The University of San Francisco USF Scholarship: a digital repository @ Gleeson Library | Geschke Center Master's Theses Theses, Dissertations, Capstones and Projects 1996 The Effects of the Geometer's Sketchpad Software on Achievement of Geometric Knowledge of High School Geometry Students Margaret Lynn Lester Follow this and additional works at: https://repository.usfca.edu/thes Part of the Education Commons The University of San Francisco THE EFFECTS OF THE GEOMETER'S SKETCHPAD SOFTWARE ON ACHIEVEMENT OF GEOMETRIC KNOWLEDGE OF HIGH SCHOOL GEOMETRY STUDENTS A Dissertation Presented to The Faculty of the School of Education Private School Education Program In Partial Fulfillment Of the Requirements for the Degree of Doctor of Education by Margaret Lynn Lester, BVM San Francisco May, 1996 .0 ~~ ;t~\~<f> This dissertation, written under the direction of the candidate's dissertation committee and approved by the members of the committee, has been presented to and accepted by the Faculty of the School of Education in partial fulfillment of the requirements for the degree of Doctor of Education. ~Mb=~/10( Candidate Date Dissertation Committee Mathew Mitchel Ph.D. Chairperson Macy Peter Trayjss op Ph.D In~£&~ tPI? William Schwarz, Ph 0 ~~~ Keyjna Keating CCVI Ed 0 .j~-~~ ii TABLE OF CONTENTS LIST OF TABLES ............................................................................................... viii LIST OF FIGURES............................................................................................ X CHAPTER I THE RESEARCH PROBLEM.................................................................. 1 Statement of the Problem................................................................. 1 Purpose of the Study......................................................................... 3 Definition of Terms............................................................................. 4 Background and Need for the Study.............................................. 8 Theoretical Rationale........................................................................ 24 Summary............................................................................................. 30 Research Questions.......................................................................... 31 Research Hypotheses....................................................................... 32 CHAPTER II REVIEW OF RELATED LITERATURE.................................................... 35 Section One................................................................................................ 38 Application of Cognitive Science to Learning Theory ................... 38 Applications of Cognitive Theory to Software Design ................... 40 Applications of Constructivist Theory to Instructional Design ...... 43 iii Section Two................................................................................................. 50 Experimental Research Studies on the Geometric Supposers ... 53 Supposer Research Studies on Learners ....................................... 54 Supposer Research Studies on Teachers ...................................... 58 Experimental Research Studies on the Geometer Sketchpad.... 61 Summary ...................................................................................................... 72 CHAPTER Ill METHODOLOGY........................................................................................ 75 Purpose of the Study ........................................................................... 75 Description of Design .......................................................................... 76 Dependent Variables.......................................................................... 80 Instrumentation........................................................................ 83 Posttest Validity ........................................................................ 84 Posttest Reliability................................................................... 85 Independent Variable......................................................................... 87 Classroom Lesson Sample................................................... 88 Classroom Lesson Procedure.............................................. 89 Description of Subjects...................................................................... 95 Description of Procedures................................................................ 1 01 Data Collection ................................................................................... 1 07 Data Sources ...................................................................................... 1 07 Data Analysis ...................................................................................... 1 08 iv CHAPTER IV RESULTS .................................................................................................. 111 Overview of Design and Variables................................................. 111 Quantitative Analysis of Statistical Data........................................ 112 Operational Research Hypothesis 1 ............................................ 114 Results for Hypothesis 1...................... .......................................... 115 Operational Research Hypothesis 2 ............................................ 121 Results for Hypothesis 2...... ..... .......... ........................................... 121 Further Analysis of Student Conjectures ....................................... 125 Summary ............................................................................................. 135 CHAPTERV SUMMARY, LIMITATIONS, DISCUSSION, AND RECOMMENDATIONS.................................................................. 140 Summary.......................................................................................... 140 Limitations........................................................................................ 142 Conclusions..................................................................................... 148 Restatement of the Purpose ................................................. 148 Research Question 1............................................................. 149 Research Question 2 ............................................................. 150 Significance ..................................................................................... 153 Conjecture Posttest Sample Problem............................... 154 Conjecture Posttest Directions ............................................ 154 Conjecture Posttest Sample Solutions .............................. 156 v Previous Research Studies and The Present Study ................ 161 Theoretical Implications on Conjecturing ................................... 163 Recommendations for Future Research..................................... 165 Recommendations for Future Practice ........................................ 170 Vision for Future Geometry Environments .................................. 171 REFERENCES ................................................................................................ 173 APPENDIXES ................................................................................................. 184 Appendix A: Posttest ............................................................................ 185 Appendix 8: Investigation Sheet Sample....................................... 186 Appendix C: Posttest Validation Panel Members .......................... 187 Appendix 0: Posttest Validation Form ............................................. 191 Appendix E: Copyright Permission for Screen Captures............. 193 Appendix F: Posttest Scores on Geometric Knowledge............. 194 Appendix G: Posttest Scores on Geometric Construction........... 197 Appendix H: Third Quarter Geometry Grades................................ 200 Appendix 1: Posttest Scores on Conjectures................................ 203 Appendix J: Transcript of Student Interviews................................ 206 vi Appendix K: Commentary and Instruction of Study ...................... 218 Appendix L: Lesson Plans of Study............................................... 224 Appendix M: Letter of Permission to Conduct the Study............. 235 Appendix N: Graph of Posttest Scores on Conjectures.............. 236 Appendix 0 Copyright Permission for Chapter Six Test............ 238 vii LIST OF TABLES Table Page 1. Number of Subjects in Each Ethnic Group ................................... 96 2. Number of Subjects in Each Age Group ....................................... 97 3. Semester Grades of Subjects in Experimental Group ............... 99 4. Semester Grades of Subjects in Control Group ........................ 100 5. Correlation Coefficients Between Third-Quarter Grades and Posttest Scores ................................................................................ 114 6. Mean Scores and Standard Deviations for Hypothesis 1 Geometric Knowledge .................................................................... 116 7. Mean Scores and Standard Deviations for Hypothesis 1 Geometric Construction ................................................................. 117 8. Univariate and Analysis of Covariance for Hypothesis 1 Geometric Knowledge .................................................................... 120 9. Mean Scores and Standard Deviations for Hypothesis 2 Geometric Conjectures .................................................................. 122 10. Univariate and Analysis of Covariance for Hypothesis 2 Geometric Conjectures.................................................................