Lawrence Joseph Pleet for the Degree of Doctor of Philosophy in Mathematics Education Presented on November 6
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AN ABSTRACT OF TilE THESIS OF Lawrence Joseph Pleet for the degree of Doctor of Philosophy in Mathematics Education presented on November 6. 1990. Title: The Effects of Computer Granhics and Mira on Acquisition of Transformation Geometry Concepts and Development of Mental Rotation Skills in Grade Eight Signature redacted for privacy. Abstract approved: Thomas P. Evans The purpose of this study was to investigate: (1) whether the use of the Motions computer program will be more effective in the acquisition of transformation geometry concepts in eighth-grade students than the use of the Mira hands-on manipulative, (2) whether the use of the Motions computer program will be more effective in the development of mental rotation skills in eighth-grade students than the use of the Mira hands-on manipulative, and (3) possible sex differences resulting from the use of the Motions computer program or the use of the Mira, hands-on manipulative in the acquisition of transformation geometry concepts by eighth-grade students. The study included 15 teachers at 15 different junior high schools teaching 560 students.The study sample consisted of 16 classes, eight classes in each of the two experimental groups. There were 14 classes in the testing effect control group. Eightteachers each taught a Motions class and a Mira class. The remaining seven teachers taught two control classes each. The subjects were pretested and posttested with The Card Rotations Test from the Kit of Factor-Referenced Tests and the researcher-designed Transformation Geometry Achievement Test.The subjects were also administeredtheresearcher-designedComputerExperience Questionnaire. During the period of time between the pretests and the posttests, the experimental group subjects studied a three-week series of lessons on transformation geometry concepts.To check for a possible mental rotation testing effect, the control group subjects studied a three- week unit on fractions and decimals. Data were analyzed by analysis of covariance.With regard to mathematics achievement of transformation geometry concepts, the analysis revealed no significant difference between the class means: (1) of the Mira and the Motions groups, (2) of the females in the Mira and the Motions groups, and (3) of the females in either the Mira, or Motions groups and of the males in either the Mira or Motions groups. A significant difference, at the 0.05 level, was found between the mean of the males in the Mira and the Motions groups. With regard to mental rotation ability, the analysis revealed no significant difference between the class means: (1) of the Mira and the Motions groups, (2) of the males in the Mira and the Motions groups, and (3) of the females in the Mira, and of the Motions groups. © Copyright by Lawrence Joseph Pleet November 6, 1990 All Rights Reserved The Effects of Computer Graphics and Mira on Acquisition of Transformation Geometry Concepts and Development of Mental Rotation Skills in Grade Eight by Lawrence Joseph Pleet A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Completed November 6, 1990 Commencement June 1991 ACKNOWLEDGEMENTS This dissertation is dedicated to the loving memory of Joseph F. and Harriette D. Pleet, the author's parents, whose love, guidance, and generosity have continued to nourish and sustain him throughout his life. May the good Lord bless them always. The author wishes to express his sincerest gratitude and appreciation to the following persons, who have given him encouragement, understanding, and guidance throughout his doctoral program and especially during the completion of this dissertation: To Professor Thomas P. Evans, the author's advisor and friend, for his many hours of dedicated help and thoughtful assistance in seeing this dissertation come to fruition. To Professors Thomas Dick, Margaret Niess, and Jake Nice for their generous time and kind efforts on the author's behalf. To Professor Norman Lederman for his interest, encouragement, expertise, and friendship. To Professors Howard L. Wilson and Carvel Wood for their friendship, counseling, encouragement, and support throughout the author's studies at Oregon State University. Special appreciation is offered to the following members of the Los Angeles Unified School District: To Dr. Tony E. Rivas, former Superintendent, Administrative Region F, and to Dr. Robert C. Reimann, former Director of Instruction, Administrative Region F, for their sincere and warm friendship, and for their kind encouragement and assistance with the preparation for the study. To the junior high school principals and administrative staffs of Administrative Region F, for their interest and enthusiasm, and for their tremendous help with supervision during the experimental period of the study. To the junior high school teachers and students of Administrative Region F,for their dedication to mathematics and enthusiastic participation in the study. To Dr. Ebrahim Maddahian, Program Evaluation and Assessment Branch, for his time and efforts in helping to compile and interpret the data. To Donna Jorgensen, Les Winters, Sara Munshin, and Les Leibovitch of the Office of Secondary Instruction for their kind encouragement and help in the preparation and evaluation of the instructional units and criterion instruments for the study. Finally, the author would like to express his sincere gratitude to the following persons: To Norman J. Gillespie, the inventor of the Mira hands-on manipulative, for his interest in the study and for his generous donation of materials. To Patrick W. Thompson, the creator of Motions: A Micro world for Exploring Motion Geometry, for his interest in the study and for his permission to replicate and use his computer program. To Dr. Lorraine L. Foster, Professor of Mathematics, California State University Northridge, for considerable assistance in the preparation of this manuscript on the Macintosh. TABLE OF CONTENTS Page INTRODUCTION 1 Historical Background 1 Importance of the Study 3 The Importance of Spatial Abilities 5 Assumptions 9 Purpose of the Study 10 Statement of Hypotheses 10 Definition of Terms 12 Limitations 13 Delimitations 13 Design of the Study 14 Organization of the Remainder of the Study 15 REVIEW OF THE LITERATURE 16 The Definition of Spatial Visualization/Mental Rotation Ability 16 Enhancing Spatial Visualization Ability by Course Work, Training, and Practice 18 Using Computer Graphics to Improve Spatial Visualization Ability Using Mampulatives to Improve Spatial Visualization Ability 31 The Need for Informal Hands-On Activities in Geometry 39 The Relationship Between the Study of Transformation Geometry Concepts and Spatial Visualization Ability 41 The Need for Computers in the Study of Transformation Geometry Concepts 45 The Relationship Between Mathematics Achievement and Spatial Visualization Ability 48 Sex-Related Differences in Spatial Visualization Ability 53 Summary of the Theoretical Framework 57 T.HE STUDY 59 Hypotheses 59 Selection of the Computer Program and the Manipulative 61 Description and Rationale for Use of the Motions Computer Program 61 Description and Rationale for Use of the Mira Hands-On Manipulative 64 Criterion Instruments 66 Page The Card Rotations Test The Transformation Geometry Achievement Test The Computer Experience Questionnaire The Experiment Experimental Design Procedures Preliminary Preparations Outline of the Study Statistical Analysis of the Data Summary RESULTS OF THE STUDY 76 Sample and Sample Characteristics 76 Method of Statistical Analysis 78 Design of the Study 81 Preliminary Findings 82 Analysis and Disposition of Null Hypotheses 86 First Null Hypothesis 87 Second Null Hypothesis 90 Third Null Hypothesis 92 Fourth Null Hypothesis 96 Fifth Null Hypothesis 99 Findings Not Directly Related to the Hypotheses 103 Place Where Student First Learned to Use the Computer 106 Grade in Which Student First Learned to Use the Computer 107 Use of Computer in Mathematics Class 108 Students Who Have Studied BASIC 108 Students Who Have Studied Logo 109 Summary 110 Findings Directly Related to the Hypotheses 110 Findings Not Directly Related to the Hypotheses 112 SUMMARY, CONCLUSIONS, DISCUSSION, AND RECOMMENDATIONS 114 Summary 114 The Problem 114 Design of the Study 115 Procedure 115 Results Directly Related to the Hypotheses 117 Results Not Directly Related to the Hypotheses 119 Conclusions and Discussion 119 Recommendations for Practice and Further Study 125 Practice 125 Page Further Study 125 BIBLIOGRAPHY 1 APPENDICES Appendix A.Summary of Group Means on Criterion Tests 141 Appendix B.Summary of School Means on Criterion Tests 143 Appendix C.The Transformation Geometry Achievement Test 145 Appendix D.The Computer Experience Questionnaire 150 Appendix E.List of Instructional Units 153 Appendix F.Sample Instructional Unit Using the Mira to Teach About Reflections 155 LIST OF FIGURES Title Page The Effect Upon the Plane ofF 70 63 The Effect Upon the Plane of T 30 100 64 The Effect Upon the Plane of R 130 64 Sample Card Rotations Test 67 LIST OF TABLES Table Page Comparison of Sample Class Sizes 77 Comparison of Class Means on Mathematics Achieve- ment Pretest 78 ComparisonofClassMeansonMathematics Achievement Posttest 79 Comparison of Class Means on Mental Rotation Pretest 80 Comparison of Class Means on Mental Rotation Posttest 81 Descriptive Statistics for Covariates and Dependent Variables on Mathematics Achievement and Mental Rotation Pretests 83 Descriptive Statistics for Covariates