FOSTERING EFFECTIVE MATHEMATICS TEACHING: PROFESSIONAL COACHING AND TEACHERSʼ INSTRUCTIONAL PRACTICES AND BELIEFS By JAMES A. NEUBERGER A dissertation submitted to The Graduate School of Education Rutgers, The State University of New Jersey in partial fulfillment of the requirements for the degree Doctor of Education Graduate Program in Mathematics Education Approved by _____________________________ Carolyn A. Maher, Chair _____________________________ Alice S. Alston, Committee _____________________________ Harold R. Melnick, Committee New Brunswick, New Jersey January, 2010 c 2009 by James A. Neuberger i Abstract of the Dissertation Fostering Effective Mathematics Teaching: Professional Coaching and Teachersʼ Instructional Practices and Beliefs By James A. Neuberger Dissertation Chair: Carolyn A. Maher, Ed. D. Two decades ago the National Council of Teachers of Mathematics challenged the mathematics education community to promulgate a comprehensive set of learning goals for K-12 students that would guide mathematics curriculum, teaching, and assessment for the future. One consequence was an emphasis on professional development of teachers. Accordingly, in 2003, New York Cityʼs public schools started a math coaching program, whereby math education experts worked closely with math teachers for an extended period of time in the teachersʼ schools. This program became an opportunity for important research regarding the effectiveness of coaching This study describes the collaboration between one coach and one teacher in the implementation of the coaching system. The researcher observed and videotaped a lesson and the subsequent debriefing between the teacher and coach; and interviewed the teacher, coach, and principal. The benefit to the classroom teacher was supported by analysis of the data. The teacher reported that, for the first time, math was “fun,” she was more confident, and more class time was devoted to mathematics. The teacher paid closer attention to student work, reflected on her own practice, grouped students more beneficially, ii encouraged them to interact, and to make their thinking public. She did not view answers as just right or wrong, but rather as part of a process of making sense of ideas. The data suggest: 1. The teacher reported that some of her beliefs about math teaching had changed due to the coaching process. 2. Teacher practices mirrored teacher beliefs. There are signs that the coaching is influencing the teacherʼs practice. 3. The coach helped the teacher learn mathematics and pay attention to the math learning of her students. 4. The teacher is in a state of transition in many of her emerging beliefs, suggesting that some of them are fragile. While results of the study are promising, further research is recommended to examine long term effects of coaching with more teachers and coaches over several cycles. iii Acknowledgements The completion of this dissertation is something of a miracle. I had many obstacles to overcome, some self-imposed. One and a half years ago, I told my advisor, Carolyn Maher, that I was finally giving in to the inevitable and dropping out of the program. She would have none of it. And she was right. What I have accomplished means a great deal to me. I thank her for helping to bring that fulfillment to me and for her essential support and enthusiasm. My late mother, Marie Salant Neuberger, had an insatiable mind and would never settle for the obvious or popular answer. She also had impeccable ideals and integrity. I would like to think that she planted some seeds in me that continue to germinate. My remarkable father, Roy R. Neuberger, who is one hundred and six years old, has always encouraged me to follow my passion. I love and owe a great debt to him. I never liked school, nor was I good at it until, later in life, I studied at Bank Street College of Education. Bank Street was a wonderful place for me, and elicited skills and insights that were long buried. When I got there I was already taken with the idea of helping math teachers, but Hal Melnick was instrumental in guiding me to develop my ideas. Alice Alston contributed invaluable insights. Charlene Marchese connected me to the Melville School and helped in many ways. Of course, without the cooperation of the people who go by the names Angela, Matt, and Jane at the school, this study would have been impossible. Over the years, others have assisted me in countless ways, including Liz Uptegrove, Ralph Pantozzi, and the indispensable Marjory Palius. Lastly I want to express my profound love and gratitude to my wife, Helen Stambler Neuberger, who was always encouraging despite my resistance (and is a terrific editor); and to two old and very dear friends, the late Denis Berger, who was exuberant, insistent and persistent in his unique way; and the brilliant, supportive Mark Jacobs. iv Dedication I would like to dedicate this dissertation to the late Robert B. Davis, a superb and beloved person. He was extremely smart, but always modest. He was seemingly curious about everything. He was very generous to me. I adored him. I first considered coming to Rutgers after reading an article written by Bob (and Carolyn Maher). Bob was brilliant, but he always wanted to hear what I was thinking. That was his way. He died suddenly and much too soon, after I had known him for only three years. But his sense of curiosity, childlike in many ways, animates this program at Rutgers. I am grateful that I was able to spend as much time with him as I did, for he taught me much. For carrying on his spirit, Carolyn deserves special kudos. v Table of Contents Abstract of the Dissertation........................................................................................... ii Acknowledgements....................................................................................................... iv Dedication .................................................................................................................. v List of Figures ................................................................................................................ ix Chapter 1 Introduction ............................................................................................. 1 1.1. REGION 9........................................................................................................... 3 1.2. STATEMENT OF THE PROBLEM ............................................................................ 3 Chapter 2 Research Questions ............................................................................... 5 Chapter 3 Review of the Literature ......................................................................... 6 3.1 EDUCATION WOES.............................................................................................. 6 3.2 MATHEMATICS REFORM AND THE NCTM STANDARDS.......................................... 7 3.3 PROFESSIONAL DEVELOPMENT ......................................................................... 10 3.4 INSTRUCTIONAL PRACTICES .............................................................................. 13 3.5 KNOWLEDGE BASE FOR TEACHING.................................................................... 17 Chapter 4 Methodology.......................................................................................... 20 Chapter 5 Results ................................................................................................... 25 5.1 SUMMARY OF INTERVIEW WITH SCHOOL PRINCIPAL ........................................... 25 5.1.1 The history of the Melville School ................................................................ 25 5.1.2 The Melville School now. ............................................................................. 26 5.1.3 The math program and the coaching process. ............................................ 27 5.2 SUMMARY OF TEACHER INTERVIEWS ................................................................. 29 5.2.1 The teacherʼs background. .......................................................................... 29 5.2.2 What the teacher wanted help with from the coach..................................... 31 5.2.3 The teacherʼs impressions of coaching and its effect. ................................. 32 5.3 SUMMARY OF COACH INTERVIEWS .................................................................... 33 5.3.1 The coachʼs background.............................................................................. 33 5.3.2 What the coach wanted to work on in coaching generally and with this teacher.................................................................................... 37 5.3.3 The school and coaching............................................................................. 39 5.4 THE LESSON .................................................................................................... 40 5.4.1 Students were active during lesson............................................................. 41 5.4.2. Teacher often directive in describing tasks.................................................. 43 5.4.3 The class showed a feeling of community. .................................................. 49 5.4.3.1 Students Share Their Thinking ............................................................................ 50 5.4.3.2 Contrasts Between Students Made Public .......................................................... 50 5.4.3.3 Teaching Aide Took Active Roll........................................................................... 51 5.4.3.4 Students Encouraged To Help