variance 4.368 4.1 4.5 .4 1.1 .043 Scale Sca1e Item-Total Mean Variance Corrected Squared .Alpha Statistics if Item if Item Item'T°ta‘ "“‘t‘p‘e ‘1 Item Deleted Deleted Correlation Correlation Deleted A55 8.595 1.669 .498 .252 .480 A60 8.974 1.243 .499 .257 .491 A61 8.638 2.024 .388 .151 .625 A value of 99.0 is printed if a coefficient cannot be computed. Reliability coefficients Alpha a .63967 3 items Standardized item alpha = .64570 162 Table D-6.--Re1iabi1ity analysis for scale: Dimension 6--Preparation for School Teaching. A36: Modern mathematics A38: Insight to develop math curricula A50: Half material taught never used in schools A51: College ignores differences in schools A52: College does not prepare adequately Means Std. Dev. Cases A36 1.836 1.046 116 A38 3.293 1.004 116 A50 3.836 1.172 116 A51 3.983 1.055 116 A52 3.569 1.232 116 Correlation Matrix: A36 A38 A50 A51 A52 A36 1.00000 A38 .21156 1.00000 A50 .21200 .41794 1.00000 A51 -.03410 .17715 .25800 1.00000 A52 .35636 .33495 .37244 .38242 1.00000 N of cases a 116 Statistics for Mean Variance Std. Dev. Variables sca‘e 16.517 12.808 3.6 5 Item Means Mean Min. Max. Range Min./Max. Variance 3.303 1.8 4.0 2.1 2.2 .742 Scale Sca1e Item-Total Mean Variance Corrected Squared .Alpha Statistics if Item if Item Item‘T°t?‘ ”u‘t‘P‘? If Item Deleted Deleted Correlation Correlation Deleted A36 14.681 9.906 .274 .179 .659 A38 13.224 9.167 .433 .218 .592 A50 12.681 8.219 .479 .253 .565 A51 12.534 9.764 .293 .200 .651 A52 12.948 7.476 .567 .341 .515 A value of 99.0 is printed if a coefficient cannot be computed. Reliability coefficients 5 items Alpha = .65407 Standardized item alpha = .64773 163 Table D-7.--Re1iabi1ity analysis for scale: Dimension 8--Student Teaching. A18: Educational media A20: Student Teaching (1 A26: Student Teaching (2 Means Std. Dev. Cases A18 1.526 .918 116 A20 1.241 .668 116 A26 1.233 .533 116 Correlation Matrix: A18 A20 A26 A18 1.00000 A20 .24514 1.00000 A26 .28062 .62239 1.00000 N of cases = 116 Statistics for Mean Variance Std. Dev. Variables sca‘e 4.000 2.591 1.6 3 Item Means Mean Min. Max. Range Min.[Max. Variance 1.333 1.2 1.5 .3 1.2 .028 Scale Sca1e Item-Total Mean Variance Corrected Squared .Alpha Statistics if Item if Item Item-Total “"1t1p19 1f Item Deleted Deleted Correlation Correlation Deleted A18 2.474 1.173 .289 .087 .755 A20 2.759 1.402 .470 .393 .392 A26 2.767 1.589 .534 .405 .378 A value of 99.0 is printed if a coefficient cannot be computed. Reliability coefficients 3 i Alpha = .58953 Standardized tems item alpha = .65035 164 Table D-8.--Re1iabi1ity analysis for scale: Dimension 9--Educationa1 Thought. A12: Introduction to education and psychology A13: Social and philosophical foundations of education A14: Development of educational thought Means Std. Dev. Cases A12 2.422 1.181 116 A13 2.716 1.141 116 A14 2.819 1.184 116 Correlation Matrix: A12 A13 A14 A12 1.00000 A13 .35476 1.00000 A14 .19204 .56682 1.00000 N of cases = 116 Statistics for Mean Variance Std. Dev. Variables 50”" 7.957 7.120 2.7 3 Item Means Mean Min. Max. Range Min./Max. Variance 2.652 2.4 2.8 .4 1.2 .042 Scale Sca1e Item-Total Mean Variance Corrected Squared Alpha . . . . Item-Total Multiple if Item Statistics if Item if Item . . Deleted Deleted Correlation Correlation Deleted A12 5.534 4.234 .307 .126 .723 A13 5.241 3.333 .597 .384 .322 A14 5.138 3.650 .457 .321 .523 A value of 99.0 is printed if a coefficient cannot be computed. Reliability coefficients 3 items Alpha = .63693 Standardized item alpha = .63913 165 Table D-9.--Re1iabi1ity analysis for scale: Dimension 10--Curricu1um Design. A17: Principles of curriculum A24: Curriculum design A62: Better preparation for testing and evaluation Means Std. Dev. Cases A17 2.000 1.047 116 A24 2.379 1.069 116 A62 4.379 .730 116 Correlation Matrix: A17 A24 A62 A17 1.00000 A24 .43536 1.00000 A62 -.27306 -.24173 1.00000 N of Cases - 116 Statistics for Mean Variance Std. Dev. Variables scale 8.759 2.950 1.7 3 Item Means Mean Min. Max. Range Min.1Max. Variance 2.920 2.0 4.4 2.4 2.2 1.634 Sca1e Sca1e Item-Total Mean Variance Corrected Squared Alpha . - . . Item-Total Multiple if Item Statistics if Item if Item . . Deleted Deleted Correlation Correlation Deleted A17 6.759 1.298 .233 .219 -.581 A24 6.379 1.211 .254 .206 -.689 A62 4.379 3.211 -.304 .093 .607 A value of 99.0 is printed if a coefficient cannot be computed. Reliability coefficients 3 items Alpha = .09118 Standardized item alpha = -.08387 166 Table D-10.--Re1iabi1ity analysis for scale: Dimension 11--Educationa1 Psychology. A12: Introduction to education and psychology A16: Educational psychology (childhood and adolescence) A23: Introduction to counseling and mental hygiene Means Std. Dev. Cases A12 2.422 1.181 116 A16 1.974 1.017 116 A23 2.543 1.321 116 Correlation Matrix: A12 A16 A23 A12 1.00000 A16 .36407 1.00000 A23 .20283 .32117 1.00000 N of cases = 116 Statistics for Mean Variance Std. Dev. Variables scale 6.940 6.544 2.6 3 Item Means Mean Min. Max. Range Mini/Max. Variance 2.313 2.0 2.5 .6. 1.3 .090 Scale Sca1e Item-Total Mean Variance Corrected Squared .Alpha Statistics if Item if Item Item'T°t91 M““‘”‘? ‘f Item Deleted Deleted Correlation Correlation Deleted A12 4.517 3.643 .334 .141 .474 A16 4.966 3.773 .440 .196 .335 A23 4.397 3.302 .312 .112 .529 A value of 99.0 is printed if a coefficient cannot be computed. Reliability coefficients Alpha = .54327 3 items Standardized item alpha = .55782 167 Table D-11.--Re1iability analysis for scale: Factor 13. A18: Educational media A21: Education in Saudi Arabia A41: Competent in methods of teaching math Means Std. Dev. Cases A18 1.526 .918 116 A21 3.112 1.053 116 A41 2.250 1.118 116 Correlation Matrix: A18 A21 A41 A18 1.00000 A21 -.09746 1.00000 A41 -.06989 .21233 1.00000 N of cases = 116 Statistics for Mean Variance Std. Dev. Variables scale 6.888 3.370 1.8 3 Item Means Mean Min. Max. Range, Min./Max. Variance 2.296 1.5 3.1 1.6 2.0 .631 Scale Sca1e Item—Total Mean Variance Corrected Squared Alpha . . . . Item-Total Multiple if Item Statistics if Item if Item . . Deleted Deleted Correlation Correlation Deleted A18 5.362 2.859 -.107 .012 .350 A21 3.776 1.949 .106 .052 -.l47 A41 4.638 1.763 .120 .048 -.214 A value of 99.0 is printed if a coefficient cannot be computed. Reliability coefficients 3 items Alpha a .07481 Standardized item alpha = .04366 168 Table D-12.--Re1iabi1ity analysis for scale: Dimension 12--Prob1ems of Teaching Mathematics. A44: Concept development in mathematics A45: Problems of teaching mathematics A46: Mathematics in general Means Std. Dev. Cases A44 3.103 1.025 116 A45 2.690 1.091 116 A46 2.828 1.113 116 Correlation Matrix: A44 A45 A46 A44 1.00000 A45 .37905 1.00000 A46 .38923 .39233 1.00000 N of cases - 116 Statistics for Mean Variance Std. Dev. Variables scale 8.621 6.168 2.5 3 Item Means Mean Min. Max. Range Min./Max. Variance 2.874 2.7 3.1 .4 1.2 .044 Scale Scale Item-Total Mean Variance Corrected SQUSFEd oAlpha Statistics if Item if Item Item'T°tal ”U‘t‘p‘e ‘I Item Deleted Deleted Correlation Correlation Deleted A44 5.517' 3.382 .460 .212 .563 A45 4.931 3.178 .463 .214 .559 A46 5.793 3.087 .471 .221 .549 A value of 99.0 is printed if a coefficient cannot be computed. Reliability coefficients Alpha - .65382 3 items Standardized item alpha - .65433 169 Table D-13.--Re1iabi1ity analysis for scale: Factor 15. A15: Developmental psychology A59: Present program needs improvement A63: More emphasis on abstract math Means Std. Dev. Cases A15 1.716 .976 116 A59 4.233 .738 116 A63 3.612 1.061 116 Correlation Matrix: A15 A59 A63 A15 1.00000 A59 -.22095 1.00000 A63 -.22492 .32700 1.00000 N of cases - 116 Statistics for Mean Variance Std. Dev. Variables scale 9.560 2.353 1.5 3 Item Means Mean Min. Max. Range Min.[Max. Variance 3.187 1.7 4.2 2.5 2.5 1.720 Sca1e Sca1e Item-Total Mean Variance Corrected Squared .Alpha Statistics if Item if Item Item-Total Multiple 1f Item Deleted Deleted Correlation Correlation Deleted A15 7.845 2.184 -.272 .075 .469 A59 5.328 1.613 .103 .130 -.578 A63 5.948 1.180 .020 .131 -.540 A value of 99.0 is printed if a coefficient cannot be computed. Reliability coefficients 3 items Alpha - -.17348 Standardized item alpha 3 -.12910 170 Table D-14.--Re1iabi1ity analysis for scale: Factor 16. A22: Educational administration and planning A23: Introduction to counseling and mental hygiene A12: Introduction to education and psychology Means Std. Dev. Cases A22 2.405 1.165 116 A23 2.543 1.321 116 A12 2.422 1.181 116 Correlation Matrix: A22 A23 A12 A22 1.00000 A23 .34175 1.00000 A12 .20964 .20283 1.00000 N of cases = 115 Statistics for Mean Variance Std. Dev. Variables sca‘e 7.371 6.757 2.6 3 Item Means Mean Min. Max. Range Min./Max. Variance 2.457 2.4 2.5 .1 1.1 .006 Scale Sca1e . Corrected Squared Alpha Item-Total Mean Variance Item-Total Multiple if Item Statistics if Item if Item . , Deleted Deleted Correlation Correlation Deleted A22 4.966 3.773 .360 .137 .335 A23 4.828 3.327 .349 .135 .347 A12 4.948 4.154 .251 .063 .506 A value of 99.0 is printed if a coefficient cannot be computed. Reliability coefficients 3 items Alpha = .50192 Standardized item alpha = .50187 171 Table D-15.--Re1iabi1ity analysis for scale: Factor 17. A34: Statistics A28: Understand objectives of teaching mathematics A51: College ignores differences in schools Means Std. Dev. Cases A34 2.362 1.168 116 A28 3.233 .963 116 A51 3.983 1.055 116 Correlation Matrix: A34 A28 A51 A34 1.00000 A28 .21819 1.00000 A51 -.10078 -.05592 1.00000 N of cases = 116 Statistics for Mean Variance Std. Dev. Variables scale 9.578 3.533 1.9 3 Item Means Mean Min. Max. Range Min./Max. Variance 3.193 2.4 4.0 1.6 1.7 .658 Scale Sca1e Item-Total Mean Variance Corrected Squared Alpha Item-Total Multiple if Item Statistics if Item if Item Correlation Correlation Deleted Deleted Deleted A34 7.216 1.927 .075 .055 -.118 A28 6.345 2.227 .131 .049 -.223 A51 5.595 2.782 -.103 .011 .353 A value of 99.0 is printed if a coefficient cannot be computed. Reliability coefficients 3 items Alpha = .05474 Standardized item alpha = .05907 APPENDIX E ANALYSIS OF VARIANCE 172 173 Table E-1.--Ana1ysis of variance of Dimension 1--Understand the objec- tives of teaching mathematics--by sex and graduated with 40 or 60 credits. DOl Understand the Objectives of Teaching Mathematics By A01 Sex A03 Graduated with 40 or 60 credits With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .005 2 .003 .005 .995 A04 .003 1 .003 .006 .941 A05 .000 1 .000 .000 .988 Main effects .538 2 .269 .548 .580 A01 .263 1 .263 .537 .465 A03 .097 1 .097 .197 .658 2-way interactions .000 1 .000 .001 .980 A01 A03 .000 l .000 .001 .980 Explained .543 5 .109 .222 .953 Residual 53.950 110 .490 Total 54.493 115 .474 Cell Means A01 S A03: 40/60 Credits T : ex otal 40 60 Sex 1 = Male 5' 2.86 2.79 2.84 n (59) (17) (76) 2 = Female 5' 2.75 2.69 2.72 n (15) (25) (40) Total m' 2.83 2.74 2.80 40/60 credits n (74) (42) (116) 174 Table E-2.--Ana1ysis of variance of Dimension 1--Understand the objec- tives of teaching mathematics--by sex and teaching at which level. DOl Understand the Objectives of Teaching Mathematics By A01 Sex A08 Teaching at which level? With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .016 2 .008 .015 .985 A04 .015 l .015 .030 .862 A05 .012 1 .012 .023 .879 Main effects .737 2 .369 .736 .482 A01 .445 1 .445 .889 .348 A08 .323 1 .323 .644 .424 2-way interactions .043 1 .043 .087 .769 A01 A08 .043 1 .043 .087 .769 Explained .796 5 .159 .318 .901 Residual 53.105 106 .501 Total 53.901 111 .486 Cell Means A08: Teaching Level A01: Sex - . Total Middle High Sex School School 1 = Male 6' 2.88 2.74 2.85 n (55) (19) (74) 2 = Female 16 2.74 2.69 2.72 n (28) (10) (38) Total m 2.83 ' 2.72 2.81 teaching level n (83) (29) (112) 175 Table E-3.--Ana1ysis of variance of Dimension l--Understand the objec- tives of teaching mathematics--by sex and percent of mathematics teaching duty. DOl Understand the Objectives of Teaching Mathematics By A01 Sex A09 Percent of mathematics teaching duty With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .016 2 .008 .017 .984 A04 .015 1 .015 .033 .857 A05 .012 1 .012 .025 .874 Main effects 1.833 2 .942 2.010 .139 A01 .523 1 .523 1.116 .293 A09 1.469 1 1.469 3.136 .079 2-way interactions 2.354 1 2.354 5.025 .027 A01 A09 2.354 1 2.354 5.025 .027 Explained 4.252 5 .850 1.816 .116 Residual 49.649 106 .468 Total 53.901 111 .486 Cell Means , A09: Mathematics Teaching Duty Total A01. Sex Sex 80% 100% 1 = Male E? 2.87 2.84 2.85 n (16) (58) (74) 2 = Female 5 3.31 2.57 2.72 n ( 8) (30) (38) Total .11 3.02 2.75 2.81 percent teaching duty n (24) (88) (112) 176 Table E-4.--Analysis of variance of Dimension 1--Understand the objec- tives of teaching mathematics--by year graduated from Mecca College of Education (male teachers). DOl Understand the Objectives of Teaching Mathematics By A02 Year Graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for male teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .414 2 .207 .406 .668 A04 .296 1 .296 .581 .448 A05 .048 1 .048 .095 .759 Main effects 1.179 4 .295 .578 .679 A02 1.179 4 .295 .578 .679 Explained 1.593 6 .266 .521 .791 Residual 35.168 69 .510 Total 36.762 75 .490 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 1977—78 1978-79 1979-80 Total m 2.92 2.87 2.96 2.83 2.56 2.84 (15) (22) (17) ( 9) (13) (76) 177 Table E-5.--Analysis of variance of Dimension l--Understand the objec- tives of teaching mathematics--by year graduated from Mecca College of Education (female teachers). DOl Understand the Objectives of Teaching Mathematics By A02 Year graduated from Mecca College of Education With A04 Mathematics GPA A05 Mathematics GPA Selected for female teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .477 2 .238 .536 .590 A04 .435 l .435 .977 .330 A05 .128 1 .128 .288 .595 Main effects 1.262 2 .631 1.418 .256 A02 1.262 2 .631 1.418 .256 Explained 1.739 4 .435 .977 .433 Residual 15.573 35 .445 Total 17.312 39 .444 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 1977-78 1978-79 1979-80 T°ta‘ m' 0 0 2.91 2.73 2.55 2.72 n ( 0) ( 0) (12) (13) (15) (40) 178 Table E-6.—-Ana1ysis of variance of Dimension 2--Understand basic math to teach mathematics--by sex and graduated with 40 or 60 credits. 002 Understand Basic Math to Teach Mathematics By AOl Sex A03 Graduated with 40 or 60 credits With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .721 2 .360 .786 .458 A04 .048 1 .048 .105 .746 A05 .450 1 .450 .982 .324 Main effects .672 2 .336 .733 .483 A01 .372 l .372 .812 .369 A03 .528 1 .528 1.152 .285 2-way interactions .001 1 .001 .003 .955 A01 A03 .001 l .001 .003 .955 Explained 1.395 5 .279 .608 .694 Residual 50.422 110 .458 Total 51.816 115 .451 Cell Means A03: 40/60 Credits Total 401‘ 59X 40 60 Sex 1 = Male m’ 2.06 1.93 2.03 n (59) (17) (76) 2 = Female E' 2.20 2.11 2.14 n (15) (25) (40) Total m' 2.09 2.04 2.07 40/60 credits n (74) ‘ (42) (115) 179 Table E-7.--Ana1ysis of variance of Dimension 2--Understand basic math to teach mathematics--by sex and teaching at which level. 002 Understand Basic Math to Teach Mathematics By A01 Sex A08 Teaching at which level? With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .514 2 .257 .561 .572 A04 .071 1 .071 .155 .695 A05 .380 1 .380 .829 .365 Main effects 1.038 2 .519 1.132 .326 A01 .256 1 .256 .560 .456 A08 .742 l .742 1.618 .206 2-way interactions .167 1 .176 .384 .537 A01 A08 .176 1 .176 .384 .537 Explained 1.728 5 .346 .754 .585 Residual 48.587 106 .458 Total 50.315 111 .453 Cell Means A01. 5 A08: Teaching Level Total - ex Middle High Sex School School 1 = Male 5' 2.07 1.86 2.02 n (55) (19) (74) 2 = Female m' 2.16 2.11 2.15 n (28) (10) (33) Total m' 2.10 1195 2.06 teaching level n (83) (29) (112) 180 Table E-8.--Ana1ysis of variance of Dimension 2--Understand basic math to teach mathematics--by sex and percent of mathematics teaching duty. 002 Understand Basic Math to Teach Mathematics By A01 Sex A09 Percent of mathematics teaching duty With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .514 2 .257 .565 .570 A04 .071 l .071 .156 .694 A05 .380 1 .380 .835 .363 Main effects 1.302 2 .651 1.430 .244 A01 .227 l .227 .498 .482 A09 1.006 1 1.006 2.210 .140 2-way interactions .238 1 .238 .522 .472 A01 A09 .238 1 .238 .522 .472 Explained 2.054 5 .411 .902 .483 Residual 48.261 106 .455 Total 50.315 111 .453 Cell Means A01: Sex A09: Mathematics Teaching Duty Total 80% 100% Sex 1 = Male 5' 2.14 1.98 2.02 n (16) (58) (74) 2 = Female m' 2.45 2.07 2.15 n ( 8) (30) (38) Total 6' 2.24 2.01 2.06 percent teaching duty n (24) (88) (112) Tab1e E-9. 181 --Analysis of variance of Dimension 2--Understand basic math to teach mathematics--by year graduated from Mecca College of Education (male teachers). 002 By A02 With A04 Understand Basic Math to Teach Mathematics Year graduated from Mecca College of Education Overall GPA A05 Mathematics GPA Selected for male teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates 1.088 2 .544 1.168 .317 A04 .015 1 .015 .031 .860 A05 .534 1 .534 1.146 .288 Main effects 4.305 4 1.076 2.309 .066 A02 4.305 4 1.076 2.309 .066 Explained 5.393 6 .899 1.929 .088 Residual 32.153 69 .466 Total 37.546 75 .501 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 1977-78 1978-79 1979-80 T°tal m' 2.06 2.22 2.19 1.89 1.58 2.03 n (15) (22) (17) ( 9) (13) (76) 182 Table E-10.--Ana1ysis of variance of Dimension 2—-Understand basic math to teach mathematics--by year graduated from Mecca College of Education (female teachers). 002 Understand Basic Math to Teach Mathematics By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for female teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .249 2 .124 .327 .723 A04 .201 1 .201 .528 .472 A05 .036 1 .036 .095 .760 Main effects .412 2 .206 .542 .586 A02 .412 2 .206 .542 .586 Explained .661 4 .165 .435 .782 Residual 13.298 35 .380 Total 13.959 39 .358 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 1977-78 1978-79 1979-80 Total 0 0 2.14 2.25 2.05 2.14 ( 0) ( 0) (12) (13) (15) (40) :al 183 Table E-11.--Analysis of variance of Dimension 3--Preparation for higher mathematics-~by sex and graduated with 40 or 60 credits. DO3 Preparation for Higher Mathematics By A01 Sex A03 Graduated with 40 or 60 credits With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates 1.260 2 .630 1.406 .249 A04 1.257 1 1.257 2.807 .097 A05 .748 1 .748 1.670 .199 Main effects 1.673 2 .836 1.867 .159 A01 1.654 1 1.654 3.693 .057 A03 .103 1 .103 .231 .632 2-way interactions .007 1 .007 .016 .900 A01 A03 .007 l .007 .016 .900 Explained 2.939 5 .588 1.313 .264 Residual 49.270 110 .448 Total 52.210 115 .454 Cell Means A01: Sex A03: 40/60 Credits Total 40 60 Sex 1 = Male 111' 3.27 3.20 3.26 n (59) (17) (76) 2 = Female m' 3.61 3.48 3.53 n (15) (25) (40) Total m' 3.34 3.37 3.35 40/60 credits n (74) (42) (115) 184 Table E-12.--Ana1ysis of variance of Dimension 3--Preparation for higher mathematics--by sex and teaching at which level. 003 Preparation for Higher Mathematics By A01 Sex A08 Teaching at which level? With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates 1.328 2 .664 1.458 .237 A04 1.298 1 1.298 2.852 .094 A05 .639 1 .639 1.404 .239 Main effects 1.715 2 .858 1.884 .157 A01 1.213 1 1.213 2.665 .106 A08 .436 l .436 .959 .330 2-way interactions .214 1 .214 .471 .494 A01 A08 .214 1 .214 .471 .494 Explained 3.257 5 .651 1.431 .219 Residual 48.250 106 .455 Total 51.507 111 .464 Cell Means A08: Teaching Level A01; Sex Middle High 7:321 School School 1 = Male m‘ 3.30 3.19 3.27 n (55) (19) (74) 2 = Female m' 3.61 3.34 3.54 n (28) (10) (38) Total m' 3.40 3.24 3.36 teaching level n (83) (29) (112) 185 Table E-13.--Ana1ysis of variance of Dimension 3--Preparation for higher mathematics--by sex and percent of mathematics teaching duty. 003 Preparation for Higher Mathematics By A01 Sex A09 Percent of mathematics teaching duty With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates 1.328 ' 2 .664 1.459 .237 A04 1.298 1 1.298 2.852 .094 A05 .639 1 .639 1.404 .239 Main effects 1.842 2 .921 2.024 .137 A01 1.163 1 1.163 2.555 .113 A09 .563 1 .563 1.238 .268 2-way interactions .102 l .102 .224 .637 A01 A09 .102 1 .102 .224 .637 Explained 3.272 5 .654 1.438 .217 Residual 48.235 106 .455 Total 51.507 111 .464 Cell Means A01: Sex A09: Mathematics Teaching Duty Total 80% 100% Sex 1 = Male m" 3.34 3.25 3.27 n (16) (58) (74) 2 = Female m' 3.70 3.49 3.54 n ( 8) (30) (38) Total m" 3.46 3.33 3.36 percent teaching duty n (24) (88) (112) 186 Table E-14.--Ana1ysis of variance of Dimension 3--Preparation for higher mathematics--by year graduated from Mecca College of Education (male teachers) 003 Preparation for Higher Mathematics By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for male teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates 2.660 2 1.330 2.667 .077 A04 2.573 1 2.573 5.158 .026 A05 2.099 1 2.099 4.208 .044 Main effects .266 4 .067 .134 .097 A02 .266 4 .067 .134 .970 Explained 2.927 6 .488 .978 .447 Residual 34.418 69 .499 Total 37.345 75 .498 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 1977-78 1978-79 1979-80 Total m 3.24 3.25 3.46 3.09 3.14 3.26 (15) (22) (17) ( 9) (13) (76) 187 Table E-15.--Analysis of variance of Dimension 3--Preparation for higher mathematics--by year graduated from Mecca College of Education (female teachers). DO3 Preparation for Higher Mathematics By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for female teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .545 2 .272 .779 .467 A04 .487 1 .487 1.393 .246 A05 .133 l .133 .379 .542 Main effects .136 2 .068 .195 .824 A02 .136 2 .068 .195 .824 Explained .681 4 .170 .487 .745 Residual 12.243 35 .350 Total 12.924 39 .331 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 1977-78 1978-79 1979-80 T°ta1 ‘m' 0 0 3.47 3.60 3.52 3.53 n ( 0) ( 0) (12) (13) (15) (40) 188 Table E-l6.--Analysis of variance of Dimension 4--College-school relations--by sex and graduated with 40 or 60 credits. 004 College-School Relations By A01 Sex A03 Graduated with 40 or 60 credits With A04 Overall GPA A06 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .016 2 .008 .062 .940 A04 .005 1 .005 .041 .841 A05 .000 l .000 .000 .989 Main effects .225 2 .112 .848 .431 A01 .003 1 .003 .019 .890 A03 .211 l .211 1.591 .210 2-way interactions .084 1 .084 .637 .427 A01 A03 .084 1 .084 .637 .427 Explained .325 5 .065 .491 .782 Residual 14.569 110 .132 Total 14.894 115 .130 Cell Means A01: Sex A03: 40/60 Credits Total 40 60 Sex 1 = Male El 4.76 4.81 4.77 n (59) (17) (76) 2 = Female m 4.70 4.86 4.80 n (15) (25) (40) Total m' 4.75 4.84 4.78 40/60 credits n (74) (42) (116) 189 Table E-17.--Ana1ysis of variance of Dimension 4--College-school relations-~by sex and teaching at which level. 004 College-School Relations By A01 Sex A08 Teaching at which level? With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .015 2 .008 .057 .945 A04 .007 l .007 .049 .826 A05 .000 1 .000 .000 .984 Main effects .263 2 .132 .977 .380 A01 .034 l .034 .251 .617 A08 .237 l .237 .756 .188 2-way interactions .100 1 .100 .741 .391 A01 A08 .100 1 .100 .741 .391 Explained .379 5 .076 .562 .729 Residual 14.291 106 .135 Total 14.670 111 .132 Cell Means A08: Teaching Level A01: Sex Middle High 1:221 School School 1 = Male m' 4.75 4.80 4.76 n (55) (19) (74) 2 = Female m' 4.75 4.95 4.80 n (28) (10) (33) Total m' 4.75 4.85 4.78 teaching level n (83) (29) (112) Table E-18.--Ana1ysis of variance of Dimension 4--College-school 190 relations--by sex and percent of mathematics teaching duty. DO4 College-School Relations By A01 Sex A09 Percent of mathematics teaching duty With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .015 2 .008 .057 .945 A04 .007 l .007 .048 .826 A05 .000 1 .000 .000 .984 Main effects .215 2 .107 .793 .455 A01 .037 l .037 .272 .603 A09 .188 1 .188 .389 .241 2-way interactions .072 l .072 .533 .467 A01 A09 .072 1 .072 .533 .467 Explained .303 5 .061 .446 .815 Residual 14.367 106 .136 Total 14.670 111 .132 Cell Means A : ° ' A01: Sex 09 Mathematics Teaching Duty Total 80% 100% Sex 1 = Male Rf 4.72 4.78 4.76 n (16) (58) (74) 2 = Female m' 4.66 4.84 4.80 n ( 8) (30) (38) Total m' 4.70 4.80 4.78 percent teaching duty n (24) (88) (112) 191 Table E-l9.--Ana1ysis of variance of Dimension 4--College-school relations--by year graduated from Mecca College of Education (male teachers). 004 College-School Relations By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for male teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .136 2 .068 .474 .625 A04 .136 1 .136 .947 .334 A05 .084 l .084 .588 .446 Main effects .931 4 .233 1.622 .179 A02 .931 4 .233 1.622 .179 Explained 1.067 6 .178 1.239 .297 Residual 9.903 69 .144 Total 10.970 75 .146 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 1977-78 1978-79 1979-80 Total 4.73 4.66 4.75 4.92 4.92 4.77 (15) (22) (17) ( 9) (13) (76) 192 Table E-20.--Analysis of variance of Dimension 4--College-school relations--by year graduated from Mecca College of Education (female teachers). DO4 College-School Relations By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for female teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .168 2 .084 .867 .429 A04 .158 1 .158 1.631 .210 A05 .132 1 .132 1.367 .250 Main effects .350 2 .175 1.810 .179 A02 .350 2 .175 1.810 .179 Explained .517 4 .129 1.338 .275 Residual 3.383 35 .097 Total 3.900 39 .100 Cell Means A02: Year Graduated From Mecca College of Education T t 1 1975-76 1976-77 1977-78 1978-79 1979-80 ° 3 ii 0 O 4.79 4.67 4.92 4.80 n ( 0) ( 0) (12) (13) (15) (40) 193 Table E-21.--Ana1ysis of variance of Dimension 5--Emphasis on practical problems-~by sex and graduated with 40 or 60 credits. DOS Emphasis on Practical Problems By A01 Sex A03 Graduated with 40 or 60 credits With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .235 2 .118 .332 .718 A04 .197 1 .197 .556 .458 A05 .055 l .055 .156 .694 Main effects .813 2 .407 1.148 .321 A01 .725 1 .725 2.047 .155 A03 .000 1 .000 .001 .974 2-way interactions .088 l .088 .248 .619 A01 A03 .088 1 .088 .248 .619 Explained 1.136 5 .227 .642 .668 Residual 38.948 110 .354 Total 40.084 115 .349 Cell Means A01: Sex A03: 40/60 Credits Total 40 60 Sex 1 = Male m‘ 4.34 4.25 4.32 n (59) (17) (76) 2 = Female El 4.40 4.49 4.46 n (15) (25) (40) Total 6’ 4.35 4.40 4.37 40/60 credits n (74) (42) (116) 194 Table E-22.--Analysis of variance of Dimension 5--Emphasis on practical problems--by sex and teaching at which level. DOS Emphasis on Practical Problems By A01 Sex A08 Teaching at which level? With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .237 2 .118 .398 .673 A04 .126 1 .126 .424 .516 A05 .235 1 .235 .788 .377 Main effects 1.044 2 .522 1.753 .178 A01 .785 1 .785 2.637 .107 A08 .298 1 .298 1.002 .319 2-way interactions .003 l .003 .009 .924 A01 A08 .003 1 .003 .009 .924 Explained 1.284 5 .257 .862 .509 Residual 31.569 106 .298 Total 32.853 111 .296 Cell Means AOl- S A08: Teaching Level Total . ex Middle High Sex School School 1 = Male ii 4.31 4.44 4.34 n (55) (19) (74) 2 = Female ii 4.48 4.60 4.51 n (28) (10) (38) Total El 4137 4.49 4.40 teaching level n (83) (29) (112) 195 Table E-23.--Analysis of variance of Dimension 5--Emphasis on practical problems--by sex and percent of mathematics teaching duty. 005 Emphasis on Practical Problems By A01 Sex A09 Percent of mathematics teaching duty With A04 Overall Gpa A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .237 2 .118 .399 .672 A04 .126 1 .126 .426 .516 A05 .235 1 .235 .790 .376 Main effects .746 2 .373 1.256 .289 A01 .743 l .743 2.503 .117 A09 .000 1 .000 .000 .990 2-way interactions .401 1 .401 1.351 .248 A01 A09 .401 1 .401 1.351 .248 Explained 1.384 5 .277 .932 .463 Residual 31.469 106 .297 Total 32.853 111 .296 Cell Means A01: Sex A09: Mathematics Teaching Duty Total 80% 100% Sex 1 = Male 6 4.44 .432 4.34 n (16) (58) (74) 2 = Female El 4.38 4.54 4.51 n ( 8) (30) (33) Total El 4.42 4.39 4.40 percent teaching duty n (24) (88) (112) 196 Table E-24.--Ana1ysis of variance of Dimension 5--Emphasis on practical problems--by year graduated from Mecca College of Educa- tion (male teachers). 005 Emphasis on Practical Problems By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for male teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .588 2 .294 .714 .493 A04 .398 1 .398 .967 .329 A05 .054 l .054 .130 .719 Main effects 1.521 4 .380 .923 .456 A02 1.521 4 .380 .923 .456 Explained 2.110 6 .352 .853 .534 Residual 28.433 69 .412 Total 30.542 75 .407 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 1977-78 1978-79 1979-80 T°tal 61 4.60 4.20 4.27 4.22 4.33 4.32 n (15) (22) (17) ( 9) (13) (76) 197 Table E-25.--Ana1ysis of variance of Dimension 5--Emphasis on practical problems--by year graduated from Mecca College of Educa- tion (female teachers). 005 Emphasis on Practical Problems By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for female teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .038 2 .019 .076 .927 A04 .022 1 .022 .087 .770 A05 .001 1 .001 .003 .958 Main effects .109 2 .055 .215 .808 A02 .109 2 .055 .215 .808 Explained .148 4 .037 .145 .964 Residual 8.894 35 .254 Total 9.042 39 .232 Cell Means A02: Year Graduated From Mecca College of Education Total 1975-76 1976-77 1977-78 1978-79 1979-80 0 0 4.42 4.41 4.53 4.46 ( 0) ( 0) (12) (13) (15) (40) :al 198 Tab1e E-26.-—Analysis of variance of Dimension 6--Preparation for school teaching--by sex and graduated with 40 or 60 credits. 006 Preparation for School Teaching By A01 Sex A03 Graduated with 40 or 60 credits With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .696 2 .348 .668 .515 A04 .307 1 .307 .590 .444 A05 .004 1 .004 .008 .929 Main effects .969 2 .484 .930 .397 A01 .084 1 .084 .160 .689 A03 .965 1 .965 .854 .176 2-way interactions .000 1 .000 .000 .997 A01 A03 .000 1 .000 .000 .997 Explained 1.664 5 .333 .640 .670 Residual 57.254 110 .520 Total 58.919 115 .512 Cell Means A03: 40/60 Credits A01: Sex 40 60 Total 1 = Male m' 3.38 3.14 3.33 n (59) (17) (76) 2 = Female El 3.37 3.19 3.26 n (15) (25) (40) Total 61 3.38 3.17 3.30 40/60 credits n (74) (42) (116) 199 Table E-27.--Analysis of variance of Dimension 6--Preparation for school teaching--by sex and teaching at which level. 006 Preparation for School Teaching By A01 Sex A08 Teaching at which level? With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .530 2 .265 .498 .609 A04 .195 1 .195 .365 .547 A05 .000 1 .000 .000 .998 Main effects .163 2 .081 .153 .859 A01 .005 1 .005 .010 .920 A08 .159 1 .159 .299 .585 2-way interactions .279 1 .279 .523 .471 A01 A08 .279 1 .279 .523 .471 Explained .971 5 .194 .365 .872 Residual 56.467 106 .533 Total 57.439 111 .517 Cell Means A08: Teaching Level A01: Sex Middle High nggl School School 1 = Male 6 3.33 3.32 3.32 n (55) (19) (74) 2 = Female m’ 3.34 3.06 3.26 n (28) (10) (331 Total 6’ 3.33 3.23 3.30 teaching level n (83) (29) (112) 200 Table E-28.--Analysis of variance of Dimension 6--Preparation for school teaching--by sex and percent of mathematics teaching duty. 006 Preparation for School Teaching By A01 Sex A09 Percent of mathematics teaching With A04 Overall GPA A05 Mathematics GPA duty . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .530 2 .265 .498 .609 A04 .195 1 .195 .366 .547 A05 .000 1 .000 .000 .998 Main effects .252 2 .126 .237 .789 A01 .008 1 .008 .015 .903 A09 .249 1 .249 .468 .495 2-way interactions .275 1 .275 .516 .474 A01 A09 .275 1 .275 .516 .474 Explained 1.057 5 .211 .397 .850 Residual 56.382 106 .532 Total 57.439 111 .517 Cell Means A09: Mathematics Teaching Duty Total A01: Sex S 80% 100% ex 1 = Male '6 3.36 3.31 3.32 n (16) (58) (74) 2 = Female m’ 3.53 3.19 3.26 n ( 8) (30) (38) Total m' 3.42 3.27 3.30 percent teaching duty n (24) (88) (112) 201 Table E-29.--Ana1ysis of variance of Dimension 6--Preparation for school teaching--by year graduated from Mecca College of Education (male teachers). 006 Preparation for School Teaching By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for male teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates 1.465 2 .733 1.435 .245 A04 .082 1 .082 .161 .689 A05 .244 l .244 .478 .492 Main effects 1.140 4 .285 .558 .694 A02 1.140 4 .285 .558 .694 Explained 2.605 6 .434 .850 .536 Residual 35.223 69 .510 Total 37.827 75 .504 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 1977-78 1978-79 1979-80 T°ta1 HI 3.37 3.22 3.41 3.07 3.52 3.33 n (15) (22) (17) ( 9) (13) (76) 202 Table E-30.--Analysis of variance of Dimension 6--Preparation for school teaching--by year graduated from Mecca College of Education (female teachers). 006 Preparation for School Teaching By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for female teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .494 2 .247 .431 .653 A04 .102 1 .102 .177 .676 A05 .427 1 .427 .746 .393 Main effects .437 2 .219 .382 .685 A02 .437 2 .219 .382 .685 Explained .932 4 .233 .407 .803 Residual 20.044 35 .573 Total 20.976 39 .538 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 1977-78 1978-79 1979-80 T°tal m' 0 0 3.25 3.38 3.16 3.26 n ( 0) ( 0) (12) (13) (15) (40) 203 Table E-3l.--Analysis of variance of Dimension 7--Method of teaching mathematics--by sex and graduated with 40 or 60 credits. 007 Method of Teaching Mathematics By A01 Sex A03 Graduated with 40 or 60 credits With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .233 2 .116 .263 .769 A04 .156 1 .156 .353 .553 A05 .022 1 .022 .049 .825 Main effects .369 2 .185 .418 .659 A01 .353 1 .353 .798 .374 A03 .008 1 .008 .017 .896 2-way interactions 3.320 1 3.320 7.510 .007 A01 A03 3.320 1 3.320 7.510 .007 Explained 3.923 5 .785 1.775 .124 Residual 48.629 110 .442 Total 52.552 115 .457 Cell Means A01: Sex A03: 40/60 Credits Total 40 60 Sex 1 = Male m' 1.42 1.15 1.36 n (59) (17) (76) 2 = Female 31 1.00 1.44 1.27 n (15) (25) (40) Total 11 1.33 1.32 1.33 40/60 credits n (74) (42) (116) 204 Table E-32.--Ana1ysis of variance of Dimension 7--Method of teaching mathematics--by sex and teaching at which level. 007 Method of Teaching Mathematics By A01 Sex A08 Teaching at which level? With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .330 2 .165 .355 .702 A04 .119 1 .119 .256 .614 A05 .000 1 .000 .000 .993 Main effects 1.059 2 .529 1.136 .325 A01 .337 1 .337 .724 .397 A08 .678 1 .678 1.456 .230 2-way interactions 1.339 1 1.339 2.875 .093 A01 A08 1.339 1 1.339 2.875 .093 Explained 2.728 5 .546 1.171 .328 Residual 49.379 106 .466 Total 52.107 111 .469 Cell Means A08: Teaching Level A01: Sex Middle High 13::‘ School School 1 = Male BI 1.36 1.37 1.36 n (55) (19) (74) 2 = Female m' 1.14 1.70 1.29 n (28) (10) (38) Total m' 1.29 1.48 1.34 teaching level n (83) (29) (112) 205 Table E-33.--Analysis of variance of Dimension 7--Method of teaching mathematics--by sex and percent of mathematics teaching duty. 007 Method of Teaching Mathematics By A01 Sex A09 Percent of mathematics teaching duty With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .330 2 .165 .342 .711 A04 .119 1 .119 .246 .621 A05 .000 1 .000 .000 .993 Main effects .503 2 .252 .521 .596 A01 .351 1 .351 .725 .396 A09 .123 1 .123 .254 .615 2-way interactions .048 l .048 .099 .753 A01 A09 .048 1 .048 .099 .753 Explained .882 5 .176 .365 .872 Residual 51.226 106 .483 Total 52.107 111 .469 Cell Means A A09: Mathematics Teaching Duty Total 01. Sex 80% 100% Sex 1 = Male 11 1.31 1.38 1.36 n (16) (58) (74) 2 = Female m' 1.13 1.33 1.29 n ( 8) (30) (38) Total 51 1.25 1.36 1.34 percent teaching duty n (24) (88) (112) 206 Table E-34.—-Analysis of variance of Dimension 7--Method of teaching mathematics--by year graduated from Mecca College of Education (male teachers). 007 Method of Teaching Mathematics By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for male teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .717 2 .358 .818 .446 A04 .611 1 .611 .395 .242 A05 .175 1 .175 .400 .529 Main effects 1.960 4 .490 .118 .355 A02 1.960 4 .490 .118 .355 Explained 2.676 6 .446 .018 .421 Residual 30.231 69 .438 Total 32.908 75 .439 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 1977-78 1978-79 1979-80 T°tal m' 1.23 1.50 1.56 7 1.12 1.36 n (15) (22) (17) ) (13) (76) 207 Table E-35.--Analysis of variance of Dimension 7--Method of teaching mathematics--by year graduated from Mecca College of Education (female teachers). 007 Method of Teaching Mathematics By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for female teachers . . Sum of Mean Signif. Source of Variation Squares df Square of F Covariates .108 2 .054 .100 .905 A04 .040 l .040 .074 .787 A05 .104 1 .104 .192 .664 Main effects .370 2 .185 .341 .714 A02 .370 2 .185 .341 .714 Explained .478 4 .120 .220 .925 Residual 18.997 35 .543 Total 19.475 39 .499 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 1977-78 1978-79 1979-80 T°ta1 m' 0 O 1.29 1.38 1.17 1.27 n ( 0) ( 0) (12) (13) (15) (40) 208 Table E-36.--Ana1ysis of variance of Dimension 8--Student teaching-- by sex and graduated with 40 or 60 credits. 008 Student Teaching By A01 Sex A03 Graduated with 40 or 60 credits With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square of F Covariates 1.215 2 .607 2.127 .124 A04 1.176 1 1.176 4.119 .045 A05 .556 l .556 1.947 .166 Main effects .220 2 .110 .385 .681 A01 .008 l .008 .028 .867 A03 .160 1 .160 .560 .456 2-way interactions .879 1 .879 3.076 .082 A01 A03 .879 1 .879 3.076 .082 Explained 2.313 5 .463 1.620 .161 Residual 31.417 110 .286 Total 33.731 115 .293 Cell Means A03: 40/60 Credits Total A01. Sex 40 60 Sex 1 = Male El 1.33 1.06 1.27 n (59) (17) (76) 2 = Female m' 1.03 1.26 1.17 n (15) (25) (40) Total m' 1.27 1.18 1.24 40/60 credits n (74) (42) (116) 209 Table E-37.--Ana1ysis of variance of Dimension 8--Student teaching-- by sex and teaching at which level. 008 Student Teaching By A01 Sex A08 Teaching at which level? With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates 1.280 2 .640 .196 .116 A04 1.274 1 1.274 .371 .039 A05 .720 l .720 .471 .119 Main effects .169 2 .085 .290 .749 A01 .061 l .061 .210 .648 A08 .115 1 .115 .393 .532 2-way interactions 1.164 1 1.164 .995 .048 A01 A08 1.164 1 1.164 .995 .048 Explained 2.613 5 .523 1.793 .120 Residual 30.885 106 .291 Total 33.498 111 .302 Cell Means A08: Teaching Level A01: Sex - - Total Middle High Sex School School 1 = Male m' 1.33 1.13 1.28 n (55) (19) (74) 2 = Female m' 1.13 1.35 1.18 n (28) (10) (38) Total m' 1.26 1.21 1.25 teaching level n (83) (29) (112) 210 Table E-38.--Ana1ysis of variance of Dimension 8--Student teaching-- by sex and percent of mathematics teaching duty. 008 Student Teaching By A01 Sex A09 Percent of mathematics teaching duty With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square of F Covariates 1.280 2 .640 2.131 .124 A04 1.274 1 1.274 4.242 .042 A05 .720 l .720 2.398 .124 Main effects .073 2 .037 .122 .885 A01 .058 1 .058 .195 .660 A09 .019 1 .019 .063 .802 2-way interactions .323 1 .323 1.077 .302 A01 A09 .323 1 .323 1.077 .302 Explained 1.676 5 .335 1.117 .356 Residual 31.822 106 .300 Total 33.498 111 .302 Cell Means A09: Mathematics Teaching Duty Total AO“ 59* 80% 100% Sex 1 = Male 01 1.41 1.24 1.28 n (16) (58) (74) 2 = Female m’ 1.13 1.20 1.18 n ( 8) (30) (38) Total m“ 1.31 1.23 1.25 percent teaching duty n (24) (88) (112) 211 Table E-39.--Analysis of variance of Dimension 8--Student teaching-- by year graduated from Mecca College of Education (male teachers). 008 Student Teaching By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for male teachers . . Sum of Mean Signif Source of Variation Squares df Square F of F Covariates 1.011 2 .506 1.437 .245 A04 .997 l .997 2.835 .097 A05 .515 1 .515 1.463 .231 Main effects 2.935 4 .734 2.086 .092 A02 2.935 4 .734 2.086 .092 Explained 3.947 6 .658 1.870 .098 Residual 24.274 69 .352 Total 28.220 75 .376 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 1977-78 1978-79 1979-80 Total E1 1.40 1.50 1.15 1.11 1.00 1.27 n (15) (22) (17) ( 9) (13) (76) 212 Table E-40.--Ana1ysis of variance of Dimension 8--Student teaching-- by year graduated from Mecca College of Education (female teachers). 008 Student Teaching By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for female teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .129 2 .064 .444 .645 A04 .125 1 .125 .862 .359 A05 .093 1 .093 .644 .428 Main effects .071 2 .035 .244 .785 A02 .071 2 .035 .244 .785 Explained .199 4 .050 .344 .846 Residual 5.076 35 .145 Total 5.275 39 .135 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976—77 1977-78 1978-79 1979-80 Total m' 0 O 1.21 1.19 1.13 1.17 n ( 0) ( 0) (12) (13) (15) (40) 213 Table E-41.--Analysis of variance of Dimension 9--Educational thought-- by sex and graduated with 40 or 60 credits. 009 Educational Thought By A01 Sex A03 Graduated with 40 or 60 credits With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates 1.839 2 .920 .845 .432 A04 1.524 1 1.524 1.401 .239 A05 1.750 1 1.750 1.608 .207 Main effects .184 2 .092 .085 .919 A01 .122 l .122 .002 .738 A03 .012 1 .012 .011 .916 2-way interactions .008 l .008 .007 .934 A01 A03 .008 1 .008 .007 .934 Explained 2.031 5 .406 .373 .866 Residual 119.684 110 1.088 Total 121.716 115 1.058 Cell Means A03: 40/60 Credits . Total A01. Sex 40 60 Sex 1 = Male m' 2.79 2.79 2.79 n (59) (17) (76) 2 = Female m' 2.83 2.66 2.72 n (15) (25) (40) Total m‘ 2.80 2.71 2.77 40/60 credits n (74) (42) (116) 214 Table E-42.--Analysis of variance of Dimension 9--Educational thought-- by sex and teaching at which level. 009 Educational Thought By AOl Sex A08 Teaching at which level? With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates 2.171 2 1.086 .990 .375 A04 1.675 1 1.675 1.528 .219 A05 2.119 1 2.119 1.933 .167 Main effects .193 2 .096 .088 .916 A01 .049 1 .049 .045 .833 A08 .136 l .136 .124 .725 2-way interactions .896 l .896 .817 .368 A01 A08 .896 l .896 .817 .368 Explained 3.260 5 .652 .595 .704 Residual 116.231 106 1.097 Total 119.491 111 1.076 Cell Means A08: Teaching Level A01: Sex . . Total Middle High Sex School School 1 = Male m' 2.81 2.66 2.77 n (55) (19) (74) 2 = Female m' 2.64 3.00 2.74 n (28) (10) (38) Total m“ 2.75 2.78 2.76 teaching level n (83) (29) (112) 215 Table E-43.--Analysis of variance of Dimension 9--Educational thought-- by sex and percent of mathematics teaching duty. 009 Educational Thought By A01 Sex A09 Percent of mathematics teaching duty With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates 2.171 2 1.086 .999 .372 A04 1.675 1 1.675 .542 .217 A05 2.119 1 2.119 .950 .165 Main effects .154 2 .077 .071 .932 A01 .067 1 .067 .061 .805 A09 .098 1 .098 .090 .765 2-way interactions 1.989 1 1.989 .831 .179 A01 A09 1.989 1 1.989 .831 .179 Explained 4.315 5 .863 .794 .556 Residual 115.176 106 1.087 Total 119.491 111 1.076 Cell Means A01- Sex A09: Mathematics Teaching Duty Total ' 80% 100% Sex 1 = Male 11 2.97 2.27 2.77 n (16) (58) (74) 2 = Female 01 2.38 2.83 2.74 n ( 8) (30) (38) Total 10 2 . 77 2 . 76 2 .76 percent teaching duty n (24) (88) (112) 216 Table E-44.--Ana1ysis of variance of Dimension 9--Educational thought-- by year graduated from Mecca College of Education (male teachers). 009 Educational Thought By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for male teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .482 2 .241 .196 .822 A04 .061 l .061 .049, .825 A05 .041 1 .041 .034 .855 Main effects 1.848 4 .462 .376 .825 A02 1.848 4 .462 .376 .825 Explained 2.330 6 .388 .316 .927 Residual 84.801 69 1.229 Total 87.132 75 1.162 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 1977-78 1978-79 1979-80 Total In“ 2.80 2.91 2.65 2.50 2.96 2.79 (15) (22) (17) ( 9) (13) (76) 217 Table E-45.--Analysis of variance of Dimension 9--Educational thought-- by year graduated from Mecca College of Education (female teachers). 009 Educational Thought By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for female teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates 6.554 2 3.277 4.357 .020 A04 6.552 1 6.552 8.711 .006 A05 3.560 1 3.560 4.733 .036 Main effects 1.595 2 .798 1.060 .357 A02 1.595 2 .798 1.060 .357 Explained 8.150 4 2.037 2.709 .046 Residual 26.325 35 .752 Total 34.475 39 .884 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 1977-78 1978-79 1979-80 T°t31 O O 3.04 2.58 2.60 2.72 :31 ( 0) ( 0) (12) (13) (15) (40) 218 Table E-46.--Analysis of variance of Dimension 10--Curricu1um design-- by sex and graduated with 40 or 60 credits. DlO Curriculum Design By A01 Sex A03 Graduated with 40 or 60 credits With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates 2.128 2 1.064 1.328 .269 A04 1.898 1 1.898 2.369 .127 A05 .653 1 .653 .814 .369 Main effects 2.060 2 1.030 1.285 .281 A01 1.720 1 1.720 2.147 .146 A03 1.010 1 1.010 1.261 .264 2-way interactions .000 1 .000 .000 .990 A01 A03 .000 1 .000 .000 .990 Explained 4.188 5 .838 1.045 .395 Residual 88.139 110 .801 Total 92.328 115 .803 Cell Means A01: Sex A03: 40/60 Credits Total 40 60 Sex 1 = Male H1 2.21 1.94 2.15 n (59) (17) (76) 2 = Female m" 2.33 2.22 2.26 n (15) (25) (40) Total m 2.24 2.11 2.19 40/60 credits n (74) (42) (116) 219 Table E-47.--Ana1ysis of variance of Dimension 10--Curriculum design-- by sex and teaching at which level. 010 Curriculum Design By A01 Sex A08 Teaching at which level? With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates 2.177 2 1.088 1.386 .255 A04 2.176 1 2.176 2.770 .099 A05 1.403 1 1.403 1.786 .184 Main effects 2.456 2 1.228 1.563 .214 A01 1.003 1 1.003 1.277 .261 A08 1.556 1 1.556 1.980 .162 2-way interactions .027 l .027 .035 .852 A01 A08 .027 l .027 .035 .852 Explained 4.660 5 .932 1.186 .321 Residual 83.260 106 .785 Total 87.920 111 .792 Cell Means A08: Teaching Level AO“ sex Middle High lgzgl School School 1 = Male m' 2.11 2.39 2.18 n (55) (19) (74) 2 = Female m' 2.23 2.50 2.30 n (28) (10) (38) Total m' 2.15 2.43 2.22 teaching level n (83) (29) (112) 220 Table E-48.--Analysis of variance of Dimension 10--Curricu1um design-- by sex and percent of mathematics teaching duty. 010 Curriculum Design By A01 Sex A09 Percent of mathematics teaching duty With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square of F Covariates 2.177 2 1.088 1.415 .248 A04 2.176 1 2.176 2.829 .096 A05 1.403 1 1.403 1.824 .180 Main effects 3.666 2 1.833 2.383 .097 A01 1.118 1 1.118 1.453 .231 A09 2.766 1 2.766 3.596 .061 2—way interactions .542 1 .542 .705 .403 A01 A09 .542 1 .542 .705 .403 Explained 6.385 5 1.277 1.660 .151 Residual 81.535 106 .769 Total 87.920 111 .792 Cell Means : ' T h’ D T 1 A01: Sex A09 Mathematics eac ing uty g6: 80% 100% 1 = Male m’ 2.03 2.22 2.18 n (16) (58) (74) 2 = Female m' 1.94 2.40 2.30 n ( 8) (30) (38) Total E1 2.00 2.28 2.22 percent teaching duty n (24) (88) (112) Tab1e E-49.--Analysis of variance of Dimension lO--Curricu1um design-- teachers 221 by year graduated from Mecca College of Education (male 010 Curriculum Design By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for male teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates 6.171 2 3.086 3.912 .025 A04 5.139 1 5.139 6.516 .013 A05 1.366 1 1.366 1.732 .193 Main effects 1.420 4 .355 .450 .772 A02 1.420 4 .355 .450 .772 Explained 7.591 6 1.265 1.604 .159 Residual 54.419 69 .789 Total 62.010 75 .827 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 1977-78 1978-79 1979-80 T°tal E' 2.03 2.32 1.88 2.28 2.27 2.15 n (15) (22) (17) ( 9) (13) (76) 222 Table E-50.--Ana1ysis of variance of Dimension 10--Curricu1um design-- by year graduated from Mecca College of Education (female teachers). 010 Curriculum Design By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for female teachers . . 30m of Mean Signif. Source of Variation Squares df Square F of F Covariates .354 2 .177 .223 .802 A04 .311 1 .311 .391 .536 A05 .078 1 .078 .099 .755 Main effects 1.840 2 .920 1.158 .326 A02 1.840 2 .920 1.158 .326 Explained 2.193 4 .548 .690 .604 Residual 27.800 35 .794 Total 29.994 39 .769 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 1977-78 1978-79 1979-80 a I c: c: 2.17 2.58 2.07 2.15 ( 0) ( 0) (12) (13) (15) (40) Tab1e E-5l.--Analysis of variance of Dimension ll-—Educational 223 psychology--by sex and graduated with 40 or 60 credits. 011 By A01 A03 With A04 Educational Psychology Sex Graduated with 40 or 60 credits Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of variation Squares df Square of F Covariates 3.636 2 1.818 .558 .082 A04 .327 l .327 .460 .499 A05 .415 1 .415 .583 .447 Main effects 1.797 2 .898 .264 .287 A01 .372 1 .372 .523 .471 A03 .819 1 .819 .152 .286 2-way interactions .000 l .000 .001 .982 A01 A03 .000 l .000 .001 .982 Explained 5.433 5 1.087 .529 .187 Residual 78.187 110 .711 Total 83.620 115 .727 Cell Means A03: 40/60 Credits . Total “0" sex 40 60 Sex 1 = Male E1 2.27 2.37 2.29 n (59) (17) (76) 2 = Female m' 2.27 2.40 2.35 n (15) (25) (40) Total m' 2.27 2.39 2.31 40/60 credits n (74) (42) (116) 224 Table E-52.--Analysis of variance of Dimension 11--Educational psychology--by sex and teaching at which level. Dll Educational Psychology By A01 Sex A08 Teaching at which level? With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates 3.656 2 1.828 2.507 .086 A04 .464 1 .464 .636 .427 A05 .299 l .299 .410 .524 Main effects 1.662 2 .831 1.139 .324 A01 1.080 1 1.080 1.480 .226 A08 .515 1 .515 .706 .403 2-way interactions .030 1 .030 .041 .840 A01 A08 .030 l .030 .041 .840 Explained 5.348 5 1.070 1.467 .207 Residual 77.303 106 .729 Total 82.651 111 .745 Cell Means A08: Teachi Level AOl' Sex . "g - T°tal - Middle High Sex School School 1 = Male 1E 2.35 2.16 2.30 n (55) (19) (74) 2 = Female E1 2.45 2.13 2.37 n (28) (10) (38) Total E1 2.38 2.15 2.32 teaching level n (83) (29) (112) 225 Table E-53.--Analysis of variance of Dimension ll--Educational psychology--by sex and percent of mathematics teaching duty. Dll Educational Psychology By A01 Sex A09 Percent of mathematics teaching duty With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates 3.656 2 1.828 2.508 .086 A04 .464 1 .464 .636 .427 A05 .299 1 .299 .410 .523 Main effects 1.173 2 .587 .805 .450 A01 1.118 1 1.118 1.534 .218 A09 .027 1 .027 .037 .848 2-way interactions .550 1 .550 .755 .387 A01 A09 .550 1 .550 .755 .387 Explained 5.380 5 1.076 1.476 .204 Residual 77.271 106 .729 Total 82.651 111 .745 Cell Means A09: Mathematics Teaching Duty Total AO“ sex 80% 100% Sex 1 = Male 5' 2.27 2.30 2.30 n (16) (58) (74) 2 = Female E1 2.71 2.28 2.37 n ( 8) (30) (38) Total m' 2.42 2.30 2.32 percent teaching duty n (24) (88) (112) AIL-i Table E-54.--Ana1ysis of variance of Dimension ll--Educational 226 psychology--by year graduated from Mecca College of Education (male teachers). Dll Educational Psychology By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for male teachers . . Sum of Mean Signif. Source of Variation Squares df Square of F Covariates 1.118 2 .559 .816 .446 A04 .212 l .212 .309 .580 A05 .048 l .048 .070 .791 Main effects 2.501 4 .625 .913 .461 A02 2.501 4 .625 .913 .461 Explained 3.619 6 .603 .881 .514 Residual 47.262 69 .685 Total 50.882 75 .678 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 1977-78 1978-79 1979-80 Total 11 2.44 2.32 2.02 .56 2.26 2.29 n (15) (22) (17) 9) (13) (76) 'EJH- - Tab1e E-55.--Analysis of variance of Dimension ll--Educational 227 psychology--by year graduated from Mecca College of Education (female teachers). 011 By A02 With A04 Educational Psychology Year graduated from Mecca College of Education Overall GPA A05 Mathematics GPA Selected for female teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates 4.754 2 2.377 3.304 .048 A04 .644 1 .644 .896 .350 A05 .550 l .550 .765 .388 Main effects 2.725 2 1.363 1.894 .166 A02 2.725 2 1.363 1.894 .166 Explained 7.479 4 1.870 2.599 .053 Residual 25.177 35 .719 Total 32.656 39 .837 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 l977-78 1978-79 1979-80 Total m" 0 2.56 2.10 2.40 2.35 n ( 0) ( 0) (12) (13) (15) (40) 228 Table E-56.--Analysis of variance of Dimension 12--Prob1ems of teaching mathematics--by sex and graduated with 40 or 60 credits. 012 Problems of Teaching Mathematics By A01 Sex A03 Graduated with 40 or 60 credits With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square of F Covariates .580 2 .290 .413 .663 A04 .360 l .360 .513 .475 A05 .580 1 .580 .826 .365 Main effects .891 2 .446 .635 .532 A01 .864 1 .864 1.232 .270 A03 .229 1 .229 .326 .569 2-way interactions .140 1 .140 .199 .656 A01 A03 .410 1 .140 .199 .656 Explained 1.611 5 .322 .459 .806 Residual 77.202 110 .702 Total 78.812 115 .685 Cell Means A01: Sex A03: 40/60 Credits Tgta] 40 60 ex 1 = Male m” 2.83 2.78 2.82 n (59) (17) (76) 2 = Female m" 3.04 2.93 2.98 n (15) (25) (40) Total m' 2.87 2.87 2.87 40/60 credits n (74) (42) (116) 229 Table E-57.--Analysis of variance of Dimension 12--Problems of teaching mathematics--by sex and teaching at which level. 012 Problems of Teaching Mathematics By A01 Sex A08 Teaching at which level? With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .677 2 .338 .467 .628 A04 .398 1 .398 .549 .460 A05 .675 l .675 .932 .337 Main effects .696 2 .348 .481 .620 A01 .656 l .656 .905 .344 A08 .028 1 .028 .038 .845 2-way interactions .496 l .496 .685 .410 A01 A08 .496 l .496 .685 .410 Explained 1.869 5 .374 .516 .764 Residual 76.796 106 .724 Total 78.666 111 .709 Cell Means A0]. S A08: Teaching Level Total . ex Middle High Sex School School 1 = Male m' 2.79 2.91 2.82 n (55) (19) (74) 2 = Female m" 3.05 2.80 2.98 n (28) (10) (38) Total 6' 2.88 2.87 2.88 teaching level n (83) (29) (112) 230 Table E-58.--Ana1ysis of variance of Dimension 12--Prob1ems of teaching mathematics-~by sex and percent of mathematics teaching duty. 012 Problems of Teaching Mathematics By A01 Sex A09 Percent of mathematics teaching duty With A04 Overall GPA A05 Mathematics GPA . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .677 2 .338 .471 .625 A04 .398 l .398 .554 .458 A05 .675 1 .675 .941 .334 Main effects 1.876 2 .938 1.307 .275 A01 .552 1 .552 .769 .383 A09 1.207 1 1.207 1.682 .198 2-way interactions .030 l .030 .041 .839 A01 A09 .030 1 .030 .041 .839 Explained 2.582 5 .516 .719 .610 Residual 76.084 106 .718 Total 78.666 111 .709 Cell Means A09: Mathematics Teaching Duty Total AO“ sex 80% 100% Sex 1 = Male E1 3.02 2.77 2.82 n (16) (58) (74) 2 = Female m' 3.25 2.91 2.98 n ( 8) (30) (38) Total m' 3.10 2.82 2.88 percent teaching duty n (24) (88) (112) 231 Table E-59.--Analysis of variance of Dimension 12--Prob1ems of teaching mathematics--by year graduated from Mecca College of Education (male teachers). 012 Problems of Teaching Mathematics By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Selected for male teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates .327 2 .164 .213 .809 A04 .022 1 .022 .029 .866 A05 .208 1 .208 .270 .605 Main effects 1.556 4 .389 .505 .732 A02 1.556 4 .389 .505 .732 Explained 1.883 6 .314 .408 .872 Residual 53.104 69 .770 Total 54.987 75 .733 Cell Means A02: Year Graduated From Mecca College of Education 1975-76 1976-77 l977-78 1978-79 1979-80 Total Bi 2.76 2.97 2.88 2.52 2.77 2.82 (15) (22) (17) ( 9) (13) (76) 232 Table E-60.--Ana1ysis of variance of Dimension 12--Prob1ems of teaching mathematics—-by year graduated from Mecca College of Education (female teachers). 012 Problems of Teaching Mathematics By A02 Year graduated from Mecca College of Education With A04 Overall GPA A05 Mathematics GPA Se1ected for female teachers . . Sum of Mean Signif. Source of Variation Squares df Square F of F Covariates 1.397 2 .699 1.150 .328 A04 1.300 1 1.300 2.139 .153 A05 .419 1 .419 .689 .412 Main effects .530 2 .265 .436 .650 A02 .530 2 .265 .436 .650 Explained 1.928 4 .482 .793 .538 Residual 21.270 35 .608 Total 23.197 39 .595 A02: Year Graduated From Mecca College of Education 1975-76 1976-77 1977-78 1978-79 1979-80 T°ta‘ m' 0 0 2.97 3.08 2.89 2.98 n ( 0) ( 0) (12) (13) (15) (40) BIBLIOGRAPHY 233 BIBLIOGRAPHY Abdel-Halim, A. El-Mahdi, and Shaker, Paul. "A Strategy for Promot- ing Educational Reform in Developing Countries." Paper pre- sented at the Annual Meeting of the American Educational Research Association, San Francisco, California, April 8-12, 1979. Abdul-Wasia, Abdu1wahab. Education in Saudi Arabia. Riyadh: Saudi Arabia, 1970. Al-Afendi, M. H., and Baloch, N. A., eds. Curriculum and Teacher Education. Islamic Education Series. Jeddah: King Abdul—Aziz University, Hodder and Stoughton, 1980. Al-Ahmad, Abdulrahman Ahmad. "A Study of the Effectiveness of the Teacher Preparation Program at Kuwait University, Based on a Follow-Up of 1976 Graduates." Ph.D. dissertation, Michigan State University, 1978. Al-Ajroush, Hamad Ali. "Proposed Mathematics Curriculum for the Saudi Arabian Intermediate Schools." Master's thesis, The University of Wisconsin, 1976. Al-Hamdan, Salim Fahd. "Educational System Charts of Saudi Arabia From 1952 to 1974 With Projections to 1985." M.S. thesis, University of Kansas, 1977. Al-Kazmi, Zohair Ahmad. "Student Perceptions of Parental Influence in Choice of College and Academic Field of Study at King Abdu1- aziz University in Saudi Arabia." Ph.D. dissertation, Michigan State University, 1981. Al-Nadwa (daily newspaper, Mecca), July 17, 1977. Al-Roushad, Mohammad, and Abdulatif, Ahmad. "The Colleges of Educa- tion's Role in Teacher Preparation." Paper presented at the First International Conference on Islamic Education, March 31- Aggil 7, 19772 Jeddah: King Abdul-Aziz University Press, Arab League, General Secretariate, Cultural Department. Collection of the Arab League Council Resolutions on Cultural Affairs to be executed by the Arab countries, 1946-66. (Typewritten.) 234 235 Arab Organization for Education, Culture, and Science, Department of Education. A Conference on Preparing Arab Teachers, From January 8 to 17,1972. Cairo: Al-Takadom Press, 1973. Beard, Earl M. L., and Cunningham, George S., eds. Middle School Mathematics Curriculum: A Report of the Orono Conference. 1973. ERIC ED 085 258. Belli, Gabrie1la. "Survey Method and Its Use in Research in General Mathematics." Research Series No. 54. East Lansing: Institute for Research on Teaching, College of Education, Michigan State University, June 1979. Biehler, Robert F. Psychology Applied to Teaching. 3rd ed. Boston: Houghton-Mifflin, 1978. Bochner, Salomon. The Role of Mathematics in the Rise of Science. Princeton: Princeton University Press, 1966. Borg, Walter R. Moving Toward Effective Teacher Education--One Man's Perspective. Logan: Utah State University Press, 1975. Boyer, Ernest L. "Campus-Wide Perception of Teachers: An Exercise in Collaboration." The Journal of Teacher Education 21 (September 1965): 271-74. Breslich, Ernst R. The Technique of Teaching Secondary-School Mathe- matics. Chicago: The University of Chicago Press, 1930. Burgess, Tyrell et a1. Dear Lord James: A Critique of Teacher Educa- tion. England: Penguin Books, Ltd., 1971. Chang, Paul. "Educational Trends in South-East Asia With Special Reference to Problems of Improving the Quality of Education." International Review of Education Journal 17 (1971-72): 150-63. Clark, Christopher M. "Choice of a Model for Research on Teaching Thinking." Research Series No. 20. East Lansing: Institute for Research on Teaching, College of Education, Michigan State University, July 1978. . "Five Faces of Research on Teaching." Occasional Paper No. 24. East Lansing: Institute for Research on Teaching, College of Education, Michigan State University, July 1979. , and Yinger, Robert J. "Research on Teacher Thinking." Research Series No. 12. East Lansing: Institute for Research on Teaching, College of Education, Michigan State University, April 1978. 236 College of Education, Mecca. College of Education in 25 Years, 1952-76. Mecca: College of Education Press, 1976. Cornish, Robert J. "Improving Undergraduate Elementary Training Proggams." University of Kansas Bulletin of Education 17 (May 1963 : 103. Dewey, John. The Child and the Curriculum and the School and Society. Chicago: The University of Chicago Press, 1971. Dressel, Paul L. Handbook of Academic Evaluation. San Francisco: Jossey-Bass, Inc., 1976. Goodlad, John I. "An Analysis of Professional Laboratory Experience in the Education of Teachers." The Journal of Teacher Education 16 (September 1965): 363-70. Graff, Paul. "Follow-Up Study of Graduates and Their Opinions of the Secondary Teacher Education Program of the University of Iowa, 1970-76." Ph.D. dissertation, University of Iowa, 1976. Gress, James R., ed. with Purpe1, David E. Curriculum: An Introduc- tion to the Field. California: McCutchangPublishing Corp., 1978. Hansen, Thomas Charles. "An Evaluative Study of the Effect of Secon- dary Teacher Education Courses on Student Attitudes." Disserta- tion Abstracts 37, 1-2 (1976): 234-A. Hardingham, Robert J. "The Cooperating School in Teacher Education: Source of Theory or Practice?" Technical Report No. 13. Iowa University, June 1977. ERIC ED 147 101. Hibshi, Muhammad Ali. "Educational Development: Some Basic Considera— tions." In Saudi Arabia and Its Place in the World. Edited by Dar Al-Shoroug. Jeddah: Ministry of Information, Kingdom of Saudi Arabia, 1981. Howard, A. E.; Farmer, W.; and Blackman, R. A. Teaching Mathematics. London: Longmans, Green, & Co., Ltd., 1968. Institute for Research on Teaching, College of Education, Michigan State University. Proceedings of the Research-on-Teaching Mathematics Conference. Conference Series No. 3. May 1-4, 1977. Issac, Stephen, with Michael, William B. Handbook in Research and Evaluation. San Diego, Calif.: EDITS Publishers, 1979. Joyce, Bruce R., and others. "Preservice Teacher Education." Washington, D.C.: Office of Education, Department of Health, Education and Welfare, 1977. ERIC ED 146 120. 237 Kakhleh, Emile A. The United States and Saudi Arabia: A Policy Anal sis. Washington, D.C.: American Enterprise Institute for Public Policy Research, 1975. Kilpatrick, Jeremy. "Methods and Results of Evaluation With Respect to Mathematics Education." In New Trends in Mathematics Teaching. Vol. 4. Paris: UNESCO, 1979. King Abdul-Aziz University Catalog, 1979-80. Mecca: King Abdul-Aziz University, 1979. Krygowska, A. Z. "Mathematics Education at the First Level in Post-elementary and Secondary Schools." In New Trends in Mathe- matics Teaching. Vol. 4. Paris: UNESCO, 1979. Lambert, Ruth L. "An Investigation of Attitudes of Selected Recent Graduates in Teacher Education Toward Their Education Preparation for Teaching at the University of Arkansas at Pine Bluff." Ph.D. dissertation, Michigan State University, 1977. Lanier, Judith E., and Floden, Robert E. "Research and Development Needs for the Advancement of Teacher Education." Research Series No. 8. East Lansing: Institute for Research on Teaching, College of Education, Michigan State University, February 1978. Lemons, Lawrence A. "Education Courses." NEA Journal 54 (October 1965): 26-27. Lipsky, George A. Survey of World Cultures: For Saudi Arabia: Its People, Its Society and Its Culture. Edited by Thomas Fitz- simmons. New Haven: HraflPress, 1959. Mattson, R. "An Evaluation of Teacher Educator Program at Montana State University by Graduates of That Program." Ph.D. disser- tation, Montana State University, 1972. Myers, Douglas, and Reid, Fran. Educating Teachers: Critiques and Pro osals. Ontario: The Ontario Institute for Studies in Education, 1974. Nash, Robert J., and others. "The Foundations of Education: A Suicidal Syndrome?“ Teacher College Record 92 (February 1977): 299-310. National Council for Accreditation of Teacher Education. Standards for Accreditation of Teacher Education. Washington, D. .: NCATE, 1977. National Council of Teachers of Mathematics. Curriculum Problems in Teaching Mathematics. New York: AMS Reprint Co., 1966. 238 . A General Survey of Progress in the Last Twenty-Five Years. New York: AMS Reprint Co., 1966. Nie, Norman; Hull, H.; Hadulai, C.; Jenkins, Jean 6.; Steinbrenner, Karin; and Bent, Dale. Statistical Package for the Social Sciences. New York: McGraw-Hill Book Co., 1975. Office of Admissions and Registration, Umm Al-Qura University. Commencement Issue. Mecca: Umm Al-Qura University, 1980-81. Payne, David A., ed. Curriculum Evaluation: Commentaries on Purpose, Process, Product. Lexington, Mass.: 0. C. Heath and Co., 1974. Preston, Ralph C. "Education Graduates View Education and Academic Courses." Schoo1 and Society 92 (Summer 1964): 233-37. Ramos, Pas G. "The Colle e of Education and the New Education Reforms." Education Quarterly ECollege of Education, University of the Phil- ippineSJIZO (January-March 1974): 18-30. Razik, Taher A., and Willis, Verna. Comparative Analysis of Curricu- lum Change and Development in the Arab Countries: The Process. Buffalo: State University of New York, Faculty of Educational Studies, 1978. Recommendations of the Second World Conference on Muslim Education. Islamabad: TMinistry of Education, Government of Pakistan, 1980. Saradatta, De Lamiama, and Sapianchaiy, Poj. "Curriculum Eva1uation in Teacher Education in Thailand." Paper presented at the Confer- ence on Curriculum Evaluation Teacher Education in S.E. Asia Organized by the Internal Council on Education for Teaching [ICET] and the Faculty of Education, University of Malaya [FEUM], August 3-7, 1970. Malaysia: Malaya Publishing & Printing Co., 1970. Saudi Arabia, Ministry of Education. The Educational Policy in the Saudi Arabian Kingdom. Riyadh: Ministry of Education, 1974. . Educational Statistics in theJKingdom of Saudi Arabia. Vol. 12. 1978/79. Riyadh: Ministry of Education, 1978/79. . Genera1 Directorygof Research and Curriculum. Riyadh: Ministry of Education, 1979. . Progress of Education in Saudi Arabia: A Statistical Review. Riyadh: *Ministry of Education, 1979. 239 , Primary Education Department. Primary Education Yesterday and Today. Beirut: Muassasat Manturah Liltiba'ah, 1969. Schaffarzick, Jon, and Sykes, Gary, eds. Value Conflicts and Curricu- lum Issues: Lessons from Research and Experience. National Institute of Education, Department of Health, Education, and Welfare. Berkeley, Ca1if: McCutchan Publishing Corp., 1979. Schmidt, William H. "Measuring the Content of Instruction." Research Series No. 35. East Lansing: Institute for Research on Teaching, Col1ege of Education, Michigan State University, October 1978. Secondary School Mathematics Curriculum Improvement Study. Mathematics Education in Eurgpe and Japan. Bulletin No. 6. New York: Teach- ers Co11ege, Columbia UhiVersity, Fall 1971. Shaker, Paul. "Curriculum Change in the Developing Country: The Case of Saudi Arabia." Paper presented at the Annual Meeting of the American Educational Research Association, Boston, Massachusetts, April 7-11, 1980. Shulman, Lee S., with Shroyer, Janet. "Psychology and Mathematics Education Revisited." Occasional Paper No. 10. East Lansing: Institute for Research on Teaching, College of Education, Michi- gan State University, July 1978. Shumway, Richard J., ed. Research in Mathematics Education. Profes- sional Reference Series. Reston, Va.: ’The National Council of Teachers of Mathematics, Inc., 1980. Tanner, Daniel, and Tanner, Laurel N. Curriculum Development: Theory Into Practice. 2nd ed. New York: Macmillan, 1980. Tyler, Ralph W. Basic Principles of Curriculum and Instruction. Chicago: The university ofChicagoPress, 1949. UNESCO. New Trends in Mathematics Teachigg. Vol. 1. Prepared by the International Commission of Mathematical Instruction (ICMI). Paris: UNESCO, 1966. New Trends in Mathematics Teachigg, Vol. 2. Prepared by the International Commission of Mathematical Instruction (ICMI). Paris: UNESCO, 1970. New Trends in Mathematics Teachigg, Vol. 3. Prepared by the International Commission of Mathematical Instruction (ICMI). Paris: UNESCO, 1972. 240 New Trends in Mathematics Teaching. Vol. 4. Prepared by the International Commission of Mathematical Instruction (ICMI). Paris: UNESCO, 1979. Van Engen, H. "Fostering Mathematical Maturity in the Middle SchooT Classroom." Paper Presented at the Orono Conference of Maine University, Orono, July 16-20, 1973. Wahbah, Hafiz. Arabian Days, London: Arthur Baker, Ltd., 1964. Yinger, Robert J. "Fieldwork as Basis for Theory Building in Research on Teaching." Research Series No. 19. East Lansing: Institute for Research on Teaching, College of Education, Michigan State University, July 1978.