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Mathematics Experience: Contributing Factors To MATHEMATICS EXPERIENCE: CONTRIBUTING FACTORS TO THE MATH ANXIETY AND AVOIDANCE BEHAVIORS OF FEMALE ELEMENTARY SCHOOL PRE-SERVICE TEACHERS by DAVID S. ALLEN, B.S.Ed., M.Ed. A DISSERTATION IN CURRICULUM AND INSTRUCTION Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF EDUCATION Approved August, 2001 ACKNOWLEDGEMENTS There are several people who deserve recognition for their support and contributions to this document. I am most grateful to my committee members. Dr. William Lan has provided many new insights into the world of statistical analysis. He was always willing to provide a few seconds of his time whenever asked, even if those few seconds turned into lengthy statistical review sessions. Dr. Larry Hovey has helped guide me through a rigorous program during my studies and has provided many opportunities for me as a student that may not have been available to me had he not been interested in my success. Dr. Charles Geer provided a measure of stability at all the right times. His gentle pushing and constant reminders of deadlines helped to ensure that I never failed to be prepared at the appropriate time. When I began to feel overwhelmed I could always count on a gentle smile and sound advice. His guidance and thought provoking questions have contributed greatly to the quality of this document. I can only hope that as I begin a new aspect of my own career I can contribute as much to my future doctoral students as these individuals have to me. I would also like to take the opportunity to thank Dr. Sandi Cooper for leaving her door open for me at all times. She has always been available to listen to my crazy ideas and help me to put order into my thinking. Dr. Camille Debell deserves more credit than I can give her here. She has provided support and advice to numerous graduate students in the College of Education and has been a wonderful colleague and friend. I would also like to thank Dr. Cari Sequist for his interest and support of this document. Perhaps most important to the success I have achieved in the doctoral program, as represented through this document, was the love and support I received from my family. My wife Jene' deserves a great deal of the credit for this accomplishment. I would like to take this opportunity to say thank you for many wonderful years together and for making the last five years possible. I would also like to acknowledge the sacrifices of my daughters Janalea and Landree. Thank you for your understanding and cooperation during those much-needed naps following the all night writing sessions. Your patience and love are greatly appreciated. There are a number of other individuals whose contributions are noteworthy. John Lowry and Betty Johnson should be acknowledged here as they set my feet on this path many years ago although I did not know it at the time. In addition, I would like to acknowledge the contributions of Donna Gee, Mark Jamison, Cindy Able, and Louis Salcedo who all had input into the direction of my future. I would like to recognize the contributions of the students' enrolled in elementary education cohorts 003 and 004 during the spring semester of 2000. Without their contributions this document would not have had a beginning. Finally, I would like to thank my parents. They have always seen in me the desire and determination to be successful. Their faith in me never failed even as my own confidence was low. TABLE OF CONTENTS ABSTRACT vi LIST OF TABLES viii LIST OF FIGURES ix CHAPTER 1. GENERAL NATURE AND PURPOSE OF THE STUDY 1 Introduction 1 Statement of the Problem 2 Significance of the Study 2 Predictions 3 Assumptions 6 Limitations of the Study 6 Definition of Terms 7 Summary 10 II. REVIEW OF THE LFFERATURE 12 Gender Differences 12 Writing in Mathematics 16 Math Anxiety, Math Avoidance, and Pre-Service Teachers 20 Mathematical Experiences and Anxiety 21 Teacher Interactions 22 Pedagogical Practices 26 Mathematical Content 34 Reducing Math Anxiety Levels 37 Math Anxiety and Other Constmcts 38 Summary 42 III. RESEARCH METHODOLOGY 44 Purpose Statement and Predictions 44 Population and Sample 45 Research Design 46 Instrumentation 47 Data Collection Procedures 58 Analysis of Data 60 Summary 60 IV. RESULTS 62 Descriptive Statistics 62 Prediction One 70 Prediction Two 73 Prediction Three 74 Prediction Four 81 Summary of Findings 86 V. DISCUSSION 91 Overview of the Study 91 Discussion of Findings 95 Prediction One 95 Prediction Two 97 Prediction Three 98 Prediction Four 99 Educational Implications 100 Future Research 102 Conclusion 104 REFEERENCES 105 APPENDIX A. MEASUREMENT SCALES 111 B. MATHEMATICAL EXPERIENCE QUESTIONNAIRE 114 C. SAMPLE MATHEMATICS AUTOBIOGRAPHY 120 ABSTRACT Math anxiety is prevalent among citizens of our country, yet nowhere is it more prominent than in America's classrooms. Elementary school teachers hesitate to teach difficult, abstract concepts while students straggle to make sense of the manipulation of numbers and symbols. These struggles perpetuate the negative attitudes towards mathematics and promote math anxiety and avoidance behaviors. The purpose of this study was to identify factors that contribute to the development of math anxiety in female elementary school pre-service teachers and assess the relationship between math anxiety and math avoidance behaviors. Initial examination of 43 mathematics autobiographies identified mathematical experiences in ten separate categories. Three categories, students' experiences with math teachers, math content, and math pedagogical practices, were used to develop experience scales for these constracts. A fourth scale was developed to measure experiences with math avoidance behaviors. Math anxiety was measured using the Revised Math Anxiety Scale. A correlation matrix compared the participants' scores on the four experience scales with math anxiety. A regression analysis was conducted to determine if participants' experience with math content, math teachers, or pedagogical practices in the math classroom could be identified as predictors of math anxiety. Finally, additional regression analyses were conducted to identify math anxiety and experiences with math teachers. VI math content, and pedagogical practices in math classrooms as predictors for math avoidance behaviors. Math specialization participants and those participants specializing in other areas were analyzed separately. Results indicated a strong correlation between math anxiety and participants' mathematical content experiences for both groups. Moderate correlations w ere found for math anxiety and participants' experiences with math teachers for both groups. Math specialization participants' math anxiety was not significantly correlated with pedagogical experiences in the mathematics classroom. Non-math specialization participants' math anxiety levels were slightly correlated with pedagogical experiences in the math classroom. The results of the regression analysis identified experiences with mathematical content as a significant predictor of math anxiety for both math specialization participants and those who selected a specialization other than mathematics. Additional regression analysis identified math anxiety and participants' experiences with math content as significant predictors of math avoidance behaviors. LIST OF TABLES 3.1 Categories resulting from open coding process 49 3.2 Categorical experiences and number of occurrences 53 ?*.? Reliability coefficients for five scales 59 4.1 Reliability coefficients for Mathematics Experience Scales 63 4.2 Descriptive statistics for math and non-math specialization 65 4.3 ANOVAs-Comparison of mean scores on MEQ 66 4.4 Levene's Test for equality of variances 68 4.5 Independent t-test - Comparison of mean scores on MEQ 69 4.6 Correlation coefficients for anxiety and Mathematics Experience Scales 71 4.7 ANOVA - Anxiety linear regression analysis for math specialization participants 76 4.8 Anxiety regression coefficients for math specialization participants 77 4.9 ANOVA - Anxiety linear regression analysis for non-math specialization participants 79 4.10 Anxiety - Regression coefficients for mathematics specialization participants 80 4.11 ANOVA - Avoidance linear regression analysis for math specialization participants 82 4.12 Avoidance - Regression coefficients for mathematics specialization participants 83 4.13 ANOVA - Avoidance linear regression analysis for non-mathematics specialization participants 85 4.14 Avoidance - Regression coefficients for non-mathematics specialization participants 87 Vlll LIST OF FIGURES 1.1 Model of predictive relationships of mathematical experience, anxiety and avoidance 5 2.1 Outline of grade level clusters and respective instructor behaviors 23 IX CHAPTER 1 GENERAL NATURE AND PURPOSE OF THE STUDY Introduction In light of the recent trend to move mathematics education into the realm of a constructivist paradigm (National Council of Teachers of Mathematics, 2000), the community of mathematics educators has begun to focus upon the development of teachers who can facilitate the learning of mathematics in a constractivist manner. The National Council of Teachers of Mathematics (NCTM) recommends instractional methods that encourage learning mathematics with more emphasis on conceptual understanding and less emphasis on remembered knowledge. The development of mathematical understanding rests upon the idea that teachers can provide students with the opportunity to experience mathematics in authentic situations
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