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Finding Relationships Between Multiple-Choice Math Tests and Their Ts Em-Equivalent Constructed Responses Nayla Aad Chaoui Claremont Graduate University

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Finding Relationships Between Multiple-Choice Math Tests and Their Ts Em-Equivalent Constructed Responses Nayla Aad Chaoui Claremont Graduate University Claremont Colleges Scholarship @ Claremont CGU Theses & Dissertations CGU Student Scholarship 2011 Finding Relationships Between Multiple-Choice Math Tests and Their tS em-Equivalent Constructed Responses Nayla Aad Chaoui Claremont Graduate University Recommended Citation Chaoui, Nayla Aad, "Finding Relationships Between Multiple-Choice Math Tests and Their tS em-Equivalent Constructed Responses" (2011). CGU Theses & Dissertations. Paper 21. http://scholarship.claremont.edu/cgu_etd/21 DOI: 10.5642/cguetd/21 This Open Access Dissertation is brought to you for free and open access by the CGU Student Scholarship at Scholarship @ Claremont. It has been accepted for inclusion in CGU Theses & Dissertations by an authorized administrator of Scholarship @ Claremont. For more information, please contact [email protected]. Finding Relationships Between Multiple-Choice Math Tests And Their Stem-Equivalent Constructed Responses By Nayla Aad Chaoui A dissertation submitted to the Faculty of Claremont Graduate University in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate Faculty of Education Claremont Graduate University 2011 APPROVAL OF THE DISSERTATION COMMITTEE We, the undersigned, certify that we have read, reviewed, and critiqued the dissertation of Nayla Aad Chaoui and do hereby approve it as adequate in scope and quality for meriting the degree of Doctor of Philosophy. ______________________________________________________________ Dr. Mary Poplin Chair School of Educational Studies ______________________________________________________________ Dr. June Hilton Committee Member School of Educational Studies ______________________________________________________________ Dr. Phil Dreyer Committee Member School of Educational Studies Abstract of the Dissertation Finding Relationships Between Multiple-Choice Math Tests And Their Stem-Equivalent Constructed Responses By Nayla Aad Chaoui Claremont Graduate University, 2011 The study takes a close look at relationships between scores on a Mathematics standardized test in two different testing formats - Multiple-Choice (MC) and Constructed Response (CR). Many studies have been dedicated to finding correlations between item format characteristics with regards to race and gender. Few studies, however, have attempted to explore differences in the performance of English Learners in a low performing, predominantly Latino high school. The study also determined relationships between math scores and gender and math scores and language proficiency, as well as relationships between CAHSEE and CST scores. Statistical analyses were performed using correlations, descriptive statistics, and t-tests. Empirical data were also disaggregated and analyzed by gender, and language proficiency. Results revealed significant positive correlations between MC and CR formats. T-tests displayed statistically significant differences between the means of the formats, with boys and English Only students having better scores than their counterparts. Frequency tables examining proficiency levels of students by gender and language proficiency revealed differences between MC and CR tests, with boys and English Only students earning better levels of proficiency. Significant positive correlations were shown between CST scores and multiple-choice items, but none were found for CST scores and constructed response items. DEDICATION To my husband Nabil, whose patience and many sacrifices are what allowed me to complete this work uninterrupted. To my wonderful children, who thrived and finished their schooling while their mother was busy attending classes and focusing on her study. To my students, who are my biggest fans, and who accompanied me on this journey. May this work inspire you to always believe in yourselves and reach for the stars. And finally, to my parents, who instilled in me the love of learning, and taught me to appreciate culture and diversity. ACKNOWLEDGEMENTS I am indebted to my chairperson, Dr. Mary Poplin, whom I not only consider to be an invaluable source of information and guidance, but a very dear friend. I am eternally grateful for my committee members, Dr. June Hilton and Dr. Phil Dreyer, who graciously stepped in when I needed them the most. I would like to especially acknowledge Dr. Hilton, for her efforts in teaching me how to use the software to analyze the data. I want to thank Mr. Stacey Wilkins, my principal, without whom this study would not have been possible; Mrs. Valerie Cordova, our secretary, who patiently accessed scores and provided me with the necessary data; and to Mrs. Glenda Vazquez Hermosillo, our assistant principal in charge of testing, who supplied me with vital information as well. Finally, I would like to acknowledge my friends and colleagues, who were rooting for me and supporting me throughout this journey. Your kindness and consideration did not go unnoticed. vi Table Of Contents Dedication ......................................... Acknowledgements.....................................vi Table of Contents...................................vii List of Tables ......................................ix CHAPTER I INTRODUCTION ............................ 1 Overview...............................................1 Theoretical Framework..................................3 Background.............................................4 Significance Of the Topic..............................9 Research Questions....................................11 Methodology...........................................14 Summary...............................................17 CHAPTER II LITERATURE REVIEW........................18 Overview..............................................18 Constructed response Tests............................18 Multiple Choice Tests.................................23 MC versus CR items....................................27 Gender................................................36 Ethnicity and Language................................40 Scoring Rubrics.......................................43 Validity..............................................45 Guidelines for Writing MC Questions...................47 Guidelines for Writing CR Questions...................49 Effective Math Instruction............................51 CHAPTER III METHODOLOGY............................76 Overview..............................................76 Data Set..............................................77 Key Variables.........................................80 Instrumentation.......................................80 The CAHSEE Math Standards.............................87 The Math Test.........................................90 The CMC Scoring Rubric...............................100 Procedures...........................................102 CHAPTER IV RESULTS.................................104 Correlations between Percents of Correct Answers.....104 T-tests for Gender...................................105 T-tests for Language.................................106 Proficiency Levels on MC and CR Tests............107-110 Pearson Correlations between MC and CR Scores........111 Pearson Correlations by Gender and Language..........112 vii Pearson Correlations by Strand.......................113 T-tests for Gender...................................114 T-tests for Language.................................115 Pearson Correlations between CST and CAHSEE Scores...............................................116 Pearson Correlations for Gender and Language.........117 CHAPTER V CONCLUSION...............................119 Research Findings....................................120 Limitations of the Study.............................125 Implications of the Study............................126 Appendix A...........................................133 Bibliography.........................................136 viii List of Tables Table 1: Demographics of Students........................78 Table 2: Content Standards of the Mock CAHSEE............87 Table 3: CMC Scoring Rubric.............................100 Table 4: Correlations between Percents of Correct Answers on MC and CR Items......................................104 Table 5: T-test Results for the Differences between Percents of Correct Answers (Gender)....................105 Table 6: T-test Results for the Differences between Percents of Correct Answers (Language)..................106 Table 7: Proficiency Levels of 9th Graders on MC Test....107 Table 8: Proficiency Levels of 9th Graders on CR Test....108 Table 9: Comparison of Proficiency Levels of 9th graders on CAHSEE..................................................108 Table 10: Proficiency Levels of 10th Graders on MC Test..109 Table 11: Proficiency Levels of 10th graders on CR Test..109 Table 12: Comparison of Proficiency Levels of 10th graders on CAHSEE...............................................110 Table 13: Pearson Correlation between MC and CR Scores..111 Table 14: Pearson Correlations between MC and CR Questions by Gender...............................................112 Table 15: Pearson Correlations between MC and CR questions by Strand...............................................113 Table 16: T-test Results for Relationships between MC and CR scores by Gender.....................................114 Table 17: T-test Results for Relationships between MC and CR Scores by Language...................................115 Table 18: Correlations between CST and CAHSEE...........116 Table 19: Correlations between CST and CAHSEE for Gender and Language.....................................117
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