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AN ABSTRACT OF THE THESIS OF WILLIAM HENRY MAC FARLANE for the degree of DOCTOR OF EDUCATION inEDUCATION presented on NOVEMBER 20, 1981 Title: A STUDY OF THE MATHEMATICAL COMPETENCE REQUIREMENTS FOR GRADUATION AMONG OREGON'S A-AA-AAA SENIOR HIGH SCHOOLS for AbstractapproveRedacted privacyedactedffi for privacy Dr. Sylvia Tucker /r. Michael Colbert Competency-based education was introduced to the state of Oregon in the early 1970's, mandating that the graduating classes of 1978 would meet these competency requirements for graduation. The Oregon Department of Education allowed each school district to compile its own lists of competencies in each of the mandated areas. There were no state recommended guidelines in these areas; consequently, competencies were varied inrequire- ments and numbers. This research was designed to establish minimal mathematics competencies for Oregon's four-year public senior high schools; they would also be applicable to all other high schools in the state. The use of mean scores and the one-way analysis of variance (ANOVA) at the .05 level of significance was applied to determine if there were any significant dif- ferences between and among responses. There were significant differences in 15 of the 71 items. The LSD test was then applied to determine where the differences lay. A significant difference was revealed between AAA and AA in 15 items. AAA and A schools differed signifi- cantly on only 2 items. From this study it can be concluded that schools classified as A and AAA are more closely aligned in their interpretation of mathematical competencies at all levels. A and AAA accepted the competency list with fewer exceptions as being necessary for mathematical instruc- tion. It was further indicated that schools classified as AA felt a need for fewer competencies than the other classifications of schools. In constructing the final master list of com- petencies using a combination of F statistic scores and mean scores, 19 items were rejected, leaving 52 items that compose the finished document. The model procedure developed for this study pro- vided useful information in compiling and evaluating data. It could be used to study and evaluate the other 5 areas of competence designated by the state of Oregon. A STUDY OF THE MATHEMATICAL COMPETENCE REQUIREMENTS FOR GRADUATION AMONG OREGON'S A-AA-AAA SENIOR HIGH SCHOOLS by WILLIAM HENRY MAC FARLANE A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of DOCTOR OF EDUCATION Completed November 20, 1981 Commencement June 1982 APPROVED: Redacted for privacyRedacted for privacy Professor of Education in charge of major Redacted for privacy Division COZYdinator Redacted for privacy Dean of G74G7` duate SchIll Date thesis is presented November 20, 1981 Typed by Mary Syhiman for WILLIAM HENRY MAC FARLANE TO MY FATHER -- This book is dedicated in appreciation and love to the one member of the family who was not able to be here for its completion. ACKNOWLEDGEMENTS As William Herbert Carruth has written: We .are all dreamers of dreams, on visions our childhood is fed; and the heart of the child is undaunted, it seems, By the ghosts of dreams that are dead. The completion of this dissertation and degree is the culmination of one of my dreams. To this end, I would like to express my sincere appreciation to the members of my committee who provided support, advice and council, and encouragement to me during my studies and the writing of this dissertation: Dr. Sylvia Tucker who encouraged me to pursue this degree and who helped smooth the way for its completion; Dr. John Oades, whose critical evaluations and recommendations made the pursuit of this effort more mean- ingful; Dr. Helen Hall whose constructive advice and cheer- ful reassurance made working with her a pleasure; Dr. Harland Padfield who, through his quiet and supportive personality, provided encouragement; and Dr. Michael Colbert who, through his acceptance of me as a person, recognized some spark of talent and ability, proded, encouraged, directed, and supported me through good times and bad times to the completion of this dissertation. My appreciation is also expressed to the members of my family who encouraged me to do what I wanted to do and supported these efforts. To my wife, whose scholastic ability far out-weighs mine, for her aid in the mechanics of this paper. And to my dearest friend, Margaret, who provided care, understanding, and support for me during both a difficult and pleasant time in my life. Let him .show a brave face if he can, Let him woo fame or fortune instead - Yet there's not much to do but to bury a man When the last of his dreams is dead. TABLE OF CONTENTS CHAPTER PAGE I INTRODUCTION 1 Significance of the Study 4 Scope of the Study 7 Statement of the Problem 9 Purpose of the Study 9 Objectives of the Study 10 Design of the Study 12 Hypothesis 14 Assumptions 14 Delimitations 15 Limitations 15 Definition of Terms 16 II REVIEW OF LITERATURE 19 Introduction 19 Development of Competency Requirements for High School Graduation 20 State of the Art 30 Mathematical Competencies 33 Summary 41 III RESEARCH DESIGN 42 Introduction 42 Type of Study 42 Population and Sample 42 Instrumentation 44 Data Collection and Procedures 45 Treatment of the Data 46 Statistical Design 46 The Mathematical Model 46 Data Analysis 47 IV ANALYSIS OF THE DATA 49 Introduction 49 Findings Relative to the Hypothesis Under Investigation 51 Summary 68 V SUMMARY, FINDINGS, CONCLUSIONS AND RECOMMENDATIONS 69 Introduction 69 Summary 69 Findings 70 Conclusions 72 Discussion 74 Recommendations for Action 76 BIBLIOGRAPHY 78 APPENDICES A Letter to Don Fineran, Oregon State Depart- ment of Education Math Specialist 84 B Response from Don Fineran, Oregon State Department of Education Math Specialist 86 C Sampling Schools by Classification 89 D Delphi Committee Members 91 E Mathematical Competence Questionnaire 93 F Approved Secondary Schools in Oregon Fall of 1980 98 G Oregon School Activities Association (Revised) 110 H Letter to Building Administrators Asking Cooperation in Study 114 I List of Mathematical Competencies as Identified by A Schools 116 J List of Mathematical Competencies as Identified by AA Schools 121 K List of Mathematical Competencies as Identified by AAA Schools 125 List of Mathematical Competencies Identified as Rejected by Use of F Statistic and Mean Scores by Total Group 130 LIST OF TABLES TABLE PAGE I Total Group Means by Individual Item To Establish Levels of Acceptability 56 II Total Mean Acceptance Levels and Related Percentages 58 III Oregon's Four-Year Public Senior High Schools Classification A Mean Scores by Individual Item 59 IV Oregon's Four-Year Public Senior High Schools Classification AA Mean Scores by Individual Item 62 V Oregon's Four-Year Public Senior High Schools Classification AAA Mean Scores by Individual Item 64 VI Individual Mean Acceptance Levels and Related Percentages 66 VII Table of Rejections Based on F Probability and LSD Results 67 A STUDY OF THE MATHEMATICAL COMPETENCE REQUIREMENTS FOR GRADUATION AMONG OREGON'S A-AA-AAA SENIOR HIGH SCHOOLS CHAPTER I INTRODUCTION Prior to 1972, Oregon high school seniors received diplomas based on secondary education philosophy and guide- lines from the Oregon Board of Education. Diplomas were granted based on satisfactory attendance and course completion as well as local school options. These regula- tions concerning the awarding of the secondary school diploma had changed little since the 1920's. (27) Oregon recognized a need to study its philosophy and guidelines and applied for and was granted a study grant from the Ford Foundation in the 1960's which was later to be known as "The Oregon Program." (27) This grant allowed selected districts in Oregon to investigate their system of goal setting and competency development as a basis for their educational programs and completion requirements. In 1969, the Oregon State Department of Education sponsored a state-wide needs assessment to ascertain the views of the general public, Oregon's educators, students and dropouts, concerning the knowledge and skills needed and expected of completing twelfth graders. As the results of the needs assessment were evaluated, it became 2 evident that further researchwas necessary because of the overwhelming response for curricular change. In that same year, the Oregon Association of School Administrators pro- duced findings from their inquiries that also called for immediate change in the Oregon school curriculum and in the requirements for high school graduation. (27) Further, during the 1969-1970 academicyear, the Oregon State Board of Education and the State Superintendent of Public Instruction held Town Hall meetings in 14 Oregon cities with over two thousand citizens who expressed their educa- tional views and priorities for educational change in the state. (27) As a result of the forementioned action, the Oregon Board of Education targeted September, 1974, as a time of change for high school graduation requirements to include measurable competence for each student and to establish some general guidelines for implementation. These guidelines were based on the following assumptions: (1) Districts need freedom at the local level to adapt curriculum to the changing needs of students and sociological conditions. At the same time, districts want some general guidance as they progress toward implementa- tion of the new graduation requirements. (2) Clear goals based on student outcomes can be developed and student attainment can be measured. (3) Students should have more alternatives for meeting graduation requirements to accommo- date individual learning styles, interests, strengths, and weaknesses. Alternatives might be credit by examination, off-campus study, independent study, early and/or delayed graduation. (27) In 1972-1973 six Oregon school districts had tentatively developed guidelines for the "new" graduation requirements.

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