The Effectiveness of the National Board Certification As It Relates to the Advanced Placement Calculus AB Exam
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The Effectiveness of the National Board Certification as it Relates to the Advanced Placement Calculus AB Exam by Fernando Antunez A Dissertation Submitted to the Faculty of The College of Education In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Florida Atlantic University Boca Raton, FL December 2015 Copyright 2015 by Fernando Antunez ii Acknowledgements I would like to acknowledge my dissertation chair who has worked with me relentlessly throughout the entire project. Dr. Furner’s patience, expertise, and attention to detail played a major role in the completion of my dissertation. I also want to acknowledge my other committee members, Dr. John Morris, Dr. Emery Hyslop- Margison, and Dr. Traci Baxley for the time and incredible dedication in assisting me to complete my dissertation. I greatly appreciate Dr. Burnaford’s expertise and support. She has been an inspiration and has taught me how to effectively do research. She also guided me to complete my literature review at a very special time of my doctoral degree. Immeasurable thanks to my friend Lawrence Moorman for helping me stay focused and persevere and for acting as an unparalleled encourager throughout my dissertation. I would like to thank the research office of the participating school district for granting me permission to conduct this research. I would like to express special thanks to Beth Tillman and Jack Ciminera for their continuous help in assisting me to properly have all required paperwork processed and also for providing me with the data in such an efficient manner. Finally, I would like to thank Harvard University Professor and personal friend Dr. Natesh Pillai for his support and guidance toward the completion of my dissertation. iv Abstract Author: Fernando Antunez Title: The Effectiveness of the National Board Certification as it Relates to the Advanced Placement Calculus AB Exam Institution: Florida Atlantic University Dissertation Advisor: Dr. Joseph Furner Degree: Doctor of Philosophy Year: 2015 This study compared data related to National Board Certification (NBC) of mathematics teachers in a South Florida school district. Data included 1,162 student scores on the 2014 AP Calculus AB exam, student gender, student grade level, and eligibility for free or reduced price lunch (FRL) status. Teachers completed the Standards’ Beliefs Instrument (SBI) (Zollman & Mason, 1992) to determine alignment of their beliefs with the National Council of Teachers of Mathematics (NCTM) standards. Interviews were conducted with five NBC mathematics teachers to understand how they incorporate best mathematics teaching practices in their daily instruction. A t-test analysis revealed that students taught by NBC teachers scored significantly higher (M = 3.70) on the AP Calculus AB Exam than those taught by non- NBCTs (M = 2.74); Cohen’s d (.6429) indicated a moderately large effect size. No causation is to be implied; various confounding factors may also contribute to the variance in student scores. v Three factorial ANOVA tests were performed to test interaction effects. Two significant interaction effects were detected: (1) NBCT status and student grade level; and (2) NBCT status and student FRL (free and reduced price lunch) status. No significant interaction was found between NBCT status and student gender. With a reliability estimate using Cronbach’s alpha, a second t-test was conducted. A statistically significant difference was found regarding the mean scores of NBCTs and non-NBCTs regarding their beliefs according to the vision of the NCTM. NBCTs generally have practices that align more with the NCTM mathematics teaching standards. Interviews with five NBC teachers of AP Calculus provided rich qualitative descriptions of their teaching philosophies, approaches, and best practices contributing to student success. The results of this study reinforce evidence from previous research that the process of obtaining the NBC contributes to a teacher’s professional expertise and is related to student success; however, since there may be other confounding factors related to teachers, students, and their schools, the NBC cannot be considered the sole factor contributing to student success in AP coursework and exams. vi The Effectiveness of the National Board Certification as it Relates to the Advanced Placement Calculus AB Exam List of Tables .................................................................................................................... xii List of Figures .................................................................................................................. xiv Chapter 1. Introduction ....................................................................................................... 1 Statement of the Problem ................................................................................................ 4 Purpose of the Study ....................................................................................................... 7 Research Questions ......................................................................................................... 7 Hypotheses ...................................................................................................................... 7 Definition of Terms ......................................................................................................... 8 Limitations .................................................................................................................... 11 Significance of the Study .............................................................................................. 12 Organization of Dissertation ......................................................................................... 13 Summary ....................................................................................................................... 13 Chapter 2. Literature Review ............................................................................................ 15 Introduction ................................................................................................................... 15 The National Board Certification .................................................................................. 16 Teacher Certification ..................................................................................................... 29 vii Best Practices in Teaching Secondary Mathematics ..................................................... 39 The nature of high school math. ................................................................................ 39 Issues of mathematics performance. .......................................................................... 40 Issues with AP math .................................................................................................. 42 Gender, Race, and Equity in Mathematics .................................................................... 44 Mathematics Standards ................................................................................................. 50 National Council of Teachers of Mathematics (NCTM) ........................................... 52 The Role of the National Board for Professional Teaching Standards (NBPTS). .... 56 Studies of Best Mathematics Practices.......................................................................... 57 The Relationship Between Best Practices and AP Math Teaching ............................... 69 Historical Background of AP Math Classes .................................................................. 72 AP Calculus. .............................................................................................................. 73 AP Statistics. .............................................................................................................. 77 Relationship Between the NBC and Best Teaching Practices ...................................... 79 Discussion ..................................................................................................................... 82 Conclusion ..................................................................................................................... 87 Summary ....................................................................................................................... 93 Chapter 3. Research Methodology .................................................................................... 96 Introduction ................................................................................................................... 96 Sampling Plan, Instrumentation, and Data Collection .................................................. 97 viii Subjects ....................................................................................................................... 100 Research Design .......................................................................................................... 101 Hypothesis Test # 1. ................................................................................................ 101 Hypothesis Test # 2. ................................................................................................ 102 Hypothesis Test # 3. ................................................................................................ 102 Hypothesis Test # 4. ................................................................................................ 102 The Standards’ Beliefs Instrument (SBI) ...................................................................