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The Effects of an Experiential Learning Course on Secondary Student Achievement and Motivation in Geometry

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The Effects of an Experiential Learning Course on Secondary Student Achievement and Motivation in Geometry University of Missouri, St. Louis IRL @ UMSL Dissertations UMSL Graduate Works 3-19-2020 The Effects of an Experiential Learning Course on Secondary Student Achievement and Motivation in Geometry Chanua Ross University Missouri- St. Louis, [email protected] Ted Gray University Missouri- St. Louis, [email protected] Follow this and additional works at: https://irl.umsl.edu/dissertation Part of the Educational Methods Commons, and the Secondary Education Commons Recommended Citation Ross, Chanua and Gray, Ted, "The Effects of an Experiential Learning Course on Secondary Student Achievement and Motivation in Geometry" (2020). Dissertations. 933. https://irl.umsl.edu/dissertation/933 This Dissertation is brought to you for free and open access by the UMSL Graduate Works at IRL @ UMSL. It has been accepted for inclusion in Dissertations by an authorized administrator of IRL @ UMSL. For more information, please contact [email protected]. Running head: EFFECTS OF AN EXPERIENTIAL GEOMETRY COURSE 1 The Effects of an Experiential Learning Course on Secondary Student Achievement and Motivation in Geometry Ted Gray M.Ed., Information Science and Learning Technologies, University of MO-Columbia, 2007 B.S., Biochemistry, University of MO-Columbia, 2001 Chanua Ross M.Ed., Educational Administration, Lindenwood University, 2000 B.S., Education, University of MO-St. Louis, 1998 A Co-Authored Dissertation submitted to The Graduate School at the University of Missouri-St. Louis in partial fulfillment of the requirements for the degree Doctor of Education with an emphasis in Educational Practice. May 2020 Dissertation Committee Charles Granger, Ph. D. chairperson Keith Miller, Ph. D. Helene Sherman, Ed. D. Copyright 2020, Ted Gray and Chanua Ross EFFECTS OF AN EXPERIENTIAL GEOMETRY COURSE 2 ABSTRACT In 2012, the President’s Council on the Advancement of Science and Technology (PCAST) predicted one million jobs in the fields of science, technology, engineering, and math (STEM) would go unfilled in the United States due to the lack of interested and qualified graduates matriculating in American universities, colleges, and technical schools (PCAST, 2012). In order to bolster interest and proficiency in STEM, research suggests instructional pedagogy incorporate experiential learning focused on solving real societal problems that are relevant to learners. Few studies have investigated the effects of such pedagogy within the context of a secondary-level, geometry course. A quantitative, quasi-experimental design was employed to determine the effect of an experiential learning course, Geometry In Construction, on secondary student achievement and motivation in geometry. Data were collected from 181 secondary students in ninth and tenth grade attending a large, suburban, Midwestern, public high school. Participants experienced a full academic year of instruction in either Geometry In Construction or a traditional geometry course. Achievement in geometry was measured using scores from a Missouri Geometry End of Course Practice Exam. Motivation to learn geometry was measured using John Keller’s Course Interest Survey (Keller, 2010) based on Keller’s ARCS model of motivation (Keller, 1987a). Analysis of the data indicates significantly higher achievement in geometry and motivation to learn geometry for students experiencing the Geometry in Construction curriculum. The effect is more pronounced among females. On this basis, it is recommended that geometry curricula incorporate experiential learning focused on solving real problems that are relevant to EFFECTS OF AN EXPERIENTIAL GEOMETRY COURSE 3 learners. Further research is needed to determine how this instructional model could be applied to other courses in order to improve interest and preparation for STEM careers. EFFECTS OF AN EXPERIENTIAL GEOMETRY COURSE 4 TABLE OF CONTENTS Abstract………………………………………………………………………………… 2 List of Figures………………………………………………………………………….. 7 List of Tables…………………………………………………………………………... 10 Acknowledgments………………………………………………………………………12 Dedications…………………………………………………………………………….. 13 Chapter One: Introduction……………………………………………………………... 14 Background……………………………………………………….......... 15 Purpose………………………………………………………................. 17 Research Questions…………………………………………………….. 18 Hypotheses……………………………………………………………... 19 Significance……………………………………………………………..19 Limitations……………………………………………………………... 21 Delimitations…………………………………………………………… 21 Definitions of Terms…………………………………………………… 23 Organization……………………………………………………………. 25 Chapter Two: Literature Review………………………………………………………. 27 Theoretical Framework………………………………………………… 27 Attention, Relevance, Confidence, and Satisfaction (ARCS) Model of Motivation……………………...…………………………… 27 Origin of ARCS……………………………………………....... 28 ARCS Model…………………………………………………… 29 Related Research……………………………………………….. 33 Motivation……………………………………………………………… 34 Motivational Constructs Influencing STEM…………………… 34 Expectancy-Value Theory……………………………………... 36 Attribution Theory……………………………………………... 37 Social Cognitive Theories……………………………………… 38 Goal Orientation Theory……………………………………….. 38 Self-Determination Theory…………………………………...... 39 Motivating STEM Learners Through Experience- Constructivism…………………………………………………. 40 Mathematics Pedagogy and Achievement……………………………... 43 Instructional Practices in U.S. Mathematics Classrooms……… 44 Current State of Mathematics Achievement in the U.S………... 47 Research-Based Mathematics Pedagogy………………………. 52 EFFECTS OF AN EXPERIENTIAL GEOMETRY COURSE 5 Experiential Mathematics Instruction………………………….. 56 Geometry in Construction (GIC)………………………. 57 Algebra I in Manufacturing Processes, Entrepreneurship, and Design (AMPED)……………… 58 Drama-Based Geometry………………………………...59 Mathematics Achievement and the Underrepresentation of Women in STEM………..……………………………………... 61 Summary……………………………………………………….. 66 Chapter Three: Methodology…………………………………………………………... 68 Research Design………………………………………………………...68 Internal Threats to Validity…………………………………….. 70 External Threats to Validity……………………………………. 72 Research Questions…………………………………………………….. 72 Hypotheses……………………………………………………………... 73 Population and Sample………………………………………………… 74 Instrumentation………………………………………………………… 77 Achievement in Geometry..…………………………………..... 77 Motivation to Learn Geometry………………………………… 82 Data Collection………………………………………………………… 85 Ethics and Human Relations…………………………………… 87 Data Analysis…………………………………………………………... 88 Limitations……………………………………………………………... 92 Conclusion……………………………………………………………... 94 Chapter Four: Findings………………………………………………………………… 96 Data Description……………………………………………………….. 98 Data Analysis…………………………………………………………... 98 Results………………………………………………………………….. 100 Achievement in Geometry..…………………………………..... 103 Motivation to Learn Geometry………………………………… 108 Summary……………………………………………………………….. 121 Chapter Five: Conclusion……………………………………………………………… 122 Summary of Findings………………………………………………....... 122 Conclusions…………………………………………………………….. 124 Discussion of Implications……………………………………………... 125 Women in Stem……………….………………………………...125 Conclusion 1……………………………………….…………... 126 Conclusion 2……………………………………….…………... 131 Conclusion 3……….…………………………………………... 131 EFFECTS OF AN EXPERIENTIAL GEOMETRY COURSE 6 Recommendations for Practitioners……………………………………. 134 Recommendations for Future Research………………………………... 136 Concluding Remarks………………………………………………........ 137 References……………………………………………………………………………… 139 Appendices……………………………………………………………………………... 158 Appendix A: Comparison of Missouri Learning Standards to Common Core Standards for Geometry…………………...……..... 158 Appendix B: 2018 Missouri Geometry End of Course Practice Exam... 165 Appendix C: John Keller’s Course Information Survey……………...... 177 Appendix D: Statistical Analyses of Assumptions Passed for ANCOVA………………...……………………………... 182 Appendix E: Statistical Analyses of Assumptions Passed for t-tests..… 191 Appendix F: Statistical Analyses of Nonparametric Distributions of Motivation Data………………………..………………… 202 EFFECTS OF AN EXPERIENTIAL GEOMETRY COURSE 7 LIST OF FIGURES Figure 1. The three essential elements of each motivational category of the ARCS model………………………………………………………………………... 31 Figure 2. Contemporary theories of motivation………………………………………... 35 Figure 3. Percentage of fourth grade students and eighth grade students scoring at or above proficient on the NAEP Mathematics Test………...…………………..48 Figure 4. Average scores of fourth and eighth grade students on the NAEP Mathematics Test…………………………..…………………………….…... 48 Figure 5. Average scores of U.S. 15-year-old students on the PISA Mathematics Literacy Scale……………………………………………………….…….......50 Figure 6. Average scores of U.S. fourth and eighth grade students on the TIMSS Mathematics Test……………..…………………………………….………... 50 Figure 7. Visual model of nonequivalent pretest and posttest control-group design…... 70 Figure 8. Comparison of key curricular components of Geometry In Construction and traditional geometry…………………….……………………………………. 77 Figure 9. Motivation scores of treatment and control groups………………………….. 127 Figure 10. Motivation scores of females………………………………………………..127 Figure 11. Achievement scores in geometry: Comparison by gender and group……... 132 Figure 12. Achievement scores in geometry: Comparison by group…………………..133 Figure D1. Distribution of treatment group geometry EOC exam scores by gender….. 183 Figure D2. Distribution of treatment group algebra I EOC exam scores by gender…... 184 Figure D3. Distribution of control group geometry EOC exam scores by gender…...... 184 Figure D4. Distribution of control group algebra I
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