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Development and Validation of Indicators of Secondary Mathematics Teachers' Positive Dispositions Toward Problem Solving. Alison L

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Development and Validation of Indicators of Secondary Mathematics Teachers' Positive Dispositions Toward Problem Solving. Alison L University of Louisville ThinkIR: The University of Louisville's Institutional Repository Electronic Theses and Dissertations 5-2014 Development and validation of indicators of secondary mathematics teachers' positive dispositions toward problem solving. Alison L. Mall University of Louisville Follow this and additional works at: https://ir.library.louisville.edu/etd Part of the Curriculum and Instruction Commons Recommended Citation Mall, Alison L., "Development and validation of indicators of secondary mathematics teachers' positive dispositions toward problem solving." (2014). Electronic Theses and Dissertations. Paper 895. https://doi.org/10.18297/etd/895 This Doctoral Dissertation is brought to you for free and open access by ThinkIR: The nivU ersity of Louisville's Institutional Repository. It has been accepted for inclusion in Electronic Theses and Dissertations by an authorized administrator of ThinkIR: The nivU ersity of Louisville's Institutional Repository. This title appears here courtesy of the author, who has retained all other copyrights. For more information, please contact [email protected]. DEVELOPMENT AND VALIDATION OF INDICATORS OF SECONDARY MATHEMATICS TEACHERS’ POSITIVE DISPOSITIONS TOWARD PROBLEM SOLVING By Alison L. Mall B.A., Mathematics, University of Alaska Anchorage, 1994 M.A., Teaching, University of Alaska Anchorage, 1995 Graduate Certificate, Educational Leadership, University of Alaska Anchorage, 2006 A Dissertation Submitted to the Faculty of the College of Education and Human Development of the University of Louisville in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Curriculum and Instruction University of Louisville Louisville, Kentucky May 2014 Copyright 2014 by Alison L. Mall All rights reserved DEVELOPMENT AND VALIDATION OF INDICATORS OF SECONDARY MATHEMATICS TEACHERS’ POSITIVE DISPOSITIONS TOWARD PROBLEM SOLVING By Alison L. Mall B.A., Mathematics, University of Alaska Anchorage, 1994 M.A., Teaching, University of Alaska Anchorage, 1995 Graduate Certificate, Educational Leadership, University of Alaska Anchorage, 2006 A Dissertation Approved on April 17, 2014 by the following Dissertation Committee Dissertation Director Dr. William S. Bush Dr. Ann E. Larson Dr. Maggie M. McGatha Dr. Carl Lee Dr. Judy R. Wilkerson ii DEDICATION This dissertation is dedicated to my parents Mr. Martin “Duffy” Mall and Mrs. Karen Dee Mall who guided me in finding the Self I am disposed to be. iii ACKNOWLEDGEMENTS Throughout my life I have been blessed with guardian angels, and 2007 was certainly no exception. So it is with gratitude that I begin by acknowledging Dr. Bill Bush, Dr. Vena Long and Dr. Carl Lee, along with all of the co-PIs and members of the management team, for creating and sustaining the Appalachian Collaborative Center for Learning, Assessment, and Instruction in Mathematics (ACCLAIM). This collaborative encouraged me to develop in new and exciting ways as a mathematics teacher and mathematics teacher educator. Due to my interactions with ACCLAIM faculty, particularly with respect to the mathematical diversions provided by Dr. Lee, Dr. Mays and Dr. Anderson, I found the heart of my research agenda: teachers’ positive dispositions toward problem solving. Similarly, Dr. Jaci Webb-Dempsey’s positive disposition toward qualitative research methodology inspired and grounded me during the study. In 2007, I also began my work as faculty in the Master of Arts in Teaching (MAT) Program at the University of Alaska Anchorage. I would like to thank the Dean of the College of Education, Dr. Mary Snyder, and the Director of the MAT Program, Jim Seitz, for taking a chance on a variable quantity! Without the support of the staff in the College of Education, and the teacher candidates in the MAT Program, I would not have been able to complete my doctoral program. For this opportunity and experience, I am eternally grateful. Every teacher has at least n + 1 great mentors. Recognizing that it is nearly impossible to list them all, I would like to acknowledge a few. First and foremost, I would like to express my gratitude to the entire faculty of the MAT Program, with specific acknowledgements to Jim Seitz, for his commitment to excellence in teacher education, Susan Barstow, for her commitment to iv walking the talk, and Janet Steinhauser, for her graceful approach to mentoring. Looking back further to my years teaching high school mathematics, I would simply not be the same teacher dispositionally without the influences of Mary “Elvis” Moran, Martha Dennis, Jim Seitz, Alison Vail, Ruth Mount, Dagny Fritsche and David Souza, and the mathletes that graced the halls of Bartlett High School. No better example of gracious and tireless mentoring exists than serving on a doctoral candidate’s dissertation committee. I would like to acknowledge my dissertation director, Dr. Bill Bush, for his guidance and positive disposition. This dissertation would not have been made possible without the patience and advice from additional committee members: Dr. Maggie McGatha, Dr. Ann Larson, Dr. Carl Lee and Dr. Judy Wilkerson. Without Dr. Wilkerson laying the foundation for assessing teachers’ dispositions, my study would not have been possible. The contributions of the entire committee ultimately strengthened my research and final product. I have been blessed with individuals in my life who have encouraged me throughout this process. Each member of the third ACCLAIM cohort enhanced my experience with their professional insights. I would like to offer a “high pi” and a “pounds all around” to Eleanor E- Dawg, Candy Sandy, Dianne, Mick Dundee, Robin, Landrea and Victoria for making the hours of coursework both meaningful and entertaining! I would like to give a special thanks to random rays of sunlight who shined so brightly during my process: Dr. Gloria Eldridge for making foundations of psychological testing understandable and enjoyable; Forrest, Logan and Sage – for being the best 3.14 nephews an aunt could hope for; Shanna, Troy and Sunil – for being supportive siblings; and my dear sweet adopted Abbi-Gale – for eliciting my unbeknown-to-me, positive disposition toward dogs. v ABSTRACT DEVELOPMENT AND VALIDATION OF INDICATORS OF SECONDARY MATHEMATICS TEACHERS’ POSITIVE DISPOSITIONS TOWARD PROBLEM SOLVING Alison L. Mall April 17, 2014 This dissertation examines disposition from a historical, theoretical and practical viewpoint. Chapter I introduces the purpose of the study: to apply Wilkerson and Lang’s (2007) Disposition Assessment Aligned with Teacher Standards (DAATS) model to develop an assessment framework for measuring secondary mathematics teachers’ dispositions toward mathematical problem solving. The study assumes secondary mathematics teachers’ positive dispositions toward problem solving and students’ productive dispositions toward problem solving are significant, beneficial factors in the mathematics classroom. Chapter II examines the historical, theoretical and professional literature on teachers’ dispositions and builds a case for: (1) the inherent value of teachers’ dispositions toward problem solving and (2) the examination of teachers’ dispositions toward problem solving from a normative theoretical perspective. Chapter III outlines the research design for developing indicators of secondary mathematics teachers’ positive dispositions toward problem solving. The study employed a mixed-methods design with two steps corresponding to the first two steps of Wilkerson and Lang’s (2007) five-step DAATS model and informed by the foundations of psychological testing (i.e, APA Standards for Educational and Psychological Testing) outlined by Miller, McIntire and Lovler (2011). Chapter III provides the rationale and assumptions for the design, descriptions of vi participants, data sources and data collection procedures, data analysis and validation procedures, methods for verification and trustworthiness, and limitations of the study. Chapter IV presents the results of the study chronologically by D. The chapter presents the observable behaviors, attitudes, and practices that are likely to be consistent with a secondary mathematics teacher exhibiting a positive disposition toward problem solving. The chapter concludes with an assessment framework designed to generate assessment items and methods at varying levels of inference. Chapter V examines the three central research questions, along with four refined research questions that emerged, and draws conclusions about assessing secondary mathematics teachers’ positive dispositions toward problem solving. The chapter provides implications for practice and recommendations for further research, and concludes with personal insights on teachers’ dispositions toward problem solving. vii TABLE OF CONTENTS ACKNOWLEDGEMENTS ................................................................................................................... iv ABSTRACT ........................................................................................................................................ vi LIST OF TABLES .................................................................................................................................xi LIST OF FIGURES ............................................................................................................................. xiii CHAPTER I: INTRODUCTION ............................................................................................................. 1 Problem Statement ..................................................................................................................
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