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I .I.\ IIIrII III Iu‘lUIIIi‘IILIIIfl.I .. hIIII.‘ I II III-“I II I u , ‘lI-I.H.HIII, III I. .IIII.Iu.| IIHIIu III ll...IId IMIIIIIIIII. IIIUIII \III I.rIII\pIfiIUI€I..I\\.IIH IblII‘I IIuIdHIJIuIIleHIIIIIflIJHI (IIII‘IIIII HF“ IHHHII‘IIIJII IIIIIIIII .I III ' I I I I! III I. I I IIII II U‘ HIIUIIIVIIIII I ...III .In I6“! I. IJI IIII IIIIII III! yup. - I I I“ II (I. ‘.I I ‘IV I ‘II' III | I lauIIII, I. I II I II .II , II I“I.\ IIIIGa. I I THESIS mm“ IIIIIIIIIIIIIIIIIIIIIIIIIIIIII gr ! m 3 1293 104759 ”JJ i’hI 7,553 Sig-539.2 Univ rein- This is to certify that the dissertation entitled A Study of How Supervisors' Evaluations, Teachers' Behaviors, and Students' Attitudes Towards Teachers are Related to Instructionally Effective Teachers of Ninth Grade Mathematics presented by Abdulrazzag A. Dhafar has been accepted towards fulfillment of the requirements for Philosophy degreein Teacher Education Date April 5; 1982 MS U is an Affirmative Action/Equal Opportunity Institution 0-12771 RETURNING MATERIALS: IVIESI_J Place in book drop to IJBRARJES remove this checkout from .aal-zglliL. your record. FINES wiII be charged if book is returned after the date stamped below. i SEP 1 91999 A STUDY OF HOW SUPERVISORS' EVALUATIONS, TEACHERS' BEHAVIOR, AND STUDENTS' ATTITUDES TOWARD TEACHERS ARE RELATED TO INSTRUCTIONALLY EFFECTIVE TEACHERS OF NINTH—GRADE MATHEMATICS By Abdulrazzag Ahmad Dhafar A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Teacher Education 1982 ABSTRACT A STUDY OF HOW SUPERVISORS' EVALUATIONS, TEACHERS' BEHAVIOR, AND STUDENTS' ATTITUDES TOWARD TEACHERS ARE RELATED TO INSTRUCTIONALLY EFFECTIVE TEACHERS OF NINTH-GRADE MATHEMATICS By Abdulrazzag Ahmad Dhafar The purpose of this study was to determine how-supervisors' evaluations of teachers, teachers' behavior, and students' attitudes toward teachers are related to instructionally effective teachers of ninth-grade mathematics. Procedures Forty ninth-grade mathematics teachers were chosen from 24 schools in three cities in Saudi Arabia. These teachers agreed to teach a unit of instruction from the ninth-grade algebra book for three weeks. Students of these teachers were pre- and posttested on the content of the unit so that the teachers could be ranked in terms of their instruc- tional effectiveness. Residual-gain scores were used to do the rank- ing; these were computed for each teacher's students with the pretest score as a covariate. The four most instructionally effective and the four least instructionally effective teachers available were chosen for the study. Five instruments were used to measure the dependent variables: the supervisor's report, designed by the Jeddah Board of Education, Abdulrazzag Ahmad Dhafar Saudi Arabia, for supervisors to evaluate the teachers; a question- naire designed by the researcher to measure students' attitudes toward their teachers; and three instruments for coding teachers' classroom behavior, taken from the Brophy-Good Dyadic Interaction System. The following analyses were performed: one-way analysis of variance to test individual behaviors, two-tailed t-tests to test hypotheses con- cerning students' attitudes, and discriminant analysis. Findings l. No significant difference was found between supervisors' ratings of the most and least effective teachers for the overall rat- ings and for each of the 12 subscales. 2. As independent variables, teacher "clarity" and "rephras- ing students' correct answers" were behaviors found to be significantly different between the instructionally more effective and less effective teachers. 3. Three discriminant functions were identified that best distinguished between the two groups of teachers. 4. At the end of the 1980-81 school year, students judged instructionally effective teachers as those who demonstrated more con- cern for their students, were more knowledgeable about the subject matter, and made their teaching more enjoyable than did instructionally less effective teachers. At the beginning of the l981-82 school year, students judged instructionally effective teachers as those who praised less and punished more than instructionally less effective teachers did. [in t4; nanu: 0/541” M: most mzzciful'ana/ “I: most gang/iciuzt Copyright by ABDULRAZZAG AHMAD DHAFAR 1982 This dissertation is dedicated to the memory of my parents, Khadiga Mirza and Ahmad Dhafar, and of my father-in-law, Abdulgafar Saati. ii ACKNOWLEDGMENTS Praise and thanks be to God, first and last, Lord and Cherisher of all the world, who taught humankind everything they knew not. The writer wishes to offer sincere appreciation and thanks to his major advisor, Dr. Patrick DeMarte, and to his doctoral guid- ance committee members, Dr. Robert Hatfield, Dr. Richard Gardner, and Dr. William Fitzgerald, for their professional assistance and con- tinuous support. Special thanks is offered to Drs. DeHarte and Hatfield for their encouragement and assistance throughout the gradu- ate study. Appreciation is offered to Mr. Mustafa Filimban, Mr. Omar Meri, Mr. Gamil Yamani, Mr. Mohamed Gazali Yamani, Dr. Abdulla Alzaid, and to all of those teacher educators on the Board of Educa- tion at Makkah, Jeddah, and Taif who made this study possible. The writer also wishes to express his greatest appreciation and gratitude to his parents, who have offered a great deal of concern, support, encouragement, and prayers for many years, and to his brothers, sisters, and mother-in-law for their continuous care, encouragement, and prayers throughout the five years of study in the United States. Finally, the investigator extends his deepest gratitude and appreciation to his wife, Thoria Saati, for much help, encouragement, and emotional support, and to his children, Ayman, Walid, Amani, and Salman, who understood this work in their own way. iii TABLE OF CONTENTS Page LIST OF TABLES ......................... vi Chapter I. THE PROBLEM ....................... 1 Introduction ..................... 1 Purpose of the Study ................. 2 Importance of the Study ................ 2 Research Questions .................. 4 Limitations of the Study ............... 5 Teacher Supervision and Evaluation in Saudi Arabia . . 5 Organization of the Study ............... 8 II. CONCEPTUAL FRAMEWORK OF THE STUDY ............ 9 Theoretical Conceptualization for This Study ..... 9 Research on General Supervision ............ lO Clinical Supervision ................. 12 Recent Research on Clinical Supervision ....... 14 Using Observation for Improving Teaching ...... 15 Research on Teacher Evaluation ............ l6 Three Phases of Research on Teaching ......... 20 First Phase of Research on Teaching ......... 2l Second Phase of Research on Teaching ........ 22 Third Phase of Research on Teaching ......... 23 Research on Effective Instruction ........... 24 Teaching Junior High Mathematics .......... 28 Summary ........................ 3l III. RESEARCH DESIGN AND PROCEDURE .............. 32 Research Questions .................. 32 Design of the Study .................. 33 Research Hypotheses .................. 33 Hypotheses Pertaining to Supervisors' Evaluations . . 33 Hypotheses Pertaining to Classroom Observations . . . 35 Hypotheses Pertaining to Students' Attitudes . . . . 37 Population of the Study ................ 38 Sample of the Study .................. 39 Instruments ...................... 42 iv Instrument Used to Evaluate Teachers by Supervisors . 43 Instruments Used for Classroom Observations ..... 43 Instruments Used to Measure Students' Attitudes . . . 44 Questionnaire Reliability .............. 44 Questionnaire Content Validity ........... 48 Training the Observers ................ 49 Training of Observers Prior to Their Going Into the Classroom ................... 49 Guidelines for Observers .............. 50 Training in the Classroom .............. 51 IV. ANALYSIS AND INTERPRETATION OF THE DATA ......... 54 Supervisors' Evaluations of Teaching ......... 54 Teachers' Behavior .................. 59 Students' Attitudes Toward Their Teachers ....... 63 Test at the End of the 1980-81 School Year ..... 64 Test at the Beginning of the 1981-82 School Year . . 67 Overall Analysis of Supervisors' Evaluations, Teachers' Behavior, and Students' Attitudes Toward Their Teachers ................ 71 Summary of the Results ................ 72 V. SUMMARY, DISCUSSION, AND RECOMMENDATIONS ........ 75 Summary ........................ 75 Conclusions and Implications ............. 79 Conclusions ..................... 79 Implications .................... 82 Recommendations for Further Research ......... 83 APPENDICES ........................... 85 A. CONTENT VALIDITY OF THE PRETEST-POSTTEST ........ 86 B. THE ARABIC VERSION OF THE SUPERVISORS' REPORT AND THE ENGLISH TRANSLATION ................ 88 C. BRIEF DEFINITIONS OF VARIABLES CODED IN THE BROPHY- GOOD DYADIC INTERACTION SYSTEM ............ 91 D. ARABIC AND ENGLISH VERSIONS OF THE COVER LETTER AND THE QUESTIONNAIRE ................... 101 E. EXPLORATORY FACTOR ANALYSIS ............... 110 F. RELIABILITY ANALYSIS OF SCALES ............. 117 BIBLIOGRAPHY .......................... 126 Table wwwwwwww \OQNO‘U‘l-th LIST OF TABLES Pretest and Posttest Measuring Students' Achievements The Average-Gain Scores of the Mathematics Teachers Items on Questionnaire Concerning Students' Attitudes Items Included in Supervisors' Evaluations ........ Brophy-Good Dyadic Interaction Scale ........... High-Inference Codings ............. A ..... Homework Assignments ................... Subscales, Clusters, and Coefficients of Reliability . . . Data for the Fridman Two-Way ANOVA Agreement Test for the Brophy-Good Dyadic Interaction Analysis ...... . Data for the Fridman Two-Way ANOVA Agreement Test for the Emmer High-Inference Scale ............. Results of One-Way Analyses of Variance of Hypotheses l and 2 ......................... Items Included in the Discriminant Analysis of Supervisors' Evaluations ................ Results of Discriminant Analysis of Hypothesis 3 ..... The Significance of the Standardized Canonical Discriminant Function for Hypothesis 3 ......... Prediction for Classifying the Effectiveness of Teachers in Hypothesis 3 .................... Results of One-Way Analysis of Variance of Hypothesis 4 Results of Discriminant Analysis of Hypothesis 5 ..... The Significance of the Standardized Canonical Discriminant Function for Hypothesis 5 ......... vi Page 39 40 41 43 45 46 47 48 52 53 55 57 57 58 58 6O 62 62 4.9. bh-b-b-b-b-b-h-b-b-b .11. .12. .13. .14. .15. .16. .17. .18. .19. .20. .21. Prediction for Classifying the Effectiveness of Teachers for Hypothesis 5 .................... Items Included in the Discriminant Analysis for Hypothesis 5 ...................... 1: Results Results Results Results Results Results Results Results Results Results of Two-Tailed of Two-Tailed of Two-Tailed of Two-Tailed of Two-Tailed of Two-Tailed of Two-Tailed of Two-Tailed of Two-Tailed of Two-Tailed Items Included in the Hypothesis 7 ...................... t-Tests t—Tests t-Tests t-Tests t-Tests t-Tests t-Tests t-Tests t-Tests t-Tests for Scale for Scale for Scale for Scale for Scale for Scale for Scale for Scale for Scale for Scale 01-500“) 01-th 1980-81 . . . . ° 1980-81 . . . . 1980-81 . . . . 1980-81 . . . . : 1980-81 . . . . : 1981-82 . . . . ° 1981-82 . . . . 1981-82 . . . . 1981-82 . . . . : 1981-82 . . . . Discriminant Analysis for Results of Discriminant Analysis of Five Scales of Hypothesis 7 ...................... Prediction for Classifying the Effectiveness of Teachers for Hypothesis 7 vii Page 63 63 65 65 66 67 67 68 69 69 7O 7O 71 72 72 CHAPTER I THE PROBLEM Introduction There is little doubt that individual teachers make an important contribution to the achievement of students (Rakow, Arusian, & Madans, 1978), or, as Good, Biddle, and Brophy (1975) stated, that teachers do make a difference. A constant concern to educators is the identification of those teachers who are most effective in making that important difference. In this regard, Saif and others (1976) reported that During the last fifteen years, voices have been raised asking for more accountability in education. . . . As the trend has become general, many states have passed laws requiring evalua- tion in education, often specifically identifying teachers as a sector to be evaluated. Why have lawmakers required evalua- tion of teachers? Some have answered this question simply by saying "to get rid of 'bad' teachers." Others have seen evalua- tion as means of determining salary scales. Educators did not feel comfortable with either answer. They, however, looking at the same question, have given different answers, namely: "to improve student learning" and "to promote the professional growth of teachers.“ (p. 126) This study considers both concerns in a way to help teachers to be instructionally more effective and, as a result of that, to maximize students' achievement. Since no empirical research from Saudi Arabia has correlated supervision of instruction and effective teaching, such a study is needed. Purpose of the Study The purpose of this study is to determine how supervisors' evaluations of teachers, teachers' behavior, and students' attitudes toward teachers are related to instructionally effective teachers of ninth-grade mathematics. This study is a partial replication and extension of earlier work at the second- and third-grade levels (BrOphy & Evertson, 1976), in fourth-grade mathematics classrooms (Good & Grouws, 1977), and in junior-high-school mathematics and English classes (Evertson, 1980). These and other studies have demonstrated that it is possible to identify those teachers whose students obtain higher achievement scores (Berliner & Tikunoff, 1976; Brophy & Evert— son, 1974; Stallings & Kaskowitz, 1974; McDonald & Elias, 1976; Good & Grouws, 1975). Therefore, in this study, the criterion for judging teacher effectiveness was based on whether students demonstrated sig- nificantly greater achievement gains on a locally developed measure of student achievement. Importance of the Study Currently, there is intense concern in Saudi Arabia for the improvement of preservice and inservice education. Much attention is being paid to the development of criteria for effective teaching by Saudi Arabian teacher educators. New programs for teacher education are currently under development. There is great interest in using research on effective instruction as the basis for those programs. In the past, teacher-education programs were created without this research base. Furthermore, the methods of supervision were developed largely on the basis of the supervisors' experiences. Also, evaluation of teacher behavior was based on criteria that may or may not have been related to student performance. In this research, the relationship between supervisors' ratings and teachers' behavior in relation to students' performance was studied. Two aspects related to teacher education emerged: 1. The identification of selected teacher behaviors as they may be related to effective instruction in ninth-grade mathematics; 2. The relationship between supervisors' ratings of teachers' behavior and how these ratings are correlated to the effective instructors . Careful study of both these aspects of teacher effectiveness will be useful in the following: 1. Preservice education. Teacher educators who develop preservice programs for teachers can use the research on teaching and effective instruction to help student teachers acquire those behaviors that have been shown by both sound theory and research to be effec- tive. In addition, they can use the research on teacher evaluation and effective supervision to introduce these concepts to student teachers so that they can know in advance how to cooperate with super- visors to improve their teaching and, as a result, maximize students' achievement. 2. Inservice education. Teacher educators who develop inservice programs for teachers and supervisors could relate both effective instruction and effective supervision to students' achieve- ment. This can be done by creating an educative environment between teachers and supervisors in such a way that teachers see supervisors as resource persons. In addition to the significance of this study for develop- mental efforts for teacher education in Saudi Arabia, the study of the supervisors' ratings is unique since no attempts to define these relationships have been made in previous works. Since supervisors in Saudi Arabia are not trained systematically and since training for supervisory personnel is only emerging, results of this study will be of great interest to persons designing programs for supervision of mathematics instruction. As a replication of the work of Brophy and Evertson (1976), Good and Grouws (1977), and Evertson (1980), this study will contribute to the body of literature on the effectiveness of teachers in mathe- matics instruction. This study will also contribute to a comparative analysis between American and Saudi Arabian studies. Research Questions The major question under investigation in this study was: Do supervisors' evaluations of teachers who are instructionally effec- tive in ninth-grade mathematics differ from evaluations of teachers who are instructionally less effective? To answer this question, several related questions also needed to be answered. They were as follows: 1. Do teachers whose students perform better on ninth- grade mathematics tests demonstrate different behaviors than those whose students do not perform well on the same tests? 2. What are some of the behavioral characteristics that dis- tinguish instructionally effective and instructionally less effective teachers? 3. Do the attitudes toward teachers of students who do well on the ninth-grade mathematics achievement test differ from the atti- tudes toward teachers of those who do not perform well on the same test? Limitations of the Study This study was limited to ninth-grade mathematics teachers in the western part of Saudi Arabia, namely, in Makkah, Jeddah, and Taif. For this reason, the results obtained may not be generalized freely to other countries, to other levels of schooling, or to other sub- jects. However, this study may provide methodological impetus for further research in this area. In addition, the sample size in this study was small (eight teachers and two supervisors), which resulted in a total of 80 observations. Teacher Supervision and Evaluation in Saudi Arabia In Saudi Arabia, before 1976, supervisors worked for the Board of Education and were assigned to school districts. All teach- ers in each district were visited by supervisors twice a year. These visits were made without the consent or advance knowledge of the teachers. The purpose of the visits was to evaluate each teacher's performance. These evaluations were based on supervisors' definitions of effective teaching rather than on scientific criteria derived from research on effective instruction. These procedures were not accept- able to teachers, school principals, and ultimately, to the Ministry of Education for the following reasons: Two visits were not enough to evaluate the teachers, criteria for evaluation were derived from the supervisors' experiences rather than from research on effective instruction, there was no real communication between principals and the supervisors, and teachers did not try innovations in teaching because the supervisors wanted them to follow certain procedures. Consequently, teacher educators in Saudi Arabia began to search for more effective means of supervision. v// In 1976, the Ministry of Education changed the procedures for supervision. The principal of each school designated a chairman for each department, such as mathematics, science, and Arabic language. The chairman for each department and the principal made a plan for teacher evaluation for that department. Teachers were evaluated according to these plans. The supervisors' duties were to do field research, give lectures to teachers on areas related to teaching, and plan for inservice education programs. This approach was judged unsatisfactory for the following reasons: Principals and chairmen were not trained as supervisors, hence the same problems regarding the validity of their observations occurred; furthermore, there were no clear rules for communication between supervisors and principals. o/’ In 1978, the Ministry of Education changed the procedures for supervision to the following: Both the supervisors and the princi- pals worked together to help evaluate the teachers. Because of the magnitude of the changes in the procedures for teachers' evaluation, Dr. Abdulla Alzaid, the Educational General Director in the West District in Saudi Arabia, asked a number of teacher educators, who were involved in supervision and teacher evaluation, in different districts and universities to a conference to present papers on what they had done in this area. This confer- ence started at the beginning of the 1979 school year. Recommenda- tions from this conference included the formation of a committee composed of the principal, a supervisor from the Board of Education district, and the chairman from each department to help evaluate teachers. Any person from the committee was considered a resource for the classroom teacher. The duties of the committee were to be as follows: 1. Develop valid instruments for collecting data from the classroom; 2. Base the criteria for teacher evaluation on sound theory and empirical research; 3. Ascertain if the school library included the current Arabic literature on teaching and the Arabic translations of the recent research on teaching; 4. Have supervisors do field research; 5. Have the committee plan for inservice education based on school and teacher needs; 6. The committee was responsible for acquiring and producing instructional media for the staff; 7. Plan extracurricular activities for the students. The Ministry of Education studied these recommendations and provided support for released time for a number of principals to go through a one-year renewal program at the Makkah and Reiyad Colleges of Education. The purpose of this training was to prepare the prin- cipals for their role as instructional leaders. In the near future, supervisors will receive the same kind of training. (For an extended (discussion of these recommendations, see the Proceedings of the First Educational Supervision Conference in Saudi Arabia, 1979.) Organization of the Study This study is divided into five chapters. In Chapter I, an introduction to the study was presented. Included in the introduc- tion were a statement of the purpose of the study, importance of the study, the research questions, limitations of the study, and a discus- sion of teacher supervision and evaluation in Saudi Arabia. The conceptual framework of the study is given in Chapter II. This chap- ter contains a presentation of the theoretical conceptualization for this study and relevant research on the following areas: research on supervision, research on teacher evaluation, research on clinical supervision, research on teaching, and research on effective instruc- tion. A brief description of the research design and the methodology used in the preparation and conduct of the study is given in Chapter III. Chapter IV is devoted to the presentation of the findings of the study. Chapter V includes a summary of the investigation, approp- riate conclusions and implications, and recommendations for further research. CHAPTER II CONCEPTUAL FRAMEWORK OF THE STUDY Development of the conceptual framework for this study involved a review of literature in the following areas of research: supervision, teacher evaluation, teaching, and effective instruc- tion. This chapter begins with a presentation of the theoretical conceptualization for this study. Following this is a presentation of the research related to this theoretical framework, which includes research on supervision, clinical supervision, teacher evaluation, teaching, and effective instruction. Theoretical Conceptualization for This Study This study was derived from the following assumptions: (1) that the supervisor's job in Saudi Arabia is to evaluate effec- tive teaching; (2) that instruction is the most significant aspect of teaching that supervisors evaluate; (3) that teachers are able to be distinguished from one another in terms of the differential perform- ances of their students. Given these assumptions, it follows that a study is possible in which an attempt is made to determine whether supervisors' evaluations of teachers correspond to teachers' per- formances. From a theoretical standpoint, it would be logical to expect supervisors to evaluate teachers who are instructionally effective as high and teachers who are instructionally less effective 9 10 as low. Recent advances in the study of teaching have made it pos- sible to rank teachers in terms of their instructional effectiveness (Good & Grouws, 1975; Berliner & Tikunoff, 1976; Brophy & Evertson, 1974; Stallings & Kraskowitz, 1974; McDonald & Elias, 1976). At present, no study has been conducted in which the hypothesis has been tested that supervisors do, in fact, make discriminating judgments between instructionally effective and instructionally less effective teachers. This study rests between the research on teaching and research on supervision and teacher evaluation. Therefore, a review of rele- vant literature from these areas of study is presented in this chap- ter. The material in this chapter represents an attempt to give perspective to the field of teacher supervision and teacher evalua- tion. The relevant literature in that area of study is reviewed. Research on General Supervision Mosher and Purpel (1972) reported that "very little research has been done on the supervision of teaching" (p. 49). Harris (1965) reported that, from 1953 to 1963, an average of one article per year was considered "supervision research." He commented: Notable indeed is the lack of research on the supervisor and supervisory programs and practices in education. We continue to emphasize studies in this field which deal with teacher opinions of supervisors, principals' opinions, contrasting per- ception of roles and role conflicts. Neither the quality nor the significance of these studies warrants much more replica- tion. (p. 49) Barr (1945) pointed out that supervisors' analysis or evalua- tions of teaching usually have both low validity and low reliability. He arrived at the following conclusion: 11 There is plenty of evidence to indicate that different practi- tioners observing the same teacher teach, or studying data about her, may arrive at very different evaluations of her; this observation is equally true of the evaluation experts [super- v1sors]; starting with different approaches, and using different data-gathering devices, they, too, arrive at very different evaluations. (Mosher & Purpel, 1972, p. 50) Mosher and Purpel (1972) reported that five skilled social- studies supervisors used tape-recorded observations and rated inde- pendently four student teachers. Their results were as follows: "The supervisors' disagreement about the teaching they were evaluat- ing ranged from 50 to 100 percent" (p. 50). They gave three reasons for these differences in their ratings. These were the absence of agreement as to the "right" way to teach, the unreliability of the rating instruments used in supervision, and supervisors either seeing different teaching behavior during their observations or evaluating the same behavior differentlyL Given the paucity of meaningful research on supervision, Sergiovanni (1982) posited the importance of a theory of supervisory practice sensitive to the needs of professional action. He reported that Such a theory would serve to inform the intuition of super- visors and teachers alike and would emphasize both explanation and understanding in the analysis of teaching. Its purpose would be to provide a helpful framework to supervisors and teachers in an effort to improve teaching. (p. 67) Because this theory has not been empirically tested, McNeil (1982) suggested a modern approach to scientific supervision, which he explained as follows: At this time, the concept of scientific supervision changed from that of regarding research findings as fixed conclusions, formulated into a pattern for all to follow, to that of regarding 12 such findings as data for sharpening observations and direct- ing further thinking. Supervisors and teachers together were to adopt an experimental attitude, trying out new procedures and studying the effects of each newly introduced means of improvement until satisfactory results were attained. (p. 19) Clearly, the research and thinking on supervisors suggest the use of research on teaching as a vehicle for supervision. Clinical supervision, a special form of general supervision, is examined next in terms of its relationships to this study. Clinical Supervision ‘ Snyder (1981) defined clinical supervision as follows: (:"Clinical supervision is an important branch of general supervision; [itl focuses on helping teachers improve their performance through the analysis and feedback of observed events in the classroom" (p. 521). Clinical supervision has been characterized as "a‘structurembymwhichw instructional adequacy can be_establishedi (Krey, Netzer, & Eye, 1977, p. 21). Teacher and supervisor should deal with problems together through the cycle of clinical supervision and rest on "the conviction that instruction can only be improved by direct feedback to a teacher on aspects of his or her teaching that are of concern to that teacher (rather than items on an evaluation form or items that are pet concerns of the supervisor only" (Reavis, 1976, p. 360). The I clinical-supervision approach fitted the definition of Burton and Brueckner (1955) of "modern supervision" because "it involves the sys- -""” tematic study and analysis of the entire teaching-learning situation utilizing a carefully planned program that has been coopergfiiYély 13 .derixgdwftom“thewsituatjgn and_which is adapted_to theneeds of_thqseh involved in it" (p. 13). The clinical approach to supervision took its name and assump- tions from the works of Cogan (1973), Goldhammer (1969), and others. The model associated with clinical supervision is a process model, the cycle of clinical supervision. The processes, which are initiated by a teacher who requests aid, involve conferences, observation, and analysis. The roles of the teacher and the supervisor are prescribed (as opposed to defined) and include instructing, conferencing, analyzing, and data gathering as activities. Both teacher and supervisor are to be open, flexible individuals who are careful in making judg- ments. Each is to contribute toward a productive working rela— tionship that benefits both. (Sullivan, 1980, p. 13) In his review of research in clinical supervision, Sullivan (1980) reported that "several studies, though not specifically based on clinical supervision, support some of the basic tenets of clinical supervision" (p. 182). Edgar (1972) reported an empirical study in which the autonomy attitudes of new teachers changed significantly toward the attitude of the evaluators more in situations in which there was high affect between the new teacher and the evaluator than in situations in which there was low affect (p. 15). Parsons (1972) found that closeness of the supervisor to the teacher was identified as a major factor in effectiveness. Gordon (1976) indicated that supervisors were perceived most effective by teachers when supervisors were being supportive. Thus, "general research, then, indicates that the supervisor who is close and supportive is favored by teachers. Further, the way the supervisor is perceived affects the teacher's morale and the way the teacher expects to be perceived" (Sullivan, 1980, p. 16). 14 Recent Research on Clinical Supervision Arbucci (1978) did an experimental study for implementing clinical supervision. A significant difference was found between control and experimental groups in the amount of supervision. Reavis (1977) conducted a study to investigate differences in verbal exchanges between supervisors and teachers, contrasting clinical supervision and traditional supervision. His results were as follows: "The data revealed a significant difference between the treatment groups favoring the clinical supervision style. Teachers responding on a semantic differential scale also favored the clinical supervision style" (p. 311). Sullivan (1980) reported on the research that had been done by Eaker (1972), which dealt with the perceptions of clinical super- vision by different educators. The sample included teachers and administrators in the seven largest school systems in Tennessee. His results led to the following conclusions: 1. Most teachers and administrators agreed with the basic assump- tions of clinical supervision; 2. Although the teachers tended to agree with the procedure of clinical supervision, they agreed more strongly with the assumptions than with the specific procedures; 3. No firm conclusions could be drawn as to how teachers felt about being trained in observational techniques for the pur- pose of analyzing each other's teaching; 4. Administrators tended to agree more strongly with the assump- tions and procedures of clinical supervision than did teachers; 5. There was insufficient evidence to conclude that there exists significant differences in views of teachers with three years' or less experience and those with more than three years' experience. (p. 17) Turner (1976) developed a case-study approach in which she used five stages of the Goldhammer model with three elementary 15 teachers. The case study was found to be a reliable method for study— ing the process of supervision. Sullivan (1980) summarized the pre- vious findings as follows: Taken together, these studies yield some findings in support of the clinical supervision model. There is evidence which points 'U) validation of the model (Turner, 1976) and indica- tions that the model's tenets and processes are compatible with the desires of teachers and administrators (Eaker, 1972). (p. 23) f 3 Using Observation for { Improving Teaching, 1' Brophy (1979) started his introduction to using valid obser- vation instruments for improving teaching as follows: Philip Jackson (1968), in Life in Classrooms, pointed out that classrooms are very busy places, especially for teachers, who share hundreds of interactions with their students each day. Most teachers are too busy coping with the demanding pace of classrooms to have much time to monitor or reflect upon their behavior, so much of their behavior is habitual and not delib- erate. Such teacher behavior can persist indefinitely without evaluation or revision even where it is inappropriate, because teachers are not aware of it and their students do not provide feedback about it. (p. 1) Moore, Schaut, and Fritzger (1978); Tuckman, McCall, and Hyman (1969); Withall (1956); and Brophy and Good (1974) suggested that teaching can be improved by providing teachers with feedback about their behavior. Simon and Boyer (1970) developed more than 100 systems for classroom observations. Flanders (1970) developed one instrument for collecting data in the classroom. Brandt (1972) provided a readable survey of naturalistic approaches in schools for data collection. Good and Brophy (1978) gave detailed suggestions about classroom behavior that can be measured and methods for measur- ing them. Good and Brophy (1969) also used dyadic interaction systems 16 for coding teachers' behavior. This instrument was used in the present study. It should be clear that the data that could be collected by observation of classroom teachers were not supposed to be for evaluations of teachers. Both supervisors and teachers should work together in analyzing and interpreting these data. Research on Teacher Evaluation Weisenstein (1976) summarized research on teacher evaluation as follows: A review of the literature in teacher evaluation revealed little evidence that agreement exists among the professionals in education as to the key elements in the teacher evaluation process. Major issues generated by the teacher evaluation process were grouped into three very general categories and were felt to be characteristic of the dissonance affecting decisions relative to the process of accountability in educa- tion. In dealing with the first question, "Who is respon- sible for evaluating teachers?" it was suggested that the principal must play at least a passive role in the evaluation of the teaching staff, and that the degree of the principal's direct involvement in the evaluation process varies consider- ably. The wisdom of the principal who assumes complete respon- sibility for the evaluation process was questioned, with alter- nate plans provided which enable the principal to share responsibility in this area. Basic criteria to be applied in the selection of the evaluation modes identified are also pro- vided. The second major question dealt with the identification and selection of an appropriate evaluation instrument. Con- siderations in this selection included the following: relevance, reliability, validity, fidelity, and ease of administration. In addition, the purposes of teacher evaluation, as a prerequisite to the identification and selection of an evaluation instrument, was surveyed, with primary emphasis given to the pros and cons of evaluating either the instructional process or the instructional product. The third major question pertained to the human relations difficulties which could arise as a result of the evaluation process. Characteristic human relations problems were identi- fied and a non-inclusive list of preventive measures available to the principal was given. In conclusion, it was implied that, regardless of the frailties of current evaluation systems, a 17 great deal of success in teacher evaluation can be achieved through adequate planning, staff involvement, and emphasis being placed)on professional growth rather than teacher incompetence. p. 19 Natriello and others (1977) also reviewed the recent litera- ture on the evaluation of teachers. Their review dealt with seven aspects of evaluation. 1. Basis for evaluation. "Alvir (1975) defines five teacher roles as the basis for evaluation: classroom facilitator, resource person, academic advisor, nonacademic liaison, and researcher- innovator" (Natriello et al., 1977, p. 30). 2. Pre-post conference. The Redfern (1972) approach has recently gained popularity. First, the evaluator and evaluatee have a conference to estab- lish job targets based on broad educational goals. After the evaluator has assessed the teacher's performance, they meet again to discuss ways to improve teaching and to establish new targets. (Natriello et al., 1977, p. 31) 3. Pretest-posttest. Hunter (1973) suggests that the evaluator should observe the teacher teach one lesson to a student who has been pretested on the subject matter. Afterward, the student should be re-evaluated. At the end of the process, the evaluator has both a measure of the teacher's success and assessments made during observation. The combination may help to spot areas for improvement in the teacher's performance. Popham (1972) stressed that this method would be more objective than classroom observation, but without observa- tion the evaluator may have difficulty in pointing to specific areas a teacher should work on. (Natriello et al., 1977, p. 31) 4. Videotape. Baltus (1974) suggested videotaping of behavior to be evaluated. The principal and the teacher can then go over the tape together. Case and Brown (1970) also suggested a videotape which can be played repeatedly for the teacher and his or her colleagues. (Natriello et al., 1977, p. 32) 18 5. Students' evaluation. "Shaw (1973) and Hanson (1967) both recommended student evaluation of teachers, but Bejar (1975) warns that research on the validity of such evaluations may not justify using the results for personnel decisions" (Natriello et al., 1977, p. 32). 6. Self-evaluation. Many administrators saw self-evaluation as an essential ele- ment of any evaluation system. Olds (1973) agreed. He argued that any formulation of performance objectives involved a sub- stantial degree of the own self-evaluation and offered instruc- tions for developing a self—evaluation program. Detzner (1974) suggested that videotaping provided a "nonthreatening" means of self-evaluation. (Natriello et al., 1977, p. 33) 7. Students' achievement. Cameron (1973) found that principals, teachers, and school board members defined student achievement as the major objec- tive for student growth and that student growth is a more reliable measure than observational ratings for use in teacher evaluation. (Natriello et al., 1977, p. 34) Saif (1976) explained his views about teacher evaluation as follows: Since the primary professional activity of a teacher is teaching, the major concern of teacher evaluation should be effective student learning experiences. With focus on the improvement of student learning, an evaluation scheme should seek to help all_teachers do a better job. It does not con- centrate on defining "good" versus "bad" teachers, but assumes that each teacher is competent, and that each can improve. p. 127 Stow and Sweeney (1981) reported that A performance evaluation system should be reviewed, revised, or refined every three to five years because skills needed to operate a school effectively will change. Also, planning and participation by the involved professionals will help make the process more important to them. (p. 539) Brophy, Couleter, Crawford, Evertson, and King (1975) reported in their abstract that "a set of twelve classroom observation 19 scales developed from prior factor analytic work of Emmer and Peck (1973), which measure general process variables stressed in previous classroom research, showed good stability across years and across contexts within years" (p. 1). This stability across time and context that relates to student learning gains gives strong support to super- visors who work with the respective teachers. It is worth mentioning teachers' perceptions about super- visors' feedback. In the abstract of his dissertation, Wilson (1981) summarized his findings as follows: 1. Even when teachers previously rigorously assessed their own classroom performance, their self-perceptions are apt to change as a result of receiving feedback from others. 2. Feedback data that are externally analyzed and reported appear to have somewhat stronger influence on self-perceptions than comparable data that are analyzed and reported on by the teachers themselves. 3. Teachers change their self-perceptions in accord with the direction and magnitude of the difference between their original self-perceptions and the feedback they receive. These findings also give strong support to the need to find better ways of giving feedback to the respective teachers. More research on teacher evaluation is needed so that both teachers and students can do freely, without pressure, what they are supposed to do. The following section is presented to give a perspective on the field of research on teaching. This is in turn followed by a review of relevant literature within this field. 20 Three Phases of Research on Teaching_ Teaching is a very important profession that the community as a whole, and especially parents, care about. It is not an easy job. Educators used, in traditional schools, to be teachers without adequate training. Students used to go to school to study many subjects, and the teacher's job was to present his material by lectur- ing and not to worry himself with how and if students could learn. There was no time for a teacher to ask himself the following questions: 1. What is my objective in teaching mathematics? 2. 00 students really understand what is going on in the classroom? 3. Do I care about students' scores or their growth? 4. How can I maximize students' learning? 5. Do I know what is going on in the students' minds? 6. Do I consider individual differences? Educators in the 19605 started to realize the problems of teaching. They started to try to understand what was going on in the classroom. Clark (1979) organized this kind of research into five facets. These five approaches were: the process-product approach, the aptitude-treatment-interaction approach, the Carroll-model approach, the ethnographic approach, and the teacher-thinking approach. For the purposes of this study, Clark's categories are organized into three approaches. First, the process-product approach is combined with the teacher-thinking approach as one approach. Second, the Carroll-model approach is combined with the aptitude-treatment-interaction approach as the second kind of research on teaching. Third, the ethnographic approach is considered as the third kind of research on teaching. 21 First Phase of Research on Teaching The most important assumption in the process-product approach is that teachers' behavior influences students' achievements. Accord- ingly, the general question to be addressed on this topic is: What are the behaviors of teachers who influence students' achievements? The main assumption in the teacher-thinking approach is that teachers' thinking influences students' achievements. Teachers make judgments and decisions during classroom teaching that affect their students. This assumption can include the fact that both teachers' behavior and teachers' thinking influence students' achievements. There is a cycle of supervision that the supervisor goes through with the teacher. Cogan (1969) classified this cycle into four phases. The first one is of concern here. It is the pre- observation conference. The supervisor needs to get to know the teacher in that conference. Teacher-thinking research helps both the supervisor and the teacher to know each other. They plan the lesson together. In that phase, both supervisor and teacher agree on the way in which the supervisor will observe the teacher. One way is that in the second phase, the observation phase, the supervisor can use Flanders' instrument. Cogan (1969) and Goldhammer (1972) found that student achieve- ment is influenced by this cycle, which depends on the teacher-thinking approach and the process-product approach. The researchers in this area are more concerned with the average achievement of the class. If supervisors know more about teachers and teachers know more about 22 their own behavior in the classroom, students learn more, and they more likely enjoy learning. Second Phase of Research on Teaching In the second phase, the aptitude-treatment-interaction approach is combined with the Carroll-model approach. Assumptions 1. Different treatments cause different outcomes. 2. Aptitude of interest remains static at least during the time of treatment. 3. There are differences in mental ability, so different treatments are needed to maximize student learning. 4. Teachers should spend more time assisting those students who need help. 5. Not all students can learn in the same amount of time; some of them need more time, some less. 6. Teachers should consider individual differences. The Guiding Questions 1. How do levels of achievement interact with instructional methods and amount of instructional support? 2. In what ways can teachers give every individual the time he is supposed to (and needs to) have? Time and varied treatment should not be separated from each other. As everyone knows, students learn mathematics in segmental steps. If teachers spend adequate time and administer suitable treatment to individuals in the first lesson, students grasp the 23 material very well and do not have difficulty with the second lesson. The following methods were used in this kind of research: 1. Laboratory experiments Instructional experiments Empirical case study hook) Naturalistic comparison Third Phase of Research on Teaching In the third phase of research, there is appropriate research in teaching to be studied and understood. Teachers cannot fulfill their roles appropriately without knowing the dealing with this kind of research. Ethnographic research is clearly appropriate for analyz- ing and identifying effective teaching in intergroup settings because it permits the development of models based on concrete examples that occur in a realistic classroom. Researchers cannot explain much about any observation if they do not have an idea about the situa- tion in which the observation occurred. Researchers in the field try to understand more about the setting rather than predicting. The main questions in this research are: 1. What is really going on in the classroom and why? 2. What are people doing and why are they doing it? (Barko, 1979). This kind of research began with the idea that a researcher who knows anything about the field and his job will try to know what is happening in the field and describe the setting and not predicting. 24 Assumptions 1. Researchers should not analyze small parts before the complete picture becomes clear to them. 2. Researchers should select experiences so that they can explain to themselves and others what is going on in the setting. 3. A single individual or couple should go to the field so that they become involved in the life of that site; after a long period of time, they begin to formulate a framework for the analysis. The researcher is free to go into the field with a very loose set of notions in the hope that observation will help him disCover the criti- cal variables. Thus, the researcher's job is to collect as much data as he can. The first thing he should do when he arrives in his office is to look through his data. He should try to pull out, from his field notes, a key incident and link it to other incidents, phenomena, and other theoretical constructs so that he can describe and analyze the setting well. Teachers can do a lot for students if they realize and study carefully this kind of research. The review of literature that follows is restricted to process-product studies of teaching, as they are most relevant to this Study. Research on Effective Instruction Teachers do make a difference (Good, Biddle, & Br0phy, 1975). Good (1980) stated in his introduction on the research on teaching: 25 We know little about how students learn and how teachers and schools can facilitate learning for students generally or for specific types of students. We need to acknowledge and to understand that the attempt to describe and/or to affect class— room learning is an enormously complex task. The realization of the complexity of classroom phenomena should cause us to be suspicious of simple models of teaching that offer universal solutions and to be tolerant of (if not encourage) divergent approaches to the study of teaching. (p. l) Brophy (1979) gave some reasons for considering student out- comes as criteria for teaching effectiveness. They were: social concern about declining student achievement, teacher accountability, and related issues. The issue of considering student outcomes as criteria for teaching effectiveness is controversial. For example, Stevens (1967) theorized that achievement is determined by factors within students and little by teachers. Coleman, Campbell, Hobson, McPartland, Mood, Weinfield, and York (1966); Mosteller and Moynihan (1972); and Jencks, Smith, Acland, Bane, Cohen, Gintis, Heyns, and Michelson (1972) indicated that teachers do not have important effects on student learning. Fenstermacher (1978) declared that good teachers are born, not made, implying that there is no need for research on teaching. Popham's (1971) point of view was that there is no need for training teachers since no systematic differences in teaching behavior were found between trained and untrained teachers. In contrast, Good (1980) said, I suspect that most researchers interested in classroom behav- ior would support the contention that the 1970s were a produc— tive period for classroom research. It seems clear to me that extant evidence does support the contention that teachers can make an important difference in student learning. (p. l) 26 Brophy (1979) gave three reasons that recent classroom research efforts were successful in relating teacher behavior to student out- comes. They were: 1. The important review works by Rosenshine and Furst (1973) and Dunkin and Biddle (1974) which summarized what was known about the effects of teaching, clarified some of the weak- ness of earlier research, and brought an instrumental degree of conceptual coherence to the field of research on teaching. 2. An increased awareness of the methodological problems inherent in studying teacher effects and the concomitant willingness of investigators to begin to respond to those challenges in creative ways. 3. The willingness of the National Institute of Education to invest in large-scale process-product research and the ability of researchers to design broad exploratory studies. Good (1980) reported that "the field of teacher behavior changed its research emphasis from 'commitments' (Dunkin & Biddle, 1974) and the search for universal dimensions of teaching effectiveness to the study of particular aspects of teaching in manageable contexts.“ (p. 2) Berliner and Tikunoff (1977); Brophy and Evertson (1974, 1976); Good and Grouws (1977, 1979); McDonald (1976); McDonald, Elias, Stone, Wheeler, Lambert, Calfee, Sandoval, Ekstrom, and Lockheed (1975); Soar and Soar (1972); Stallings (1975); Stallings and Kasko- witz (1974); and Tikunoff, Berliner, and Rist (1975) began with several large-scale field correlational studies to provide a dependable body of knowledge about the relationships between teaching and student learning of basic skills in the elementary grades. Replication studies were done in junior high school (Evertson, Emmer, & Brophy, 1979; Evertson, Anderson, & Brophy, 1978; Evertson, Anderson, Anderson, & Brophy, 1979). In addition, experimental studies were developed from earlier correlational work (Good & Grouws, 1978; Anderson, Evertson, & Brophy, 1978). 27 Good (1980) categorized the general findings from recent research on teaching into the following areas: 1. Active teaching 2. Classroom management 3. Teacher expectations Brophy (1979a) characterized the pattern of active teaching as follows: Learning gains are most impressive in classrooms in which stu- dents receive a great deal of instruction from and have a great deal of interaction with the teacher, especially in public lessons and recitations that are briskly paced but conducted at a difficulty level that allows consistent success. (p. 747) Good (1980) reported that Good and Grouws in an ongoing project have produced support for the active teaching model in a field experiment in eighth grade mathematics classrooms. Active teaching may be incon- sistent with the goals of certain subjects (e.g., social studies) where process goals are more important than product goals. (p. 16) Good (1979) reported his findings about classroom management as follows: "Teachers' managerial abilities have been found to relate positively to student achievement in every process-product study con- ducted to date" (p. 58). Good (1980) defined good classroom manage- ment as "those techniques which prevent misbehavior by eliciting student cooperation in general and involvement in assigned work spe- cifically" (p. 20). Good (1980) reported the findings of Brophy and Evertson (1976) about teacher expectations as follows: "Teachers who were obtaining the highest residual achievement from students were teachers 28 who perceived students as capable of learning school work and who viewed themselves as capable of teaching the curriculum" (p. 23). Teaching Junior High Mathematics The findings of five studies related to mathematics in junior high school are reviewed in this section. Evertson, Anderson, Anderson, and Brophy (1979) did a study that gave predictors of student outcomes in junior high mathematics. The authors found that the more effective teachers 1. were active, well-organized, and strongly academically oriented. 2. tended to emphasize whole-class instruction, but some time spent in seatwork. 3. did not give their students many choices about what kinds of assignment they would do, and they rarely used self- paced materials. 4. managed their classes efficiently and stopped a disturbance before it could seriously disrupt the class. 5. asked many questions during class discussions; most were "lower-order" product questions, but "higher-order" process questions were also fairly common. 6. were rated as more enthusiastic, nurturant, and affectionate than their less successful colleagues. (p. 19) These results coincided with the findings of Good and Grouws (1977) and Flanders (1970). Based on this research, Good and Grouws (1977) conducted an experimental study of teaching mathematics at the fourth-grade level. Their results strongly correlated with increased achievement gains in fourth-grade mathematics. Evertson, Emmer, and Brophy (1979) conducted a study entitled "Predictors of Effective Teaching in Junior High Mathematics Class- rooms." They found that more effective teachers 29 spent greater amounts of class time as a group rather than in seatwork, resulting in a much higher frequency of ques- tions directed to the students; enforced rules to a greater degree, accepted less disturb- ance, had more efficient transitions, and monitored pupils better; were less likely to allow students to leave the room, but were rated as more receptive to student input; were judged to have more productive time; were rated as manifesting less anxiety, more confidence, greater task orientation, and more enthusiasm; asked more product and process questions; devoted more class time to developmental activities and less time to individual seatwork; displayed stronger management skills, greater clarity, more questioning behaviors. (pp. 11-12) Anderson, Evertson, and Brophy (1978a) did a study entitled "Process-Outcome Relationships in the Texas Junior High School Study: High Inference Ratings of General Behaviors." They reported that "the data sets depict a fairly consistent view of effective teaching in junior high math classes, when effectiveness is defined by achieve- ment on a test of math content" (p. 3). Teacher characteristics that were related positively to students' achievements in this study were: \Dmem-pr-fl 0.. CO... effectiveness of teacher's management methods; student respect for teachers; Student obedience, teacher consistency in enforcing the rules, teacher monitoring, efficiency of transitions, teacher's likability, general competence, enthusiasm, 10. ll. 12. 13. 14. 15. 16. 17. 18. 19. 3O enjoyment of teaching, moderate use of public class discussion, use of higher cognitive-level questions, concern about students' achievement, encouragement to students to perform well, responsibility for their own work, time spent on productive work, time spent in busy work, overall positive involvement with the class, adequate preparation for teaching. (pp. 3-4) Brophy and Evertson (1978) did a study entitled "Process- Outcome Relationships in the Texas Junior High School Study: Low Inference Coding of Specific Behaviors." They summarized their find- ings as follows: Effective instruction in junior high math classes was marked by an academic orientation, concentration on whole group instruc- tion rather than individualized contact, frequent public recita- tion and discussion with active student involvement and initia- tion of questions and comments, maintenance of a rapid pace by calling mostly on volunteers and minimizing length interruptions to deal with the needs of individual students on the spot, and in general, a stress on eliciting and reinforcing high quality responses to questions designed to move the class along at a good pace. This stereotype fits the high ability classes much better than the low ability classes, though. Both the level of demand and the level of discourse was a little lower in the low ability classes (appropriately so), and effective teachers in those settings spent more time dealing with individuals espe- cially attempting to elicit improved responses. There was much support for aspects of what Flanders has called indirect teach- ing, especially for the eliciting and use of student ideas, although again, more so in the high ability classes and only within the larger context of a strong academic and demanding orientation. (p. 8) Evertson and Brophy (1978) did a study entitled "Process- Outcome Relationships in the Texas Junior High School Study: Comparison of Findings for Cognitive and Affective Criteria." They summarized their findings as follows: 31 Students' attitudes seem to be affected by the amount of inter- personal warmth and competence that teachers demonstrate, whereas academic achievement is affected by a more businesslike, organ- ized, but not cold, teacher approach. Teachers who have both high ratings and high achievement in their classes could be those who are able to blend appropriate amounts of interpersonal skill, warmth, and interest in students with the more task—like demands of delivering mathematics content. (p. 5) Four conclusions can be drawn from such studies: 1. Evertson, Anderson, Anderson, and Brophy (1979) reported that these results must be interpreted with caution because of their correlational nature. They describe some of the teaching prac- tices of some successful math teachers, but by themselves they cannot be used as the basis for statements about cause and effect; neither do we know to what degree the methods used by the more successful teachers can be taught to others who are not currently using them. (p. 20) 2. Evertson, Emmer, and Brophy (1979) closed their discussions by reporting that the large number of variables differentiating the more effective and less effective teachers suggests that effective teaching has multiple facets, and is not reducible to a single trait or behav- ior. It seems reasonable to theorize that the various classes of variables tend to occur together, and to produce effects both on each other and on the product variables. (p. 13) 3. Experimental studies are needed in junior high schools to test the previous results. 4. Both supervisors and teachers should consider these find- ings and select those that are applicable to their schools. Summary Given this substantive body of empirical research, super- visors and teachers could only benefit by becoming aware of and using the findings of research on teacher evaluation, supervision, teaching, and effective instruction appropriately in their work. CHAPTER III RESEARCH DESIGN AND PROCEDURE The problem under investigation in this study was to deter- mine how supervisors' evaluations, teachers' behavior, and students' attitudes toward teachers are related to instructionally effective teachers of ninth-grade mathematics. The following components of the research are presented in this chapter: the research questions, the design of the study, the research hypotheses, a description of the population and the sample for this study, a description of the five instruments used in the study, a discussion of the validity and relia- bility of these instruments, and a description of the manner in which observers were trained to collect data. Research Questions The major question under investigation in this study was: Do supervisors' evaluations of teachers who are instructionally effective in ninth-grade mathematics differ from evaluations of teachers who are instructionally less effective? The following related questions were asked to refine specific dimensions of the general question posed in this study: 1. 00 teachers whose students perform better on ninth-grade mathematics exams demonstrate different behaviors than those whose students do not perform well on the same tests? 32 33 2. What are some of the behavioral characteristics that distinguish instructionally effective and instructionally less effective teachers? 3. Do the attitudes toward teachers of students who do well on the ninth-grade mathematics achievement test differ from the atti- tudes toward teachers of those who do not perform well on the same test? Design of the Study To address the research questions posed in this study, eight teachers were selected from a group of 40 ninth-grade mathematics teach- ers by means of a pretest-posttest to two classes of their students to identify residual-gain scores for a three-week unit of algebraic fac- toring. The eight teachers selected represented the four most instruc- tionally effective and the four least instructionally effective teachers based on their students' residual-gain scores. Data collected about these eight teachers and their students included: 1. Supervisors' evaluations of teachers, 2. Classroom observations of teachers' behavior, 3. Students' attitudes toward the eight teachers during part of two consecutive years. Research Hypotheses Hypotheses Pertaining to SuperVTsors' Evaluations Three primary null hypotheses pertaining to supervisors' evaluations were tested. They are as follows: 34 1. There is no significant difference in the supervisors' overall ratings of instructionally effective and instructionally less effective ninth-grade mathematics teachers. 2. There is no significant difference in the supervisors' ratings of instructionally effective and instructionally less effec- tive ninth-grade mathematics teachers in relation to such factors as the following: 2.1. Teachers' personalities and their ability to control their classes; 2.2. Teachers' ability to follow the outlines of lessons they prepared; 2.3. Teachers' preparations of lessons before their lectures; 2.4. Teachers structuring their concepts progressively to introduce the simpler examples and points and then the more difficult ones; 2.5. Teachers' manner of conducting classroom discussions; 2.6. Teachers' perceptiveness of individual differences among students; 2.7. Teachers' use of such aids as the blackboard and instructional media; 2.8. Students' understanding of mathematical concepts; 2.9. Teachers' knowledge of the subject matter; 2.10. Amount of homework given and whether teachers checked it; 35 2.11. Students' achievements; 2.12. Evaluation methods used. 3. Of the 12 supervisor ratings of teachers, no singular subset of factors can be found that, through the use of such a subset, instructionally effective and instructionally less effective teachers can be reliably differentiated. Hypotheses Pertaining to Classroom Observations On the basis of classroom observations by the four observers, two primary null hypotheses were tested. They are as follows: 4. There is no significant difference between instructionally effective and instructionally less effective ninth-grade mathematics teachers in the following: 4.1. How the teachers deal with homework; 4.2. The degree of attention the teachers receive from their students; 4.3. The clarity of the teachers' presentations; 4.4. The time teachers spend in presentation of the material; 4.5. The degree of enthusiasm demonstrated by the teachers; 4.6. Whether the teachers assign homework; 4.7. Whether the teachers allow their students enough time to solve each assignment; 4.8. Whether the teachers give their students time to try some problems on the next homework assignment to familiarize themselves with the work; b-b-h-b .10. .ll. .12. .13. .14. .15. .16. .17. .18. .19. .20. .21. .22. .23. 36 Whether the teachers ask discipline questions; Whether the teachers ask direct questions; Whether the teachers ask open questions; Whether the teachers let their students answer ques- tions without being called on; Whether the teachers let their students answer ques- tions as a group; Whether the teachers ask process questions; Whether the teachers ask product questions; Whether the teachers ask choice questions; Whether the teachers praise students who give correct answers; Whether the teachers give nonverbal signs for cor- rect answers; Whether the teachers summarize students' correct answers; Whether the teachers ask a second student for the correct answer if the first student has given a wrong answer; Whether the teachers neglect a student who has given a wrong answer; Whether the teachers explain their students' mistakes; Whether the teachers give the right answer if a wrong answer has been given; 37 4.24. Whether the teachers ask for more clarification from their students; 4.25. Whether the teachers praise their students if they ask for individual help; 4.26. Whether the teachers criticize their students if they ask for individual help; 4.27. Whether the teachers criticize their students for misbehavior. 5. 0f the different factors constituting the basis for evalua- tion of teachers as given in Hypothesis 4, no singular Subset of fac- tors can be found that, through the use of such a subset, instructionally effective and instructionally less effective ninth-grade mathematics teachers can be reliably differentiated. Hypotheses Pertaining to Students' Attitudes Two primary null hypotheses were formulated to test the atti- tudes of students. They are as follows: 6. There is no significant difference in students' percep- tions of instructionally effective and instructionally less effective ninth-grade mathematics teachers with respect to the following: 6.1. The degree of concern teachers express for their students; 6.2. Teachers' knowledge of their subject matter; 6.3. The way teachers praise their students; 6.4. The way teachers punish their students; 38 6.5. The degree to which the students enjoy a teacher's classes. 7. Of the three major areas of evaluation of teachers, namely, supervisors' ratings, classroom observations, and students' attitudes toward their teachers, no singular subset of factors can be found that, through the use of such a subset, instructionally effec- tive and instructionally less effective ninth-grade mathematics teach- ers may be reliably differentiated. Population of the Study Forty ninth-grade mathematics teachers were chosen from 24 schools in three cities in Saudi Arabia. The cities were Makkah, Jeddah, and Taif. The 24 schools were representative of the commu- nity characteristics and socioeconomic status of the populations they served. The 40 teachers agreed to teach a unit of instruction in algebraic factoring for a period of three weeks from the ninth-grade algebra book, which is assigned by the Ministry of Education in Saudi Arabia to all ninth-grade students. This period fell at the middle of the 1980-81 school year. The pretest and the posttest, as shown in Table 3.1, were designed by the researcher and one of the head supervisors of mathe- matics teachers in Saudi Arabia. A statement regarding the content validity of the pretest and posttest is contained in Appendix A. All tests were corrected by the researcher. To rank the teachers in terms of their instructional effec- tiveness, residual—gain scores were computed for each student of each teacher with the pretest score as a covariate. By this regression 39 technique, differences in initial (prior to instruction) student differences were statistically controlled. Thus it can be argued that the differential student gains in one given classroom, for example, were due to the particular teacher in that classroom because student differences were statistically removed. Table 3.1.--Pretest and posttest measuring students' achievements. Question: Factor to the simplest form: 2 1. x - 7x + 12 2. -3 - 4x2 - 7x 3. 12x2 - 16XY - 6012 4. 2x2 + 2x - 12 5. 3x5 - 5x - g 3 6. 6X Y - 13x1 + 6Y Sample of the Study Pretest and posttest measurements of students' achievements were made of 2,400 students of the 4O ninth-grade mathematics teachers. Each question was given a weighted score based on the operations done by the students in solving each question. The total possible score of 100 points was used in identifying the average-gain scores. These scores are presented in Table 3.2. The four teachers (1, 2, 3, and 4) whose students achieved the highest gain scores and the four teachers (37, 38, 39, and 40) whose students ahieved the lowest gain scores were chosen for this study. These eight teachers were chosen in the 1980-81 school year. Their students responded to the attitude ques— tionnaire. (See Table 3.3). 40 Table 3.2.--The average-gain scores of the mathematics teachers. Standard Code Mean Deviation Var1ance 1 7.6842 7.5994 57.7504 2 6.4535 7.0663 49.9324 3 4.5496 8.0216 64.3456 4 4.4363 7.8591 61.7661 5 4.0923 7.6471 58.4788 6 3.4071 6.5599 43.0320 7 3.4070 7.6581 58.6468 8 2.2739 9.0285 81.5133 9 2.2424 5.9320 35.1892 10 2.1927 7.6109 57.9262 11 1.9638 7.4268 55.1574 12 1.8928 7.2823 53.0325 13 1.3863 7.7336 59.8082 14 1.3419 6.4203 41.2205 15 1.2409 7.2276 52.2383 16 1.1900 6.5944 43.4863 17 0.6802 7.4621 55.6831 18 0.6440 7.8680 61.9057 19 0.0392 8.3073 69.0112 20 -0.0193 7.2423 52.4507 21 -0.1993 7.4229 55.0988 22 -0.3911 6.9664 48.5304 23 -0.5729 5.6999 32.4883 24 -0.7858 6.5030 42.2893 25 -O.8236 5.7825 33.4370 26 -O.8404 6.0021 36.0250 27 -0.8617 6.5930 43.4673 28 -l.2818 7.2217 52.1523 29 -l.2877 5.7058 " 32.5564 30 -l.3806 7.9353 62.9692 31 -1.6644 5.1105 26.1169 32 -2.1097 7.8571 61.7348 33 -2.2187 5.9642 35.5716 34 -3.1685 6.4474 41.5688 35 -3.2478 6.2475 39.0311 36 -3.6018 5.6004 31.3646 37 -4.7000 5.6331 31.7315 38 -4.8374 6.5913 42.1372 39 -7.3554 4.3033 18.5183 40 -9.7831 5.5804 31.1414 41 Table 3.3.--Items on questionnaire concerning students' attitudes. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. I feel comfortable participating in class discussion. My teacher is friendly. My teacher helps me learn mathematics. I like my math teacher. I feel comfortable with my math teacher. I am praised when I do good work. My teacher knows his subject. My teacher cares about me. I like mathematics. If I have a question, I ask my teacher right away. My teacher wants me to understand math. My teacher makes sure that I do my homework correctly. I do my best to understand math. My teacher gives us homework for every lesson. My teacher helps me when I make mistakes on my homework. My teacher encourages me to ask questions. I feel my teacher likes to teach math. My teacher does not make me feel embarrassed when I answer his question incorrectly. The teacher's blackboard is well organized. My teacher hits me when I do not behave well in the class. My teacher hurts my feelings in front of my classmates when I do not answer his question. I am told about my bad work and not about my good work. My teacher praises me when I complete my homework. My teacher prepares the lesson in advance. My teacher makes me feel stupid when I do not answer his question. When I do not answer the teacher's question correctly, he still encourages me. My teacher yells at me a lot in class when I do something wrong. My teacher hits me when I cannot answer his question. 42 Table 3.3.--Continued. 29. I do a lot of good work that goes unnoticed. 30. My teacher moves gradually from the easy examples to the more difficult ones. 31. My teacher gives enough time for each student to solve the problem. 32. My teacher checks my homework problems. 33. My teacher repeats his presentation to make sure that each student understands the concept. 34. I am able to read his writing on the blackboard. 35. My teacher builds on past experiences in introducing new concepts. 36. My teacher explains the material very well. 37. My teacher uses different methods to solve problems. 38. The presentation made by my teacher attracts my attention. At the beginning of the 1981-82 school year, two of the four instructionally effective teachers were not available; they were replaced with the next two teachers. The new group of instructionally effective teachers (as shown in Table 3.2) were Teachers 1, 4, 7, and 8. Likewise, two of the four instructionally less effective teachers had to be replaced by the next two less effective teachers. The new group of instructionally less effective teachers (as shown in Table 3.2) were Teachers 39, 37, 33, and 32. Instruments For this study, five instruments were used to measure three aspects of the data. 43 Instrument Used to Evaluate Teachers by Supervisors The first instrument used was the supervisor's report, which was designed by the Jeddah Board of Education to evaluate teachers. This instrument contained 15 items. The supervisors responded to the first 12 items. (See Table 3.4.) The last three items were to be answered by the schools' principals. The first 12 items were used in this study. (Both the Arabic version of the supervisor's report and its English translation are given in Appendix B.) Table 3.4.--Items included in supervisors' evaluations. $01. $02. $03. $04. $05. $06. $07. $08. $09. $10. $11. $12. Teacher's personality and his ability to control his classes. Teacher's ability to follow the outlines of lessons he prepared. Teacher's preparations of lessons. Teacher's structuring his concepts progressively to introduce the simpler examples and points, then more difficult ones. Teacher's manner of conducting classroom discussions. Teacher's perceptiveness of individual differences among students. Teacher's use of such aids as blackboards and instructional media. Students' understanding of mathematical concepts. Teacher's knowledge of the subject matter. Amount of homework given and whether teacher checked it. Students' achievement. Evaluation method used. Instruments Used for Classroom Observations Brophy and Good (1970) used three instruments for observing teachers in the classroom. These three instruments were used in this 44 study. The first was the Brophy-Good Dyadic Interaction scale. (See Table 3.5.) The second instrument (Emmer, 1973) measured homework given, the degree of attention the teachers received from their stu- dents, the clarity of the teachers' presentations, the degree of enthusiasm demonstrated by the teachers, and the time the teachers spent in presentation of the materials. (See Table 3.6.) The third instrument measured five factors of the homework assignment. (See Table 3.7.) Brief definitions of all variables involved in the above three instruments can be found in Appendix C, along with copies of all coding sheets. Instrument Used to Measure Students' Attitudes The researcher designed a questionnaire consisting of 38 items. (See Table 3.3.) This questionnaire was the fifth instrument used in this study. The cover sheet of the questionnaire, the ques- tionnaire, the Arabic translation of the questionnaire, and a state- ment about the validity of the translation of the questionnaire are given in Appendix D. Questionnaire Reliability The first step in analyzing the attitude scale was to do an exploratory factor analysis. Complete results of this analysis are presented in Appendix E. On the basis of the results as presented in the varimax rotated factor matrix (see Appendix E) and ofa consideration of the content of the items on the questionnaire, five scales were tentatively selected. The scales were based on the following five factors: (NOTE: Narrative continues in the middle of page 47) 45 m m m m HH 0 o m .r o H. < 2 .H A m m m u a u 4 2 ”V a H +, . 1 o + 1 m +. . u m a v. 3 3 a ._ o >, < H < my a u H m x 1 1 H Hg 0 4 m m m a 3 + a 1 a .+ 1 a .+ o H. u h “H m 4 Nu < m H x a H m m .m m z o + I m ”H < a H H h m m m < z o m u < My m o z z m < a u a a u o o o 2mm xmoz .omuomm xmoz ¥ud mmeHzahmoamo mmzommmm .mHmum compumgwsz uwumxd uooo1xcaogm11.m.m opamw 46 v m N coHumpcmmmsn EmmHmzzacm qucmHu c m N H m N H v m N H m N H v m N H m N H e m N H m N H coHucmup< xgozmso: muoo mEHH .mmchou mucmgmmcH1cmHz11.m.m «HamH 47 Table 3.7.--Homework assignments. Yes No R1. Is homework assigned? ____ ____ R2. Same assignment to all students? ____ ____ R3. Time provided in class to work on homework? -——— ———- R4. If so, how much time? min. R5. Describe homework assignment: A. Textbook B Workbook C. Commercial ditto D Teacher-made ditto 1. Concern of the teacher for the students' progress; 2. The teacher's knowledge of the subject; 3. Praise and encouragement given to the student by the teacher; 4. Punishment meted out by the teacher; 5. The student's overall enjoyment of the subject matter and the teaching. In a second step, reliability analyses were conducted for the five scales suggested by the results of the exploratory factor analysis. The following coefficients of reliability were obtained for the clusters of responses listed for each scale. (See Table 3.8.) As can be seen from Table 3.8, there was a high correlation among the responses of the students to items that had close logical relationships to one another. One can conclude, based on the internal 48 reliability of the items, that the student-attitudes questionnaire had an acceptable level of reliability for this study. The relia- bility analysis of the scales on the questionnaire concerning students' attitudes is presented in Appendix F. Table 3.8.--Subscales, clusters, and coefficients of reliability. Scale Clusters Coefficient of Reliability Concern of the teacher for A03, A12, A13, A16, 0 83 the student's progress A33, A34, A35, A39 ' The teacher's knowledge A17, A18, A20, A37, 0 77 of the subject A38 ' Praise and encouragement given to the students by figg’ ng’ figg’ AO6’ 0.82 the teacher ’ ’ Punishment meted out by A21, A22, A23, A26, 0 75 the teacher A28, A29 ' The student's overall enjoyment of the subject A01, A05, A09 0.55 matter and the teaching Questionnaire Content Validity The questionnaire was provided for review in terms of the overall content validity and clarity of the items to two Arabic educators, both of whom had had considerable experience as teachers and educational leaders in the Arab World. Their suggestions were considered in developing the final version of the questionnaire. 49 Training the Observers There were four observers, including the researcher, who observed the eight teachers. The procedures outlined by Coulter (1976) were followed to train the observers. Accordingly, two major steps were used for the training: training of observers prior to their going into the classroom and training in the classroom. Training of Observers Prior to Their Going Into the Classroom This stage was divided into three steps: 1. The coders were given an overview of their tasks. A double-blind procedure was employed so that the observers would be unaware of the teacher's status, i.e., instructionally effective or instructionally less effective. The researcher tried to reassure the observers that they would be able to learn the system and that things would become clear as they progressed. 2. The observers were given the coding manual, which con- tained a thorough discussion of the coding system, explanations and descriptions for each category with relevant examples, and instruc- tions about how and when the system was to be used. Observers were given enough time to study the coding manual. They were requested to write down any problems they had; problems were thoroughly discussed. 3. In addition, a videotape was used in further training the observers. Three classes were videotaped: the teacher of one class was given no instructions; teachers of the other two classes were asked to demonstrate certain teaching styles so that the observers had an example of all categories appearing on the Brophy-Good Dyadic 50 Interaction instrument. Viewing the videotapes gave the observers an idea of the typically fast pace of classroom events. Observers began to build up some speed in their coding, and they had an oppor- tunity to clear up questions regarding the particulars of the category system. Guidelines for Observers Before observers were sent into classrooms for the first time, they were instructed on several important points concerning their behavior at the time of observing. The guidelines included the following: 1. They were requested to sit at the back of the room at an empty desk to minimize the effects of their presence in the class- room. 2. They were requested to be in the classroom before the bell rang or the class officially began. 3. They were requested to introduce themselves to teachers when they arrived and to thank teachers for their cooperation when they left. 4. They were requested to minimize personal interactions with students. 5. They were requested not to let the teacher look at the instruments. 6. They were requested not to help students with their school work or in any way assume a teaching style. 51 7. They were requested to check coding sheets before turning them in. All identification information, such as school, teacher, and class period, was to be completed. 8. They were requested to take along plenty of coding sheets when collecting data. Training in the Classroom When the trainees had familiarized themselves thoroughly with the use of the observational system, they were requested to begin in-classroom coding practice. The researcher and the other three coders agreed to observe a ninth-grade mathematics teacher. This teacher was not one of the eight teachers whom the coders would observe for the study. At this stage, the four observers went together to the assigned classroom. All completed the coding sheets independently. From these results, an index of agreement among the observers for each instrument of the Dyadic Interaction System was computed. The following Fridman two-way ANOVA equation was used: x2 = [—(—y'2 '5 (R121- 3N 0.05); i.e., there was no significant difference 56 between supervisors' ratings of instructionally effective and instruc- tionally less effective ninth-grade mathematics teachers for the overall ratings and for each of the 12 subscales of the supervisors' ratings. Hypothesis 3: 0f the 12 supervisor ratings of teachers, no singular subset of factors can be found that, through the use of such a subset, instructionally effective and instructionally less effective teachers can be reliably differentiated. Discriminant analysis was used to test this hypothesis. In this method of analysis, a single dimension was postulated on which instructionally effective teachers were clustered at one end and instructionally less effective teachers at the other through the for- mation of one or more linear combinations of the discriminant vari- ables. These discriminant functions were of the form: where Di was the score on discriminant function i, the d's were weighting coefficients, and the 2's were the standardized values of p discriminating variables used in the analysis. The functions were formed in such a way as to maximize the separation of the groups. Stepwise variable selection was used to find the discriminant function if there was one. Six scales out of the 12 subscales of supervisors' ratings, namely, $01, $04, 507, S09, S10, and 512 (see Table 4.2), were included in the discriminant analysis. (See Table 4.3.) 57 Table 4.2.--Items included in the discriminant analysis of supervisors' evaluations. S01. Teacher's personality and his ability to control his classes. S04. Teacher's structuring his concepts progressively to introduce the simpler examples and points, then more difficult ones. S07. Teacher's use of such aids as blackboards and instructional media. 509. Teacher's knowledge of the subject matter. $10. Amount of homework given and whether teacher checked it. S12. Evaluation method used. Table 4.3.--Results of discriminant analysis of Hypothesis 3. Action . . . Step W11ks Sig M1n1mum Si Between Entered Removed Lambda ' D Squared 9' Groups 1 501 0.7368 0.1936 103.50 0.0000 1 2 2 502 0.5742 0.2498 123.52 0.0001 1 2 3 507 0.3092 0.1595 345.29 0.0001 1 2 4 512 0.1913 0.1852 1044.00 0.0004 1 2 5 $04 .. 0.0924 0.2152 2097.88 0.0036 1 2 6 S02 0.1301 0.1082 1653.39 0.0002 1 2 7 $09 .. 0.0398 0.0963 4248.11 0.0018 1 2 8 510 0.0020 0.0846 3369.16 0.0129 1 2 The standardized canonical discriminant function was in the form: F(x) = 11.19 501 + 31.10 504 - 15.80 507 - 25.05 509 - 12.35 510 + 8.97 512 58 This function, as one set, best discriminated between the two groups of teachers. As it was shown in the results of Hypotheses l and 2, no significant difference was found in each of the subscales of supervisors' evaluation, namely, $01, $04, 507, $09, $10, and 512, between the two groups if each of the subscales was considered inde— pendently of the others. The six subscales of supervisors' evalua- tions as one function were significant. It was 0.005. (See Table 4.4.) Table 4.4.--The significance of the standardized canonical discriminant function for Hypothesis 3. Wilks Lambda Chi-Square df Sig. 0.002 18.582 6 0.005 The canonical discriminant function of group means (group centereds) was -l9.15 and 19.15. The analysis showed 100 percent prediction for classifying the instructionally effective and instruc- tionally less effective ninth-grade mathematics teachers. (See Table 4.5.) Table 4.5.--Prediction for classifying the effectiveness of teachers in Hypothesis 3. Predicted Actual Group oVuggggs Group Membership Group 1 Group 2 Group 1 (instructionally 4 4 0 effective teachers) 100% 0% Group 2 (instructionally 4 0 4 less effective teachers) 0% 100% 59 These results indicated that the above hypothesis was rejected; i.e., there was one singular subset of variables, namely, 501, S04, $07, $09, $10, and S12 (see Table 4.2), which formulated F(x), that discriminated between the instructionally effective and instructionally less effective ninth-grade mathematics teachers. Teachers' Behavior The research question concerning teachers' behaviors was as follows: 00 teachers whose students perform better on ninth-grade mathe- matics tests demonstrate different behaviors than those whose students do not perform well on the same tests? The following hypotheses were generated to answer the question. Each hypothesis is stated. The results of the data analysis regard- ing each hypothesis are discussed following the statement of the hypothesis. H othesis 4: There is no significant difference between instruc- tionally effective and instructionally less effective ninth-grade mathematics teachers in the following: how the teachers deal with homework; the degree of attention the teachers receive from their students; the clarity of the teachers' presentations; the time teachers spend in presentation of the material; the degree of enthu- siasm demonstrated by the teachers; whether the teachers assign homework; whether the teachers allow their students enough time to solve each assignment; whether the teachers give their students time to try some problems on the next homework assignment to familiarize themselves with the work; whether the teachers ask discipline questions; whether the teachers ask direct questions; whether the teachers ask open questions; whether the teachers let students answer questions without being called on; whether the teachers let their students answer questions as a group; whether the teachers ask process questions; whether the teachers ask product questions; whether the teachers ask choice questions; whether the teachers praise students who give correct answers; whether the teachers give nonverbal signs for correct answers; whether the teachers summarize students' correct answers; whether the teachers ask a second student for the correct answer if the 60 first student has given a wrong answer; whether the teachers neglect a student who has given a wrong answer; whether the teach- ers explain their students' mistakes; whether the teachers give the right answer if a wrong answer has been given; whether the teachers ask for more clarification from their students; whether the teachers praise their students if they ask for help; whether the teachers criticize their students if they ask for help; whether the teachers criticize their students for misbehavior. One-way analysis of variance was used to test Hypothesis 4. (See Table 4.6.) Table 4.6.--Results of one-way analysis of variance of Hypothesis 4. Group Group Group Group Scale Mean for Mean for 5.0. for 5.0. for F Signif. Group 1 Group 2 Group 1 Group 2 H 51.250 45.750 4.7871 8.0571 1.3780 0.2850 A 102.500 115.750 10.5357 16.4596 1.8390 0.2239 C 102.250 119.500 8.6554 10.4083 6.4950 0.0436* P 111.250 119.750 10.3401 20.9821 0.5282 0.4907 E 75.750 63.750 11.4419 18.0831 1.3110 0.2959 R1 ~9.750 10.000 3.3040 2.1602 0.0160 0.9033 R4 81.375 64.000 49.1704 19.9039 0.4291 0.5367 R8 15.625 25.000 17.2548 12.6029 0.7700 0.4140 DISP 3.675 1.150 3.4645 1.5177 1.7830 0.2302 DIRC 14.050 12.925 6.5292 8.6477 0.0431 0.8424 OPEN 70.100 69.050 16.5233 9.0732 0.0124 0.9149 CALL 4.975 5.650 4.6205 4.6033 0.0428 0.8429 GROUP 6.650 11.225 6.4697 6.4994 0.9955 0.3569 PROC 11.450 15.600 4.3746 5.5480 1.3800 0.2846 PROD 79.400 79.025 1.7682 7.6081 0.0092 0.9266 CHIC 8.875 5.400 3.3787 3.0056 2.362 0.1752 PRAISE 9.225 7.575 5.0910 7.1388 0.1415 0.7198 AFFR 58.600 59.325 14.1861 13.3510 0.0055 0.9431 REPF 25.418 41.025 6.6143 9.0046 7.806 0.0314* ASOT 12.900 9.175 4.6029 7.1565 0.7666 0.4149 STPR 14.975 8.375 23.4663 7.1993 0.2892 0.6101 STCR 6.925 8.200 6.4194 9.2966 0.0510 0.8289 TDIS 20.625 18.250 19.8950 7.0069 0.0507 0.8293 NEGL 6.125 3.750 2.9432 2.1378 1.7050 0.2395 EXAN 4.180 3.150 1.2259 1.2923 1.3370 0.2914 GIVA 4.575 2.575 1.7858 0.9535 3.904 0.0956 AFMC 4.675 3.625 2.7036 4.0771 0.1843 0.6827 Note Group 1 = group of instructionally effective teachers. Group 2 = group of instructionally less effective teachers. 61 The results indicated that, in only two out of the 27 scales, significant differences between the two groups of ninth-grade mathe- matics teachers were found. They were as follows: 1. In the scale "Teacher's clarity," a significant differ- ence (o < 0.0436) was found between the two types of teachers. Instructionally effective teachers were judged to make their teaching clearer than the instructionally less effective teachers did. The respective means were 119.50 and 102.25. 2. In the scale "Rephrasing the student's correct answers," a significant difference (a < 0.0314) was found between the two types of teachers. Instructionally effective teachers were judged to rephrase their students' correct answers more than the instructionally less effective teachers did. The respective means were 41.03 and 25.42. In the other 25 scales, no differences in the evaluation of instructionally effective and instructionally less effective teachers were found. Hypothesis 5: 0f the different factors constituting the basis for evaluation of teachers as given in Hypothesis 4, no singular subset of factors can be found that, through the use of such a subset, instructionally effective and instructionally less effec- tive ninth-grade mathematics teachers can be reliably differen- tiated. Discriminant analysis was used to test this hypothesis. Six scales of the 27 were included in the discriminant analysis. (See Table 4.7.) The standardized canonical discriminant function.was in the form: F(x) = —13.96 REPH - 24.24 STCR + 18.04 E + 12.92 AFMC + 4.84 TDIS - 6.73 ASOT 62 This function, as one set, best discriminated between the two groups of teachers. The significance of this function was 0.003. (See Table 4.8.) Table 4.7.--Resu1ts of discriminant analysis of Hypothesis 5. Action . . . W11ks . M1n1mum . Between Step Entered Removed Lambda 519' D Squared 519' Groups 1 REPF 0.4346 0.0314 5.08 0.0189 1 2 2 STCR 0.3074 0.0524 64.24 0.0004 1 2 3 E 0.1192 0.0256 333.86 0.0001 1 2 4 AFMC 0.0323 0.0143 1445.99 0.0020 1 2 5 TDIS 0.0122 0.0302 3770.90 0.0020 1 2 6 ASOT 0.0014 0.0690 39819.37 0.0163 1 2 Table 4.8.--The significance of the standardized canonical discriminant function for Hypothesis 5. Wilks Lambda Chi-Square df Sig. 0.001 19.75 6 0.003 The canonical discriminant function of group means (group centereds) was 23.28 and 23.28. The analysis showed 100 percent prediction for classifying the two groups. (See Table 4.9.) These results indicated that the above hypothesis was rejected; i.e., there was one singular subset of variables, namely, REPH, STCR, E, AFMC, TDIS, and ASOT (see Table 4.10), which formulated F(x), that discriminated between instructionally effective and instruc- tionally less effective ninth-grade mathematics teachers. 63 Table 4.9.--Prediction for classifying the effectiveness of teachers for Hypothesis 5. Predicted Actual Group Number Group Membership of Cases Group 1 Group 2 Group 1 (instructionally 4 4 0 effective teachers) 100% 0% Group 2 (instructionall 4 0 4 less effective teachers 0% 100% Table 4.10.--Items included in the discriminant analysis for Hypothesis 5. REPF: The teacher summarizes the student's answer. STCR: Teacher criticizes a student who asks individual questions. E: This scale is used to judge the extent to which the teacher displays interest, vitality, and involvement in his subject and his instruction. AFMC: Coded for teacher statements that ask the student to provide more information (I think I understand but give me . . .). TDIS: Teacher criticizes a student for misbehavior. ASOT: Whenever the child does not answer a question and the teacher moves to another child in order to get the same answer to that same question, the teacher's feedback reaction is coded for asks another. Students' Attitudes Toward Their Teachers The research question concerning students"attitudes toward their teachers was as follows: 64 Do the attitudes toward teachers of students who do well on the ninth-grade mathematics achievement test differ from the atti- tudes toward teachers of those who do not perform well on the same test? The following hypothesis was generated to answer the question. The hypothesis is stated. The results of the data analysis regarding the hypothesis are discussed following the statement of the hypothesis. Hypothesis 6: There is no significant difference in students' perceptions of instructionally effective and instructionally less effective ninth-grade mathematics teachers with respect to the following: the degree of concern teachers express for their students; teachers' knowledge of their subject matter; the way teachers praise their students; the way teachers punish their students; the degree to which the students enjoy a teacher's classes. The above hypothesis was tested twice: at the end of the 1980-81 school year and two months after the beginning of the 1981-82 school year. Test at the End of the 1980-81 School Year Two-tailed't-tests were computed to test the five subhypotheses concerning students' attitudes. The results were as follows. 1. Scale 1: Concern of teachers for students (CONC). In the scale "Concern," a highly significant difference (a < 0.000) was found between the rating of instructionally effective and instructionally less effective ninth-grade mathematics teachers in that teachers who were judged effective instructionally showed more concern for their students than instructionally less effective teach- ers did. The respective means were 3.5 and 3.2. (See Table 4.11.) 2. Scale 2: Teachers' knowledge of the subject matter (KNOW). In the scale I'Knowledge," a significant difference (a < 0.01) was found 65 Table 4.1l.--Results of two-tailed t-tests for Scale 1: 1980-81. Group 1: Instructionally less effective teachers Group 2: Instructionally effective teachers Variable ofiuggggs Mean so Std. Error Group 1 147 3.2228 0.676 0.056 Group 2 195 3.5192 0.458 0.033 Pooled Variance Estimate T-Value Degrees of Freedom Two-Tailed Prob. -4.83 340 0.000 between the rating of the two groups of teachers in the sense that instructionally effective teachers were judged to be more knowledgeable about the subject matter than instructionally less effective teachers. The respective means were 3.38 and 3.54. (See Table 4.12.) Table 4.12.--Resu1ts of two-tailed t-tests for Scale 2: 1980-81. Group 1: Instructionally less effective teachers Group 2: Instructionally effective teachers . Number Var1ab1e of Cases Mean SD Std. Error Group 1 150 3.3800 0.657 0.054 Group 2 196 3.5388 0.484 0.035 Pooled-Variance Estimate T-Value Degrees of Freedom Two-Tailed Prob. -2.59 344 0.01 66 3. Scale 3: Praise and encouragement from teachers (PRAS). In the scale "Praise," no differences were found in evaluations of instructionally effective and instructionally less effective teachers; a = 0.958, which was greater than 0.05. (See Table 4.13.) Table 4.13.--Results of two-tailed t-tests for Scale 3: 1980-81. Group 1: Instructionally less effective teachers Group 2: Instructionally effective teachers Variable ofiuggggs Mean SD Std. Error Group 1 147 3.1619 0.643 0.053 Group 2 187 3.1583 0.598 0.044 Pooled-Variance Estimate T-Value Degrees of Freedom Two-Tailed Prob. 0.05 332 0.958 4. Scale 4: Punishment received from teachers (PUNS). In the scale "Punishment,“ no differences were found in evaluations of instructionally effective and instructionally less effective teachers; a = 0.301, which was greater than 0.05. (See Table 4.14.) 5. Scale 5: Students' enjoyment of mathematics class (ENJY). In the scale "Enjoyment," a significant difference (a < 0.024) was found between the two groups of teachers in that instructionally effective teachers were judged to make their teaching more enjoyable than instructionally less effective teachers. The respective means were 3.11 and 3.25. (See Table 4.15.) 67 Table 4.14.--Results of two-tailed t-tests for Scale 4: 1980-81. Group 1: Instructionally less effective teachers Group 2: Instructionally effective teachers Number Variable of Cases Mean SD Std. Error Group 1 148 1.7392 0.775 0.064 Group 2 197 1.6609 0.626 0.045 Pooled-Variance Estimate T-Value Degrees of Freedom Two-Tailed Prob. 1.04 343 0.301 Table 4.15.--Results of two-tailed t—tests for Scale 5: 1980-81. Group 1: Instructionally less effective teachers Group 2: Instructionally effective teachers Number Variable of Cases Mean SD Std. Error Group 1 150 3.1067 0.580 0.047 Group 2 197 3.2504 0.591 0.042 Pooled-Variance Estimate T-Value Degrees of Freedom Two-Tailed Prob. -2.26 345 0.024 Test at the Beginning of the 1981-82 School Year Two-tailed t-tests were computed to test the five subhypotheses concerning the students' attitudes. The results were as follows. 68 1. Scale 1: Concern of teachers for students (CONC). In the scale "Concern," no differences in evaluations of instruc- tionally effective and instructionally less effective teachers were found; a = 0.346, which was greater than 0.05. (See Table 4.16.) Table 4.16.--Results of two-tailed t-tests for Scale 1: 1981-82. Group 1: Instructionally less effective teachers Group 2: Instructionally effective teachers Variable OVUQESES Mean SD Std. Error Group 1 169 3.3114 0.530 0.041 Group 2 186 3.2487 0.701 0.051 Pooled-Variance Estimate T-Value Degrees of Freedom Two-Tailed Prob. 0.94 353 0.346 2. Scale 2: Teacher's knowledge of the subject matter (KNOW). In the scale "Knowledge," no differences in evaluations of instruc- tionally effective and instructionally less effective teachers were found; a = 0.188, which was greater than 0.05. (See Table 4.17.) 3. Scale 3: Praise and encouragement from teachers (PRAS). In the scale "Praise," a highly significant difference (a < 0.005) was found between the two types of teachers in that instructionally effective teachers were judged to praise their students less than instructionally less effective teachers. The respective means were 3.1462 and 2.9263. (See Table 4.18.) 69 Table 4.17.--Results of two-tailed t-tests for Scale 2: 1981-82. Group 1: Instructionally less effective teachers Group 2: Instructionally effective teachers Number Variable of Cases Mean SD Std. Error Group 1 160 3.3338 0.563 0.045 Group 2 198 3.2404 0.737 0.052 Pooled-Variance Estimate T-Value Degrees of Freedom Two-Tailed Prob. 1.32 356 0.188 Table 4.18.--Results of two-tailed t-tests for Scale 3: 1981-82. Group 1: Instructionally less effective teachers Group 2: Instructionally effective teachers Variable oguggggs Mean SD Std. Error Group 1 156 3.1462 0.596 0.048 Group 2 190 2.9263 0.799 0.058 Pooled-Variance Estimate T-Value Degrees of Freedom Two-Tailed Prob. 2.85 344 0.005 4. Scale 4: Punishment received from teachers (PUNS). In the scale "Punishment," a highly significant difference (a < 0.007) was found between the two groups of teachers in that instructionally effective teachers were judged to punish their students more than 70 instructionally less effective teachers did. The respective means were 1.6393 and 1.8649. (See Table 4.19.) Table 4.19.--Results of two-tailed t-tests for Scale 4: 1981-82. Group 1: Instructionally less effective teachers Group 2: Instructionally effective teachers Variable ofiuggggs Mean so Std. Error Group 1 117 1.6393 0.627 0.058 Group 2 191 1.8649 0.746 0.054 Pooled-Variance Estimate T-Value Degrees of Freedom Two-Tailed Prob. -2.73 306 0.007 5. Scale 5: Students' enjoyment of mathematics class (ENJY). In the scale "Enjoyment," no significant difference (a = 0.405 > 0.05) was found between the two types of teachers. (See Table 4.20.) Table 4.20.--Results of two-tailed t-tests for Scale 5: 1981-82. Group 1: Instructionally less effective teachers Group 2: Instructionally effective teachers . Number Variable of Cases Mean SD Std. Error Group 1 173 3.1118 0.674 0.051 Group 2 198 3.0471 0.800 0.057 Pooled-Variance Estimate T-Value Degrees of Freedom Two-Tailed Prob. 0.83 369 0.405 71 Overall Analysis of Supervisors' Evaluations, Teachers' Behavior, and Students' Attitudes Toward Their Teachers The overall hypothesis was as follows: Hypothesis 7: 0f the three major areas of evaluation of teachers, namely, supervisors' ratings, classroom observations, and students' attitudes toward their teachers, and the respective variables, no singular subset of factors can be found that, through the use of such a subset, instructionally effective and instructionally less effective ninth-grade mathematics teachers may be reliably dif- ferentiated. Discriminant analysis was used to test this hypothesis. Five scales out of 39 variables, namely, 501, R], ENJY, NEGL, and PUNS (see Table 4.21) were included in the discriminant analysis. (See Table 4.22.) Table 4.21.--Items included in the discriminant analysis for Hypothesis 7. SOl: Teacher's personality and his ability to control his classes. R]: Teacher gives same assignment to all students. ENJY: Students' enjoyment of mathematics class. NEGL: If the teacher makes no verbal or nonverbal response whatever following the child's answer to the question, he is. coded for no feedback reaction. PUNS: Punishment received from teachers. The standardized canonical discriminant function was in the form: F(x) = ~19.26 501 - 7.17 PUNS - 26.08 ENJY - 20.22 R] + 10.23 NEGL The canonical discriminant function of group means (group centereds) 72 was 14.70 and -l4.70. The analysis showed 100 percent prediction for classifying the two groups. (See Table 4.23.) Table 4.22.--Results of discriminant analysis of five scales of Hypothesis 7. Step Act1on Wilks Si Minimum Si Between Entered Removed Lambda 9. D Squared g. Groups 1 S01 0.7368 0.1936 103.50 0.0000 1 2 2 R] 0.5950 0.2730 222.96 0.0000 1 2 3 ENJY 0.3608 0.2124 695.36 0.0000 1 2 4 NEGL 0.0299 0.0127 5215.51 0.0000 1 2 5 PUNS 0.0035 0.0086 46946.20 0.0002 1 2 Table 4.23.--Prediction for classifying the effectiveness of teachers for Hypothesis 7. Predicted Actual Group Number Group Membership of Cases Group 1 Group 2 Group 1 (instructionally 4 4 0 effective teachers) 100% 0% Group 2 (instructionally 4 0 4 less effective teachers) 0% 100% Summary of the Results With regard to the seven hypotheses proposed in this study, the overview of the results is summarized as follows: Hypotheses l and 2: No statistically significant differences were found between supervisors' ratings of instructionally effective 73 and instructionally less effective ninth-grade mathematics teachers for the overall ratings and for each of the 12 subscales of the supervisors' ratings. Hypothesis 3: There was one singular subset of variables, namely, $01, $04, $07, $09, $10, and 512, out of the 12 subscales of supervisors' evaluations, that discriminated between instructionally effective and instructionally less effective ninth-grade mathematics teachers. Hypothesis 4: Out of the 27 scales of the dyadic interaction analysis, only two scales, namely, teacher's clarity and rephrasing the students' correct answers by the teacher, showed significant dif- ferences between instructionally effective and instructionally less effective ninth-grade mathematics teachers. In the other 25 scales of the dyadic interaction analysis, no statistically significant dif- ferences were found between the two groups. Hypothesis 5: There was one singular subset of variables, namely, REPH, STCR, E, AFMC, TDIS, and ASOT, out of the 27 variables for Hypothesis 5, that discriminated between the instructionally effective and instructionally less effective ninth-grade mathematics teachers. Hypothesis 6: For the 1980-81 school year: There were three statistically significant differences out of the five scales of students' attitudes between the two groups of teachers. They were: 74 1. Teachers who were judged effective instructionally showed more concern for their students than did instructionally less effective teachers. 2. Instructionally effective teachers were judged by their students to be more knowledgeable about the subject matter than were instructionally less effective ninth-grade mathematics teachers. 3. Instructionally effective teachers were judged to make their teaching more enjoyable than did instructionally less effective ninth-grade mathematics teachers. For the 1981-82 school year: There were two statistically significant differences out of the five scales of students' attitudes between the two groups of teachers. They were: 1. Instructionally effective teachers were judged by their students to praise them less than instructionally less effective ninth-grade mathematics teachers did. 2. Instructionally effective teachers were judged by their students to punish them more than instructionally less effective ninth-grade mathematics teachers did. Hypothesis 7: Out of 44 scales mentioned in Hypotheses 2 and 4, five scales, namely, 501, R], ENJY, NEGL, and PUNS, formed one singular subset of variables that discriminated between the instruc- tionally effective and instructionally less effective ninth-grade mathematics teachers. CHAPTER V SUMMARY, DISCUSSION, AND RECOMMENDATIONS Summar The purpose of this study was to determine the relationships among supervisors' evaluations of teaching, teachers' behavior, stu- dents' attitudes toward teachers, and students' achievements in ninth-grade mathematics as these factors were found in Saudi Arabia. In this research, the relationship between supervisors' ratings and teachers' behavior in relation to students' performance was studied. Two aspects related to teacher education emerged: 1. The identification of selected teacher behaviors as they were correlated with effective instruction in ninth-grade mathematics; and 2. The relationship between supervisors' ratings and teachers' behavior and how these ratings were correlated to effective instruc- tors. A presentation of the state of the art of teacher supervision and the related area of teacher evaluation in Saudi Arabia was given, followed by a theoretical conceptualization for this study. A review of the relevant literature included discussion of research on super- vision, teacher evaluation, clinical supervision, teaching, and effective instruction. Four main analyses were made in this study: 75 76 1. Supervisors' evaluations. One-way analysis of variance tests were used--first, with overall supervisors' evaluation, in which no statistically significant difference was found between ratings of instructionally effective teachers and instructionally less effective teachers; and second, with each of the 12 subscales of supervisors' evaluations, in which no statistically significant differences in rating each subscale were found between the two groups of teachers. 2. Students' attitudes. Two-tailed t-tests were computed to test the five subhypotheses concerning students' attitudes for two consecutive years: at the end of the 1980-81 school year and at the beginning of the 1981-82 school year. From the results at the end of the 1980-81 school year, it was shown that there were no statistically significant differences for both praise and encouragement from teach- ers and punishment received from teachers. Instructionally effective teachers were judged (1) to be more knowledgeable about their subject matter than instructionally less effective teachers; (2) to be more concerned for their students than instructionally less effective teachers, and (3) to make their teaching more enjoyable than instruc- tionally less effective teachers did. From the results at the beginning of the 1981-82 school year, no statistically significant differences were shown for concern of teachers for students, teacher's knowledge of the subject matter, or students' enjoyment of studying mathematics. Instructionally effec— tive teachers were judged (l) to praise their students less than instructionally less effective teachers did and (2) to punish their students more than instructionally less effective teachers did. 77 3. Individual behaviors of teachers. Data concerning indi- vidual behaviors were tested by one-way analysis of variance. Sta- tistically significant differences were found in only two out of the 27 scales, namely, "Teacher's clarity" and "Rephrasing the students' correct answers." In other words, instructionally effective teachers were judged to make their teaching clearer than instructionally less effective teachers did, and instructionally effective teachers were judged to rephrase their students' correct answers more than the instructionally less effective teachers did. 4. Clustering of behaviors. Three discriminant analyses were used in this study. The first was used to test Hypothesis 5, which was based on the 27 behaviors of the Brophy-Good Dyadic Inter- action. Six scales of the 27 were included in the discriminant analy- sis. These were as follows: REPF: The teacher summarized the student's answer. STCR: The teacher criticized the student when the student asked for individual help. E: This scale was used to judge the extent to which the teacher displayed interest, vitality, and involvement in his subject and his instruction. AFMC: Coded for teacher statements that asked the student to provide more information, i.e., "I think I under- stand but give me . . . ." TDIS: The teacher criticized the student who misbehaved in the classroom. ASOT: Whenever the child did not answer a question, the teacher moved to another child for the answer to that same question. The teacher's feedback reaction was coded for "asks another." 78 The second discriminant analysis was used to test Hypothesis 7, which was based on the 27 behaviors of the Brophy—Good Dyadic Inter- action and the 12 subscales of supervisors'evaluations, giving a total of 39 behaviors. Five scales were included in the discriminant analy- sis. These were as follows: S01: Teacher's personality and his ability to control his classes. R]: The teacher gives same assignment to all students. ENJY: The student's enjoyment of studying mathematics. NEGL: If the teacher made no verbal or nonverbal response whatever following the child's answer to the question, he was coded for no feedback reaction. PUNS: Punishment received from teachers. The third discriminant analysis was used to test Hypothesis 3, which was based on the 12 subscales of supervisors' evaluations. Six scales were included in the discriminant analysis. They were as follows: S01: Teacher's personality and his ability to control his classes. S04: Teacher's structuring his concepts progressively to introduce the simpler examples and points, then more difficult ones. $07: Teacher's use of such aids as blackboards and instruc- tional media. 509: Teacher's knowledge of the subject matter. S10: Amount of homework given and whether the teacher checked it. S12: Evaluation method used. 79 Conclusions and Implications Conclusions Three conclusions are discussed in this section, based on both the findings of the study and related research. These issues are supervisors' evaluations, teachers' behavior, and students' attitudes. Supervisors' Evaluations The current evaluation instruments used by supervisors from the Jeddah Board of Education, Saudi Arabia, for evaluating ninth- grade mathematics teachers did not identify those teachers selected as most effective or those selected as least effective based on their students' residual-gain scores. This finding supported other research discussed in Chapter II. Mosher and Purpel (1972) reported that "five experienced, skilled supervisors did two separate evalua- tions of each of four student teachers. The results? The supervisors' disagreement about the teaching they were evaluating ranged from 50 to 100 percent" (p. 50). These researchers followed this result by answering this question, "Why do analyses of teaching behavior vary so radically?" Their answer was, “A primary reason is the absence of agreement as to the 'right' way to teach. A second explanation is the unreliability of the rating instruments used in supervision and in research" (p. 51). This researcher believes that the above two reasons are valid. Furthermore, Saif (1976) answered the following question: "Why have lawmakers required evaluation of teachers?" (p. 127). Saif 80 gave two answers: 1T0 improve student learning, and to promote the professional growth of teachers" (p. 127). With respect to this, there is a need for valid obsevational instruments and better ways of supervision. As shown in the review of literature on clinical supervision, teacher, principal, and supervisors seemed to prefer clinical supervision as a better way of supervision. As Evertson, Emmer, and Brophy (1978) reported: "It seems reasonable to theorize that the various classes of variables tend to occur together, and to produce effects both on each other and on the product variables" (p. 13). Thus it was preferable to conduct dis- criminant analyses for the 12 subscales of supervisors' evaluations, for the 27 variables of the Brophy-Good Dyadic Interaction scale, and for the 39 variables of both the Brophy-Good Dyadic Interaction and the 12 subscales of supervisors' evaluations to ascertain if a set of variables existed that best discriminated between the two groups of teachers. The discriminant analysis indicated that six subscales of supervisors' evaluations, as a set, discriminated between the two groups of teachers. (See page 78.) Results of the five studies concerning junior-high-school mathematics, which were reported in Chapter II, supported those results. The set of variables that best discriminated between the two groups could be considered as criteria for teachers' evaluations if the limitations of this study are kept in mind. It should be pointed out that, although the other variables were useful in defin- ing effective instruction, these variables were not significant to show differences between the two groups. 81 Teachers' Behaviors Two variables, teacher's clarity and teacher's rephrasing the students' correct answers, showed significant differences between instructionally effective and instructionally less effective teachers. This finding was, however, supported by other research such as that of Brophy and Evertson (1978) and Good and Grouws (1975). One reason for these results was the limitation of the process-product methodology in addition to general limitations of the study. The use of discriminant analysis for analyzing the 27 vari- ables of the Brophy-Good Dyadic Interaction resulted in six variables that discriminated between instructionally effective and instructionally less effective teachers. The six variables, REPF, STCR, E, AFMC, TDIS, and ASOT, were shown on page 77. When the 27 variables of the Brophy-Good Dyadic Interaction were combined with the 12 items from the supervisors' evaluation, five variables were found to discriminate between the two groups of teachers. (See page 78.) The findings in both discriminant analyses supported other research reported in Chapter II as follows: Evertson, Anderson, Anderson, and Brophy (1979) reported that the more effective teach- ers "managed their classes efficiently and tended to 'nip trouble in the bud,’ stopping a disturbance before it could seriously disrupt the class, and they did not give their students many choices about what kinds of assignments they would do" (p. 19). Anderson, Evertson, and Brophy (1978a) reported that teachers' enthusiasm, enjoyment of 82 teaching, and use of higher-cognitive-level questions were related positively to students' achievements in their study. Students' Attitudes Students' attitudes toward their teachers at the beginning of the 1981-82 school year indicated that instructionally effective teachers punished more than instructionally less effective teachers and gave less praise. The finding supported other research such as that of Evertson (1975). Evertson examined the relationship of praise and criticism to socioeconomic status (SES). His findings regarding second- and third-grade teachers in high-SES versus low-SES schools were as follows: In low SES schools praise was regularly but weakly associated with learning gains on several measures, but was relatively unimportant in high SES classes. Criticism was negatively related in low SES but positively so in high SES classrooms. (p. 2) The students' attitudes toward their teachers at the end of the 1980-81 school year indicated that instructionally effective teachers were more knowledgeable, exhibited more concern, and the students enjoyed the mathematics classes more than the students of instructionally less effective teachers. This led to the conclusion that the best time for rating teachers is at the end of the school year. Teachers could use these evaluations from their students as feedback. Implications Three implications can be suggested on the basis of the find- ings of this study: 83 1. Some modification of the supervisory instrument could be made to give greater visibility to the set of variables that dis- tinguished the most effective teachers from the least effective teachers. 2. Teacher educators in both preservice and inservice pro- grams should consider teaching the variables that highly correlated with the most effective teachers; in addition, these variables should be considered as assets rather than as individual behaviors. 3. Teachers should recognize that students' attitudes toward effective teachers may vary between the beginning and the end of the school year. Recommendations for Further Research Given that the number of participants in this study was small (two supervisors and eight teachers) and that there were other limi- tations to the study, replication of this study is recommended. In addition, the following areas of research appear to be warranted: l. A study of the validity of the set of supervisory scales that best discriminates between instructionally effective and instruc- tionally less effective ninth-grade mathematics teachers. 2. Investigations of the validity of the set of teacher behaviors that best discriminates between instructionally effective and instructionally less effective ninth-grade mathematics teachers as criteria for effective instruction. 3. A study of the change in students' attitudes toward teachers over the course of an entire school year. 84 4. Research designed to find criteria for effective instruc- tion in areas of teaching and learning other than mathematics. 5. Experimental studies conducted to verify the findings of correlation studies for effective instruction. APPENDICES 85 APPENDIX A CONTENT VALIDITY OF THE PRETEST-POSTTEST 86 87 WWDH' . Dlnctonto of Education Western Province 1:951! 41311 cm LLJ SJIaYI “"3“” of mutation 331:.“ 33)}: Dec: Al Mokarrnmah SAUDI Alunu LfillKeldH zrho-«II 19,41 In.“ 13/2/1982 76 may 72‘ w/iome Concern M3 oer/1f} (4611' the following qusfions, oxfiyxwz 21-3413. 7 x 3) ’2X2_16xy- 6092 41 2x? +21: -12 5) 3x2 .5x -8 2 t 3 6) 6X9 - [370:1 +69 Are Valid and enough to measure the students ' understanding For the materials W/liC/l COL/efed by the ”1117’! grade TeaChEl'S within three weeks -periods, flat/1 - 51pm... 6.1.1.1 9.71.111... N. G- “A My Rb Mohamed W man; Gamll yamahi APPENDIX B THE ARABIC VERSION OF THE SUPERVISORS' REPORT AND THE ENGLISH TRANSLATION 88 89 (sawiwfl 12"“ 51.31.31.911 tummy), 1533‘ etfl'ds-U. "H'v"‘ :,.J_:11L.n.;u, pull 21,3311 23,10 ‘ 7 7 - __ I 7 "32.15131.” .4 )1 3,1 M1 H4, 2| W.“ 1*" Lat-AL“) ”A" ‘f;.d‘ troy DJUI , Stu-1“ 9243' . -1 0‘ .| ‘0 M (LT-3, ¢)J“ ‘1‘“; _\ o yfiuhibualflymtl}; __y ‘0. bw)’w\“ 42.“. _r o )TL—L—I! CALI”: bei‘jp)‘ _ i o L'JL'I‘ ~~+ 7“ 0.3. . «43.411501 .13, —r e, -1 1. 1.4411 332,11, ”#1191320 _ . 1; a cow HALO 91-2.(134; -A , 1.1.11 .sul. «.Lll .5 1° NW: Vii-‘5 J “.n’vi“ JV“ -'1 1‘ 9351‘ Llj‘d‘ L5)”. -Y a (U) J31:- U“ 9"}4“ («:33 -A ° 9:351) é'r-‘J‘: $11? :1” 473 154* «‘1 O LIMA-U ‘3 «3,1113, (kl...) _\ o 3 (L11 {31:11 \o I {#1 51‘ ,;11 _L -;‘_1-.m Hm; . ... , _ 4.503.111, 303,211 9.21. : QAJ‘J’ 9}“ PHI -_-. O- ClonJI 0‘-.. Lu,lal',\_'. O W.v‘-».A‘-A7‘A‘.’At..\’. - x. )1;- 90 Sgpervisor's Report Card 4.: Criteria 3m cm .CS- 0.3;. CDC >0 .Pu 'I-U Im L'Jm SOl. Teacher's personality and his ability to 10 control his classes. $02. Teacher's ability to follow the outlines 5 of lessons he prepared. $03. Teacher's preparations of lessons. 10 $04. Teacher's structuring his concepts progressively to introduce the simpler examples and points, 5 then more difficult ones. $05. Teacher's manner of conducting classroom 5 discussions. $06. Teacher's perceptiveness of individual differ- ences among students. 5 $07. Teacher's use of such aids as blackboards and 10 instructional media. 508. Students' understanding of mathematical concepts. $09. Teacher's knowledge of the subject matter. SlO. Amount of homework given and whether teacher 10 checked it. Sll. Students' achievements. lo .512. Evaluation method used. 5 Overall Evaluation: 80 Summary of supervisor's comments: Signature Principal's opinion: Supervisor name: Signature: APPENDIX C BRIEF DEFINITIONS OF VARIABLES CODED IN THE BROPHY—GOOD DYADIC INTERACTION SYSTEM 91 92 Brief Definitions of Variables Coded in the Brophy:fiood DyadicTInteraction System Part One: Response Opportunities 1. TD. Discipline Question (DISP): The discipline question is a unique type of direct question in which the teacher uses the question as a control technique, calling on the child to force him to pay better attention rather than merely providing a response opportu- nity in the usual sense. Direct Question (DIRC): The teacher calls on a child who is not seeking a response opportunity. Open Question (OPEN): The teacher creates the response opportu- nity’by asking a public question and also indicates who is to respond by calling on an individual child, but chooses one of the children who has indicated a desire to respond by raising his hand. Call Outs (CALL): Response opportunities are created by children who call out answers to teachers' questions without waiting for permission to respond. Process Question (PROC): In a process question, students must explain something in a way that requires them to integrate facts or to show knowledge of their interrelationships. It most fre- quently is a "Why?" or "How?" question. Product Question (PROD): In product questions, single correct answers are elicited that can be expressed in a single word or short phrase. Product questions usually begin with "Who?," "Nhat?," "When?," "Nhere?," "How much?," or "How many?" Choice Question (CHIC): In the choice question, the child does not have to produce a substantive response but may instead simply choose one of two or more implied or expressed alternatives. Correct Answers (f): If the child answers the teacher's question in a way—that satiSfies the teacher, the answer is coded as correct. Part-Correct Answers (I): Part-correct answers are answers that are correct‘BUt incomplete as far as they go or answers that are correct from one point of view but are not the answer that the teacher is looking for. Incorrect Answers (-1: Responses coded as incorrect answers are those in which the child's response is treated as simply wrong by the teacher. ll. 12. 13. T4. 15. 16. T7. 18. 19. 20. 21. 22. 93 Don't Know (D.K.): The student verbally says, "I don't know" (or its equivalent) or nonverbally indicates that he doesn't know (shakes head). No Response (N.R.): The student makes no response (verbally or nonverballY) to teacher's question. Praise (PRIS): Praise refers to the teacher's evaluative reac- tions that go beyond the level of simple affirmation or positive feedback by verbally complimenting the child. Affirmation of Correct Answers (AFFR): An answer is coded as affirmation when the teacheriindicates that the child's response is correct or acceptable. Summary (REPF): The teacher summarizes the student's answer (generally as part of the affirmation process). No Feedback Reaction(NEGL): If the teacher makes no verbal or nonverbal response whatever following the child's answer to the question, he is coded for no feedback reaction. Negation of Incorrect Answers_(NIA): This is simple provision of impersonal feedback regarding the incorrectness of the response, with no further communication of a personal reaction to the child. As with affirmation, negation can be communicated both verbally ("No," "That's not right," "hmm-mm") and nonverbally (shaking the head). Criticism (CRIT): Coded for evaluative reactions that go beyond the level of simple negation by expressions of anger or personal criticism of the child in addition to indications of the incor- rectness of his response. Process Feedback_(EXAN): Coded when the teacher goes beyond merely providing the right answer and discusses the cognitive or behavioral processes that are to be gone through in arriving at the answer. Gives Answer (GIVA): This category is used when the teacher gives the child the answer to the question but the answer is not sufficient to be coded for process feedback. Asks Another (ASOT): Whenever the child does not answer a ques- tion and the teacher moves to another child in order to get the answer to that same question, the teacher's feedback reaction is coded for asks another. Call Out: The call-out category is used when another child calls out the answer to the question before the teacher has a chance to act on his own. 94 23. Repeats Question (REPT): The teacher asks a question, waits some time without getting the correct answer, and then repeats the question to the same child. 24. Rephrase or Clue (CLUE): In this feedback reaction, the teacher sustains the response opportunity by rephrasing the question or giving the child a clue as to how to respond to it. 25. New Question (NEW Q): The teacher asks a new question when he requires an answer that is different from the original question, although it may be closely related. A question requiring a new answer is coded as a new question. 26. Expansion(AFMC). Coded for teacher statements that ask the student to provide more information (I think I understand but give me . . .). Part Two: Dyadic-Teacher Contacts Dyadic teacher-child contacts are divided into procedural contacts, work-related contacts, and behavioral or disciplinary con- tacts. They also are separately coded according to whether they are initiated by the teacher (teacher-afforded) or by the child (child- created). The coding also reflects certain aspects of the teacher's behavior in such contacts. Work-related contacts.--Nork-related contacts include those teacher-child contacts that have to do with the child's completion of seatwork or homework assignments. They include clarification of the directions, soliciting or giving help concerning how to do the work, or soliciting or giving feedback about work already done. Work- related interactions are considered child-created if the child takes it upon himself to bring his work up to the teacher to talk to him about it or raises his hand or otherwise indicates that he wants to discuss his work with the teacher. Work-related interactions are coded as teacher-afforded if the teacher gives feedback about work when 95 the child has not solicited it (the teacher either calls the child to come up to his desk or goes around the room making individual comments to the students). Created contacts are not planned by the teacher and occur solely because the child has sought him out; afforded contacts are not planned by the child and occur solely because the teacher initiates them. Separate space is provided for coding child-created and teacher-afforded work-related interactions on the coding sheets, and the coder indicates the nature of an individual dyadic contact by where he codes the information. In addition to noting the interaction as work interaction and as an interaction that is child-created or teacher-afforded, the coder also indicates the nature of the teacher's feedback to the child dur- ing the interaction. He indicates this by using one or more of the five columns provided for coding teacher's feedback in work-related interaction: praises (STRR), gives explanation (PCSS), criticizes (STCR), or "don't know" (?). The first four of these categories have the same meaning as they have in other coding of teacher feedback. The additional "don't know" category is added for this coding because frequently the individual teacher-child interaction that occurs in the dyadic contacts will be carried on in hushed tones or across the room from the coder so that he cannot hear the content of the inter— action. In such cases, the coder notes the occurrence of the work- related interaction and the fact that it was either teacher-afforded or child-created, but he enters the number in the "don't know" column. Procedural contacts.--The category of procedural contacts includes all dyadic teacher-child interaction that is not coded as 96 work-related contacts or as behavioral contacts. Thus it includes a wide range of types of contacts, most of which are initiated on the basis of the immediate needs of the teacher or child involved. Pro- cedural contacts are created by the child for such purposes as seek- ing permission to do something, requesting needed supplies or equip- ment, reporting some information to the teacher (tattling on other children, calling attention to a broken desk or pencil, etc.). Three categories for coding teacher's response are provided: praise (++), feedback (fb), and criticism (--). Praise and criticism have the same meaning here as elsewhere. Behavioral contacts.--Behavioral contacts are coded whenever the teacher makes some comment upon the child's classroom behavior. They are subdivided into praise (++), warnings (N), and criticism (TDIS). Praise and criticism are coded as described above. Warning.--Usually teachers' warnings occur in situations in which the child is doing something that is not necessarily or always prohibited but which is troublesome at the moment. In such instances the teacher singles out the child to inform him that his present behav- ior is inappropriate. However, the teacher communicates no rejection or anger as in criticism. 97 High-Inference Codings (Emmer) High-inference codes were noted at lS-minute intervals during the mathematics lesson when the teacher worked with the class as a whole in recitation, development, review, and drill (if it involved frequent teacher-pupil agreement in publjg_discussion). (See Table 3.6.) Homework (H) Homework ratings indicated the extent to which time was spent in introducing homework or reviewing homework. The attention, clarify, enthusiasm, and presentation were all taken from Emmer (1973). Definitions of these variables follow: Attention (A) Attention as defined for this scale referred to pupil orienta- tion toward the teacher, the task at hand, or whatever classroom activities were appropriate. If a pupil was attending to inapprop- riate activities or was engaged in self-directed behavior when he was supposed to be engaged in a class activity, his behavior was not con— sidered attentive. Therefore, appropriate behavior was that which was focused upon or engaged in whatever activity was appropriate. At times, it was difficult to determine whether a student was being attentive, such as when the teacher presented information and the stu- dent sat facing the teacher with no observable behaviors indicating inattention. In such an instance, the pupil was considered attentive until he provided a behavioral indicator to the contrary. 98 Observers entered one of the following codes every two minutes during times when the teacher presented material to the class. I. 5. Fewer than half of the students are attentive most of the time. One-half to three-fourths of the students appear attentive most of the time; the remainder are attentive only some of the time. Most of the students are attentive, but several (four to six) are attentive only some of the time. Nearly all of the students are attentive, but a few (one, two, or three) are attentive only some of the time. All the students are attentive most of the time. Note: The phrase "most of the time" means at least 75 percent of the time the observer checked the pupils for attentiveness. Clarity (C) Clarity referred to the degree to which the teacher's presen- tation of material and his substantive interactions with students were understood by them. Low clarity meant that the teacher was "over their heads" and was confusing to the pupils. 1. Very low clarity. Pupils seem very confused by the pre- sentation. The teacher cannot answer the pupils' questions, or answers them in an unclear manner by using concepts and terms the pupils are apparently unfamiliar with or by being overly complex and ambiguous. Low clarity. Between very low and moderate. Moderate clarity. The teacher seems to be understood by most pupils, but not all of the time. Sometimes the teacher is confusing and vague. High clarity. Between moderate and very high. Very high clarity. The teacher's explanations are easy to understand and pupil questions are adequately answered. The teacher seems aware of the pupils' levels, sensing problems they are having or may have. 99 Enthusiasm (E) This scale was used to judge the extent to which the teacher displayed interest, vitality, and involvement in his subject and his instruction. l. Very low enthusiasm. The teacher's behavior is lethargic, dull, routine; there is a minimum of vocal inflection, gesturing, movement, or change in facial features. The teacher appears to lack interest in what he is doing. 2. Low enthusiasm. Between very low and moderate. 3. Moderate enthusiasm. Occasionally the teacher seems interested and involved; there is some display of activity, such as gesturing. Sometimes the teacher is dull, routine, and lacking in vigor. - 4. High enthusiasm. Between moderate and very high. 5. Very high enthusiasm. The teacher is stimulating, ener- getic, and very alert. He seems interested and involved in what he is teaching. He moves around, gestures, and inflects his voice. Presentation (P) This scale measured only one type of behavior. The observer's task was to estimate the relative amount of class time occupied by teacher presentation of substantive information. By teacher presenta- tion was meant substantive (content-oriented) verbal or nonverbal behavior that provided information, and did not imply or require pupil response nor evaluate pupil behavior. Thus, teacher questions, pro— cedural directions, praise, and criticism were not instances of teacher presentation. Lecture, reading to the class, answering pupil ques- tions, and any other activity in which the teacher gave information were instances of teacher presentation. 100 1. Teacher presentation occurs O-ZO percent of the period. Teacher presentation occurs 2l-4O percent of the period. Teacher presentation occurs 4l-60 percent of the period. Teacher presentation occurs 6l-80 percent of the period. 01-wa Teacher presentation occurs Bl-lOO percent of the period. Homework Assignments There were four scales in this instrument, namely, assigning homework (R1), same assignment to all students (R2), time provided in class to work on homework (R4), and describing the source of the homework (R5). The scales were coded at the beginning and at the end of the class. APPENDIX D ARABIC AND ENGLISH VERSIONS OF THE COVER LETTER AND THE QUESTIONNAIRE lOl 102 MICHIGAN STATE UNIVERSITY COLLEGE OF ARTS AND LETTERS EAST LANSING - MICHIGAS ' 4882* DEPARTMENT OF LlNGL’lSTlCS AVD ORlE\TAL A\D AFRICA.\ LANGUAGES WELLS HALL March 12, 1982 To whom it may concern, I hereby certify that Mr. Abdul-Razzag Dhafar has translated into Arabic the English version of the questionnaire used as a tool in his research for his doctoral dissertation. I have seen photocopies of English and Arabic versions of the questionnaire title "Students' responses to questionnaire concerning their attitudes". I also have seen his translation of a report titled “Supervisor's report card". The translation of both the questionnaire and the report is accurate and reliable. The cover letter, the questionnaire, and the report were translated into Arabic in the same format, except that it follows the standard writing style for the Arabic language. 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WJL‘JI Ja.’ 3...,» UJLJJLJI M_ry on?!» 3.3waqu CJ"; -TA 106 Students' Responses to Questionnaire Concerning Their Attitudes Dear Student: Please respond to each item below. These items concern your math teachers for this year. This information is confidential, and no one in your school will have access to it. sent to your brother who is doing research in the United States. Please do not discuss the items with your friends. Your responses will be cooperation. Directions: Follow these steps in responding to each item: Item l. My teacher gives us homework for every lesson. If your teacher always gives you homework for every lesson, put the sign X under always, as: 93: If your teacher never gives you homework for any lesson, put the sign X under never, as: Always Most of the Time Some- times: Thank you for your Never 107 Always Most of the time Sometimes Never . I feel comfortable participating in class discussion. 2. My teacher is friendly. 3. My teacher helps me learn mathematics. 4. I like my math teacher. 5. I feel comfortable with my math teacher. 6. I am praised when I do good work. 7. My teacher knows his subject. 8. My teacher cares about me. 9. I like mathematics. 10. If I have a question, I ask my teacher right away. ll. My teacher wants me to understand math. 12. My teacher makes sure that I do my homework correctly. l3. I do my best to understand math. 14. My teacher gives us homework for every lesson. l5. My teacher helps me when I make mistakes on my homework. l6. My teacher encourages me to ask questions. l7. I feel my teacher likes to teach math. 108 Always Most of the time Sometimes Never 18. My teacher does not make me feel embar- rassed when I answer his question incorrectly. 19. The teacher's blackboard is well organized. 20. My teacher hits me when I do not behave well in the class. 21. My teacher hurts my feelings in front of my classmates when I do not answer his question. 22. I am told about my bad work and not about my good work. 23. My teacher praises me when I complete my homework. 24. My teacher prepares the lesson in advance. 25. My teacher makes me feel stupid when I do not answer his question. 26. When I do not answer the teacher's question correctly, he still encour- ages me. 27. My teacher yells at me a lot in class when I do something wrong. 28. My teacher hits me when I cannot answer his question. 29. I do a lot of good work that goes unnoticed. 30. My teacher moves gradually from the easy examples to the more difficult ones. 109 Always Most of the time Sometimes Never 31. My teacher gives enough time for each student to solve the problem. 32. My teacher checks my homework problems. 33. My teacher repeats his presentation to make sure that each student understands the concept. 34. I am able to read his writing on the blackboard. 35. My teacher builds on past experiences in introducing new concepts. 36. My teacher explains the material very well. 37. My teacher uses different methods to solve problems. 38. The presentation made by my teacher attracts my attention. APPENDIX E EXPLORATORY FACTOR ANALYSIS 110 111 Table E-l.--Means and standard deviations of variables used in the factor analysis. . Standard Variable Mean Deviation Cases A01 3.3305 .6946 354 A02 3.3352 .7853 352 A03 3.5294 .6640 357 A04 3.2717 .7545 357 A05 3.1938 .8147 356 A06 3.2465 .8649 357 A07 3.6704 .5784 355 A08 3.0084 .8789 357 A09 3.0310 .8840 355 A10 2.2865 1.1540 356 All 2.9014 .9075 355 A12 3.6028 .7684 355 A13 3.1849 .9566 357 A15 3.5831 .6645 355 A15 3.4441 .8408 358 A16 3.3799 .8861 358 A17 2.9218 .9983 358 A18 3.6134 .7280 357 A19 2.7458 .9728 358 A20 3.4441 .8341 358 A21 2.0197 1.1319 356 A22 1.6732 .9449 358 A23 1.9430 1.0729 351 A24 2.8357 1.1237 353 A25 3.1770 1.1055 356 A26 1.7247 1.0140 356 A27 3.0340 1.0219 353 A28 1.6836 .9349 354 A29 1.4691 .8634 356 A30 2.0724 1.0030 359 A31 3.5527 .8431 351 A32 3.2727 .8832 352 A33 3.2670 .9072 352 A34 3.3870 .9401 354 A35 3.6742 .6633 356 A36 3.2535 .8817 355 A37 3.5014 .7605 355 A38 3.1243 .9764 354 A39 3.0761 .9957 355 112 peepe. mmmme. mmm~—. mmmpo. oommm. pmmmm. oomme. mmuem. mvmme. mopmv. mmepe. mammm. meovm. mm< cummm. pmpmm. mmmpp. mmmmo.1 mnvpp. —momm. mnmvm. mmmvm. mmpmm. mmmmm. mmmmm. mmmmm. mumso. mm< memmm. pmoom. “memo. cmeco. memm—. mwcme. mepmm. mommm. mommm. —¢mmm. mmmme. ooomm. memmp. nm< mmmmp. nmmmm. mmmmo. ompeo. pmmmo. mvmmp. mvpmm. mepmo. mo~m_. mmmmo. meme—. 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Nmmme. meme—. mmomm. mummm. memmm. memmm. pmmnm. mmmmm.I ommm—.I —ommp.u mpamm. ma< mmmmm. mmomm. aaamm. nmmep. mmomm. pmmmm. mommm. mmpmm. mmmep. emmmm.I ammma.I emamP.I mammm. ma< meaem. mmmsa. memop. ppmma.u ppmma. mmemm. moamp. mmmm—. smmma. mmpep.u ammaa.I momma.I maepp. pa< mm< mm< Nm< om< mm< em< mm< mm< —m< am< mm< mm< nm< .ea==.u=ou--.~-m apaeh 115 memep. mmmea. emmaa. maamp. momma.I emmea.u m—oma.u p—moa. mmema. mapam. mm< nomap. ommea. mmmmp.I opema. emema. eaeaa. smuma. mmnep. meapa.u masem. mm< mmmea.u mem—P.I m—ama.I meeep. mmmmp.I ammua. mmmma. emapm. ampaa. aemou. mm< meopp. mmoma.I mmema. momma.I mpmop. momma. ompma. ommmp. mmm—a. meeam. om< mopap. mnmea. mmmma. memma.I mamoa. umpap. mumma. mpmmp. momma.I ammme. mm< ommoa. mumm—.I umm—a. mmmma. emama.: mpmma. epopa.I ommmp. mmama. mmomm. em< momma.I mmmea. upmpm.n mmama.I ommoa.: mmmmp.u mmeam. mampp. ammop. m_mmo. mm< pomma.I ommoa.I moppa.u mmmma. momma. amoaa.I m—o—a. mumap. mmama. mmomm. mm< mp—ma. pmmep.u amenm. momma. emmpp. memaa.I ammma.u mmpap. mpeea.I mammm. pm< mmama. mmmma.I mpm—a. nsmma.n mmema. momma.I meama.I omm—p. ommmm. mmmme.I am< eamma.I mmnaa. apmma.I memma. mpmmm.I omoam. mpeea. mmmaa.I mommm. mmomm.n mm< maamp. mmoma. mapma. mamma. meaaa. mpmaa. mpmea.I momma. moppm. amepe.I mm< meaea. mmmma.I mmsop.u aamea.I mmmam. momem. am~m~.I mpmpa.u mmmea. meemm. ~m< mmmea. mppaa.n apoma. ——m~a.u aeoma. m—mmm.I mopmp.I emapm. mmmem. emmme.I mm< emooa.I memmp. mpmea. mamam. mmmem. mmema. mmeaa. pmsmp. mmepa.u ea_mm. mm< mmoma.I ommaa. moon—.1 ummma. aammm. eeama. emamp.I pmmap.I mmmmp. mamme. em< mmoma. meama. memma.I m—eea.I —mmmp. 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Amvmemmm. mm< —mm~a. m—mna. ammsp. ammo—. nmmma. aem—a. “ms—p. em———.I —mmom. m—mme. mm< mmemm. pomma. ammap. emo_a. emama. —e-a.u ma—oa. ee—ma.n mmepp. mmmom. —m< ammma. m—mea. mmnma.u ommea.- mmmoa. mmmea. emema.n memme. mmm~—.I .mamm. am< eemm—.I ommma.I m—mmp.u ommea.I mam——. Auvmmmmo. emeaa.- m—pmm. momma.I mom—p. mm< ma—ma.a eomma.I emmma.I momma.I momma. eammm. mmema. Anaemomo. ammmp.n emem_. mm< ammea. mommm. mmnam. ommoa.- momma. emmap. pamaa. mm—m_.I Auvm_m—e. mmmmm. nm< mmaaa.I emaea.I mmmma.I —mpma. mmaep. —moma. mmomm.- Auvpmomm. ommma.a mmmam. om< mmema. amoma. ammme. mmama. momma. m—mma.I mm—ma.I mmoaa. eopma. mmomm. mm< mo—ma.I eo—mm. mmomm. eamma. emama. m~_oa. mmpop. mpmma.u Auvomm—e. mmmmm. em< ommoa.- ammma. mu—oa. mamma. ommoa. momma.I msmma.n vvmmmme. m—oaa. pomea. mm< memaa.u emmp—.I o—mma.n mom—a. onpma. pmmmm. mme—a.I vamp—mo. aemm—.I mmaop. mm< eemaa. mmoma. mmeaa. eomoa. emama. Anymomeo. apmma. mommm. emama. mmaea. _m< mmmpa.u emoma.I mmnmm. memma.: momma. a—ee—. mmmoa. mmomm.I amme—. Anvmamme. am< mamoa. —mmma. em—oa. ppemp. nmpom. mm—em. momma. —amoa.I momma. mmepp. m—< mema—. msapa.u ammaa.n oopea. emnma. ammaa. ammea. —m_mm.I maemm. Anvmmpmm. m—< meoaa.I mmemm. eeama.I mmmea. mmemm. ammma. pammp. _mam—.I omopm. m—mmm. m—< ome~m.u mpepa.I emmaa.: mmmmm. ommsp. —maaa. momma. mm—ma.n mmmm—. Amvmmame. m—< nmmaa.u mmama.I opmma. mmoao. mummp. pmeea. momma. mmmma. aopma.I memm—. mp< mmuma. mmmn—. msoea. oemam. m~_oa. mom—a. mam—m. mm—aa. opoma. ammma. e—< mmemm.u omepp. mmema. pmaap. momma. mmmmm.n aaamm. mmmpa. —eaep. onmmpmm. m~< m—ama. mmmma.I mmema.I nm—mp. a—mm—. ommoa.o a—paa. mmmmm.I mmeom. onoammm. m—< ommoa.: emppa. oesea. moe——. maoao. ommoa.- pmoem. mmoea.I memo—. ooh—a. ——< amaoa. e_maa.o ommoa. ommoa. emmmp. mmmma. mom—a. ammm_. ommoa. e_a_a. a_< meama. pmmoa. ommoa.- pooma. mmma_. mmeaa. Amvommmo. oeNea. pmmma. emmmp. ma< mmama. mmmam. ampma.a ompa—. e—oma. mumaa.I “mmaa.u momma.- Auvemmeo. mommm. ma< ~_m~p. eoe—m.n momma. omm—a. —emma. —e—ea.n amama.I m_mma. Ammam. Anymo_oo. ma< mmmm—. —m~mm. momea. m——a—. mmmm—. emama. mmeoa. mmoma.I Auvmmome. emmem. ma< mmmma. mmmoa.I mmama. e—ama. epmoa. mmmm—.I Ao.uvmmm—m. —mmm—.I Ao.uvm~omm. mo_~m. oa< aemaa. Nome—.1 aamaa. momma.I a—p—a. mmoaa. mmmmm. mNma—.I Auvmmmom. —mmam. ea< ae~_m. ommoa.u mmoma.a omoam. mme—a. momma.I mmoop. momma.I mmmmm. Aavomamo. ma< mma—a. momma.I mmpma. omo—a.n emmma. mmmaa. mmema.I m—mma.I Auvmmoom. mmomm. ma< mamaa. e—mma.I momma. mmema. sammp. ommoa. onmomme. “map—.1 mmmam. mamsa. Fa< a. Louumm m Louumu m Lemon; m gouge. o Louuau m Louuau e Lauuou m Lemon. m segue; — Louuau Rh“ u h .1.” n I." "“41" "with “I". "n“ a.“ IHLI.FI.11"III.“ a”ll. a D "1.?“ N "inl- Fl‘ V.“ M L“. u. n lulh g.¢h.."‘lhul huh“ anal..- "(“3 "II. B’:“.qu§ adlnlq‘l ‘lllv ‘4‘ "3nd .:o_uo~._msgoc me_ox saw: cowumuoe gamma xvgume Louuau vmuouog xoewgm>--.e1m m—ao» APPENDIX F RELIABILITY ANALYSIS OF SCALES 117 118 Table F-1.--Re1iabi1ity analysis for Scale l--Concern. A03: My teacher helps me learn mathematics. A12: My teacher wants me to know mathematics. A13: My teacher assures me I do homework correctly. A16: My teacher helps with mistakes in my hOmework. A33: My teacher checks my homework. A34: My teacher makes sure that all understand his assignments. A35: I m able to read my teacher's handwriting. A39: My teacher attracts and holds my attention. Means Std. Dev. Cases A03 3.569 .638 274 A12 3.639 .709 274 A13 3.219 .951 274 A16 3.409 .878 274 A33 3.307 .886 274 A34 3.438 .909 274 A35 3.715 .640 274 A39 3.099 .973 274 Correlation Matrix: A03 A12 A13 A16 A33 A34 A35 A39 A03 1.00000 A12 .45632 1.00000 A13 .31894 .34054 1.00000 A16 .34820 .43843 .40594 1.00000 A33 .36397 .35779 .42876 .40836 1.00000 A34 .56644 .51940 .38880 .40859 .38317 1.00000 A35 .38936 .32954 .24728 .24059 .16743 .37895 1.00000 A39 .44624 .44483 .38841 .31309 .30911 .57669 .37475 1.00000 N of Cases = 274 Statistics for Mean Variance Std. Dev. Variables sca'e 27.394 20.166 4.5 8 Item Means Mean Min. Max. Range Min./Max. Variance 3.424 3.1 3.7 .6 1.2 .045 119 Table F-1.--Continued. Scale Scale Item-Total Mean Variance Corrected Squared Alpha . . . . Item-Total Multiple if Item Statistics 0:16:23 521;:23 Correlation Correlation Deleted A03 23.825 16.629 .601 .404 .806 A12 23.755 16.215 .604 .384 .803 A13 24.175 15.325 .529 .306 .813 A16 23.985 15.692 .533 .317 .811 A33 24.088 15.824 .505 .299 .815 A34 23.956 14.613 .680 .511 .789 A35 23.679 17.472 .427 .226 .823 A39 24.296 14.780 .594 .406 .803 Reliability coefficients 8 items Alpha = .82830 Standardized item alpha = .83272 120 Table F-2.--Reliabi1ity analysis for Scale 2--Knowledge. A07: My teacher knows his subject very well. A18: My teacher likes to teach math. A20: My teacher's blackboard is well . A37: My teacher explains material welgrganized. A38: My teacher uses different methods to solve problems. Means Std. Dev. Cases A07 3.679 .560 274 A18 3.628 .711 274 A20 3.478 .822 274 A37 3.540 .736 274 A38 3.139 .962 274 Correlation Matrix: A07 A18 A20 A37‘ A38 A07 1.00000 A18 .42507 1.00000 A20 .41418 .25555 1.00000 A37 .55502 .51131 .44330 1.00000 A38 .35465 .29526 .31424 .44704 1.00000 N of Cases = 274 Statistics for Mean Variance Std. Dev. Variables sca'e 17.454 7.429 2.7 5 Item Means Mean Min. Max. Range Min./Max. Variance 3.493 3.1 3.7 .5 1.2 .045 Scale Scale Item-Total Mean Variance Corrected Squared Alpha Item-Total Multiple if Item Statistics 'f Item 1f Item Correlation Correlation Deleted Deleted Deleted A07 13.785 5.554 .591 .374 .697 A18 13.836 5.347 .480 .293 .720 A20 13.985 5.040 .464 .248 .728 A37 13.923 4.723 .676 .477 .650 A38 14.325 4.586 .465 .230 .741 Reliability coefficients 5 items Alpha = .75144 Standardized item alpha = .77038 121 Table F-3.--Re1iabi1ity analysis for Scale 3--Praise. A02: My teacher is friendly. A04: I like my math teacher. A05: I feel comfortable with my teacher. A06: I'm praised when I do good work. A08: My teacher cares about me. A243 My teacher Eraises me for completed homework. A27: No answer-- eacher still encourages me, Means Std. Dev. Cases A02 3.365 .745 274 A04 3.310 .707 274 A05 3.252 .779 274 A06 3.307 .817 274 A08 3.080 .821 274 A24 2.876 1.099 274 A27 3.088 .994 274 Correlation Matrix: A02 A04 A05 A06 A08 A24 A27 A02 .OOOOO A04 .50723 .00000 A05 .40388 .61553 .00000 A06 .36315 .31649 .37900 1.00000 A08 .43677 .41710 .38619 .41070 1.00000 A24 .28368 .35590 .32760 .36476 .29912 1.00000 A27 .35725 .40907 .40182 .39517 .40842 .36528 1.00000 N of Cases = 274 Statistics for Mean Variance Std. Dev. Variables 59”" 22.277 16.963 4.1 7 Item Means Mean Min. Max. Range Min./Max. Variance 3.182 2.9 3.4 .5 1.2 .031 122 Table F-3.--Continued. Scale Scale Item-Total Mean Variance Corrected Squared .Alpha Statistics if Item if Item Item’T°ta' Mu't'P'e 'f Item Deleted Deleted Correlation Correlation Deleted A02 18.912 13.318 .568 .372 .781 A04 18.967 13.270 .619 .468 .775 A05 19.026 12.933 .611 .459 .774 A06 18.971 13.157 .530 .297 .786 A08 19.197 13.016 .552 .325 .783 A24 19.401 12.183 .466 .230 .807 A27 19.190 12.140 .553 .311 .784 Reliability coefficients 7 items Alpha = .80895 Standardized item alpha = .82074 123 Table F-4.--Reliability analysis for Scale 4--Punishment. A21: My teacher hits me if I don't behave in class. A29: My teacher hits me if I don't answer in class. A22: My teacher hurts my feelings before classmates. A23: I'm told about bad work but not good work. A26: For no answer-~teacher embarrasses me. A28: My teacher yells when I do something wrong. Means Std. Dev. Cases A21 1.974 1.107 274 A29 1.394 .769 274 A22 1.555 .851 274 A23 1.894 1.048 274 A26 1.668 .974 274 A28 1.631 .909 274 Correlation Matrix: A21 A29 A22 A23 A26 A28 A21 A29 A22 A23 A26 A28 .00000 .35597 1.00000 .24831 .43153 1.00000 .17122 .09285 .33712 1.00000 .20953 .27824 .55480 .42488 1.00000 .23067 .43901 .56816 .24329 .49007 1.00000 N of Cases = 274 Statistics for Scale Item Means Mean Variance Std. Dev. Variables 10.117 14.147 3.8 6 Mean Min. Max. Range Min./Max. Variance 1.686 1.4 2.0 .6 1.4 .046 Table F-4.--Continued. 124 Scale Scale _ . Corrected Squared Alpha Deleted Deleted Correlation Correlation Deleted A21 8.142 10.533 .332 .152 .753 A29 8.723 11.205 .457 .304 .712 A22 8.562 9.991 .638 .467 .663 A23 8.223 10.569 .364 .209 .739 A26 8.449 9.677 .582 .411 .673 A28 8.485 10.031 .571 .409 .678 Reliability coefficients 6 items Alpha = .74066 Standardized item alpha = .75422 125 Table F-5.--Re1iability analysis for Scale 5--Enjoyment. A01: I enjoy participating in class discussion. A09: I like mathematics. A05: I feel comfortable with my teacher. Means Std. Dev. Cases A01 3.354 .676 274 A09 3.062 .856 274 A05 3.252 .779 274 Correlation Matrix: A01 A09 A05 A01 1.00000 A09 .29758 1.00000 A05 .32412 .25673 1.00000 N of Cases = 274 Statistics for Mean Variance Std. Dev. Variables sca'e 9.668 2.823 1.7 3 Item Means Mean Min. Max. Range Min.[Max. Variance 3.223 3.1 3.4 .3 1.1 .022 Scale Scale Item-Total Mean Variance Corrected Squared Alpha Item-Total Multiple if Item Statistics if Item if Item Correlation Correlation Deleted Deleted Deleted A01 6.314 1.681 .391 .154 .407 A09 6.606 1.405 .338 .117 .486 A05 6.416 1.533 .354 .133 .449 Reliability coefficients 3 items Alpha = .54597 Standardized item alpha = .55400 BIBLIOGRAPHY 126 BIBLIOGRAPHY Alvir, Howard P. "How to Hit a Movin Target." New Measurement Dimensions in Teacher Education ?April 1975). ERIC ED 109 163. Anderson, L., and Brophy, J. 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