HOW ELEMENTARY SCHOOL TEACHERS’ MATHEMATICAL SELF-EFFICACY AND MATHEMATICS TEACHING SELF-EFFICACY RELATE TO CONCEPTUALLY AND PROCEDURALLY ORIENTED TEACHING PRACTICES DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Diane Kay Borton Kahle, B.S., M.A. * * * * * The Ohio State University 2008 Dissertation Committee: Approved by Professor Sigrid Wagner, Adviser Professor Patricia Brosnan __________________________________ Professor Bostwick Wyman Adviser College of Education ABSTRACT The purpose of this mixed method study was to explore the relationships among the variables of mathematics self-efficacy, mathematics teaching self-efficacy, and procedurally or conceptually-oriented teaching methods. The study included 75 practicing elementary teachers who teach mathematics as well as other subjects. These teachers completed the Mathematics Teaching and Mathematics Self-Efficacy survey, designed as part of the study and based on the Mathematics Self-Efficacy Scale - Revised (MSES-R) and the Mathematics Teaching Efficacy Beliefs Instrument (MTEBI). Sixteen of the teachers also participated in an interview probing teaching methods for two mathematics topics the teachers believed they are most confident or least confident teaching. Interviews were assessed using the Conceptually and Procedurally Oriented Teaching Method Frequency Chart, designed as part of the study. Quantitative data analysis methods include descriptive statistics, Pearson’s Product Moment correlation, and chi-square tests. Qualitative data analysis includes case study anecdotes for two of the interviewed teachers. Results indicate a strong relationship between mathematics self- efficacy and mathematics teaching self-efficacy and suggest that mathematics self- efficacy may be a precursor to mathematics teaching self-efficacy. Additionally, results indicate that when teaching their most confident mathematics topic teachers are more likely to use conceptually oriented teaching methods and when teaching their least ii confident mathematics topic teachers are more likely to use procedurally oriented teaching methods. This study offers findings to mathematics teacher educators and elementary mathematics teachers about the importance of developing mathematics self- efficacy and mathematics teaching self-efficacy because of their relationship to teachers’ choices of instructional methods. Additionally the two instruments developed in the study will help future researchers assess these variables. iii DEDICATION Dedicated to Rick, Ryan, Kelli and Adam iv ACKNOWLEDGMENTS Thanks to: Relatives: Richard Kahle : my wonderful husband, thank you for your unconditional support through our entire marriage and through the pursuit of my doctoral degree. I realize that many times you wondered why I started this degree, and sometimes I did too. Regardless, you encouraged me to pursue my goal and often made sacrifices so I could have the time and resources to do so. Ryan, Kelli, and Adam : my three wonderful children, who have brought so much joy into my life. Thank you for encouraging me and caring enough to play math with me. Joan and Garth Borton (parents) and Judy Murray (mother-in-law): Thank you for numerous hours of the best babysitting available. Thank you for giving me the confidence to pursue my goal and for supporting me along the way. Committee Members Dr. Sigrid Wagner : Thank you for your advising while I completed my Master’s degree and even more so for motivating me to pursue and to finish my doctoral program. While I have known you I have become a mother of three wonderful children, held full- and part- time teaching positions, moved three times, built a home, and been actively involved with my family, education, and community. Throughout this you have displayed only positive and supportive ways to nurture my passion for learning, motivate me to take even the smallest task and make better, and support me to become successful with my dream of earning my doctorate. Your expertise is a gem in the field of mathematics education. I strive to have the eloquence, communication skills, motivational skills, and knowledge that you do when I have the opportunity to work with future mathematics educators. Dr. Patti Brosnan: Thank you for asking me the most important question for my dissertation at exactly the right moment, “Well, what is it that you want to study?” Thank you for sharing your excellent views on mathematics education with myself and the community. Dr. Bostwick Wyman: Thank you for sharing your passion for mathematics history. You pushed me to explore topics otherwise unnoticed which have enlightened my career and my mathematical learning. v Inspirator Dr. Johnny Hill: The first day I walked into your classroom at Miami University for my junior high mathematics methods course my love of mathematics education was born. You were the stimulus that changed me from wanting to be a teacher to wanting to teach mathematics to children. The beauty of mathematics began unraveling and I am still enjoying the pieces. After your class I decided that not only did I want to teach mathematics to children but I also wanted to be a stimulus to encourage students and future mathematics teachers to appreciate mathematics. Panel of Experts for the Conceptual Procedural Skill List Michael Hunt Mary LeFever Melva Grant Panel of Experts for Survey Michael Hunt Heidi Cowan Emilie Greenwald Ann Carlson Course Instructors for Survey Pilot Lucia Flevare Debra Rucker Interview Pilot Anne Graeber Holly Saltus Joan Smith Jeff Silliman Marie DeSantis Course Director for Survey Kim Hughes Conceptual/Procedural Interrater Reliability Checker Michael Hunt vi VITA March 10, 1965 ........................................Born, Dayton, Ohio, U.S.A. 1987…......................................................B.S. Mathematics Education, 7-12 Mathematics Teaching Certification, Miami University 1987-1995 ................................................Mathematics Teacher, Westerville City Schools, Ohio 1991..........................................................K-12 Computer Science Teaching Certification, Otterbein College 1995-1997 ................................................Mathematics and Computer Teacher, Indian Hill Exempted Village Schools, Cincinnati, OH 1997..........................................................M.S. Mathematics Education, The Ohio State University 1997-2003 ................................................Mathematics and Computer Teacher, Westerville City Schools, Ohio 2005-2006 ................................................Graduate Research Assistant, Eisenhower National Clearinghouse, The Ohio State University 2006-2007 ................................................Graduate Assistant, Middle Childhood Education Supervisor, The Ohio State University 2006-present.............................................Mathematics Teacher, Upper Arlington City Schools, Ohio vii PUBLICATIONS Kahle, D. (2008). Getting to know your middle grades mathematics textbook. Adolescent Literacy in Perspective (November/December 2006), December 20, 2006 from http://www.ohiorc.org/adlit/in_perspective_content.aspx?parentID=284&recID=286 &issue=0&status=live FIELDS OF STUDY Major Field: Mathematics Education viii TABLE OF CONTENTS Page Abstract............................................................................................................................ii Dedication........................................................................................................................iv Acknowledgements..........................................................................................................v Vita…...............................................................................................................................vii List of Tables ...................................................................................................................xii List of Figures..................................................................................................................xiv Chapters: 1. Statement of the Problem.....................................................................................1 Practical Rationale ...................................................................................7 Research Questions..................................................................................10 Definitions................................................................................................13 Self-Efficacy ..................................................................................13 Procedurally Versus Conceptually Oriented Teaching..................17 Theoretical Framework............................................................................19 Self-Efficacy ................................................................................21 Procedurally and Conceptually Oriented Instruction...................24 Relational and Instrumental Understanding.................................25 Model ...........................................................................................27 Conclusion ...............................................................................................29 2. Literature Review...................................................................................................31 Self-Efficacy ...........................................................................................31 Mathematics