EXPLORING BELIEFS AND PRACTICES OF TEACHERS OF SECONDARY MATHEMATICS WHO PARTICIPATED IN A STANDARDS-BASED PRE-SERVICE EDUCATION PROGRAM Except where reference is made to the work of others, the work described in this dissertation is my own or was done in collaboration with my advisory committee. This dissertation does not contain any proprietary information. _____________________________________ Mary Alice Smeal Certificate of Approval: W. Gary Martin Marilyn E. Strutchens, Chair Professor Professor Curriculum and Teaching Curriculum and Teaching David M. Shannon Dean Hoffman Professor Professor Educational Foundations, Leadership, Mathematics and Statistics and Technology George T. Flowers Dean Graduate School EXPLORING BELIEFS AND PRACTICES OF TEACHERS OF SECONDARY MATHEMATICS WHO PARTICIPATED IN A STANDARDS-BASED PRE-SERVICE EDUCATION PROGRAM Mary Alice Smeal A Dissertation Submitted to the Graduate Faculty of Auburn University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Auburn, AL December 19, 2008 EXPLORING BELIEFS AND PRACTICES OF TEACHERS OF SECONDARY MATHEMATICS WHO PARTICIPATED IN A STANDARDS-BASED PRE-SERVICE EDUCATION PROGRAM Mary Alice Smeal Permission is granted to Auburn University to make copies of this dissertation at its discretion, upon requests of individuals or institutions and at their expense. The author reserves all publication rights. ____________________________________ Signature of Author ____________________________________ Date of Graduation ii i VITA Mary Alice Smeal, daughter of Roy and Mary Letta Shaub, was born December 15, 1958, in Nashville, Tennessee. She graduated from David Lipscomb High School in 1976. She entered David Lipscomb University in 1976 and graduated with a Bachelor of Science degree in Applied Piano in December, 1979. Upon graduation, she worked as an actuarial computer programmer/analyst at American General Insurance Company until giving birth to twins in August, 1983. In March, 1984, she moved with her husband to Southampton, New York and devoted herself to her family. While in New York, she was also elected to the Southampton Board of Education and served until moving to Florence, Alabama in 1994. After her last child began school, she entered the University of North Alabama and graduated with a Masters of Arts in Mathematics Education in 1996. She taught mathematics for the next nine years at Mars Hill Bible School. In 2004, she moved to Montgomery, Alabama. While working as a mathematics teacher at Alabama Christian Academy, she entered Graduate School at Auburn University in January, 2006. She married James Smeal on May 26, 1979. They have four children, James, Joseph, Christopher, and Nathan. iv DISSERTATION ABSTRACT EXPLORING BELIEFS AND PRACTICES OF TEACHERS OF SECONDARY MATHEMATICS WHO PARTICIPATED IN A STANDARDS-BASED PRE-SERVICE EDUCATION Mary Alice Smeal Doctor of Philosophy, December 19, 2008 (M.A.T., University of North Alabama, 1996) (B.S., David Lipscomb University, 1979) 375 Typed Pages Directed by Marilyn E. Strutchens The National Council of Teachers of Mathematics has challenged all mathematics teachers to use the Standards documents (1989, 1991, 1995, & 2000) as guidelines for teaching mathematics. Many pre-service programs are now presenting curricula that are based on the Standards (1989, 1991, 1995, & 2000). When mathematics teachers enter their own classroom, will their teaching methods reflect the guidelines of the Standards that they encountered in their pre-service education? Five case studies were used to investigate the teaching beliefs and practices of mathematics teachers who had participated in a Standards-based pre-service education. v The case studies were selected based on the results from a survey in order to arrive at a diverse, purposeful sample. A variety of data sources were used to develop a better understanding of teachers’ beliefs and practices. The researcher used a survey, classroom observations, interviews, and an observation instrument as data sources. One of the teachers held beliefs in alignment with the guidelines of the Standards and effectively implemented them in her classroom. Another teacher strongly held Standards-based beliefs but had difficulty incorporating these beliefs into her teaching practices due to the obstacles of curriculum, high-stakes testing, and classroom management. The third teacher incorporated some Standards-based teaching strategies but was heavily influenced by his administration and curriculum to follow a traditional pattern of teaching. The fourth teacher held beliefs in alignment with the Standards after participating in an internship with a cooperating teacher that provided positive Standards- based teaching experiences in a middle school setting. After she began teaching seniors, she felt that Standards-based strategies were more appropriate for students below the high school level. She incorporated traditional teaching practices. The fifth teacher held traditional beliefs even after the completion of his pre-service education and continued with traditional teaching strategies in his own classroom. Four of the teachers lowered their expectations of students based on the students’ demographics, such as academic level and socioeconomic status. vi ACKNOWLEDGEMENTS God has been my guide throughout the many paths my life has traveled. I want to give God the glory for providing me with the opportunity and guidance to pursue my educational opportunities. Thanks also to God for blessing me with my husband Jim to be my partner. Jim daily expressed his confidence in my abilities and provided me with encouragement every step of the way. Even though my mother and father are no longer alive to celebrate my achievement with me, I want to thank them for being an example of excellence in all things. Thanks also to my children—James, Joseph, Chris, and Nathan— for their continued support and interest. I want to give a special word of appreciation to my fellow graduate students; Lora who also had a patient and listening ear, and Carol for helping me survive all of my classes and always giving me an encouraging word when I needed it most. Last of all, thanks to my committee for all of their time and energy. I want to acknowledge Dr. Strutchens for always guiding me in a kind and supporting manner. She shared her expertise when my knowledge needed some “scaffolding.” I want to give a special word of gratitude for the encouragement that Dr. Martin provided me during research class. You helped me make my dreams become reality. I would be amiss unless I mentioned my two remaining committee members, Dr. Shannon and Dr. Hoffman. They were always so helpful and positive when the going got tough. vii Style manual or journal used: Publication Manual of the American Psychological Association, Fifth Edition Computer software used: Microsoft Excel, 2003; Atlas.ti, Version 5.2; Microsoft Word 2003 viii TABLE OF CONTENTS LIST OF TABLES ..................................................................................................... xvii LIST OF FIGURES ................................................................................................... xix I. INTRODUCTION ......................................................................................... 1 The New Math Era to the Agenda for Action ................................................ 1 The Mathematics Reform Movement ............................................................ 3 Math Wars ..................................................................................................... 5 Teachers Facing a Decision ........................................................................... 7 Theoretical Basis for the Study ...................................................................... 10 Purpose of the Study ...................................................................................... 12 Significance of the Study ............................................................................... 13 Definitions...................................................................................................... 14 Standards-based Mathematics ............................................................ 14 Teachers’ Beliefs ............................................................................... 15 Affect ................................................................................................. 16 II. REVIEW OF RELATED LITERATURE ..................................................... 18 Teachers’ Beliefs and Practices and Affect ................................................... 18 Students’ Affect ................................................................................. 20 The Cognitive Domain ........................................................... 20 Mood Maps ............................................................................ 21 Students’ Changing Affect ..................................................... 23 Mathematics Anxiety ............................................................. 24 Connection of Students’ Affect to Teachers’ Efficacy .......... 25 Teachers’ Affect................................................................................. 25 The Impact of a Pre-Service Methods Course on Affect ....... 26 The Expert Blind Spot in Secondary Teachers ...................... 29 ix Summary of Teachers’ Beliefs and Practices and Affect .................. 32 Teachers’ Beliefs and Practices and Other Influences .................................. 33 New