CDE Research Archive Summary Title: The Beliefs And Attitudes Of Special Educators: Mathematics, Mathematics Teaching, And Mathematics Learning Author(s): Melissa L. Colsman Date of Initial Publication: 11/26/2012 Abstract/Summary: The purpose of the study was to explore the beliefs and attitudes of special education teachers have about the discipline of mathematics, teaching mathematics, and learning mathematics. The study utilized a mixed method design that was conducted in two phases. Forty‐eight in‐service special education teachers participated in Phase One of the study, which consisted of quantitative data collection through surveys related to mathematics anxiety level and alignment of beliefs with the National Council of Teachers of Mathematics (NCTM) Standards. A sub‐sample of seven teachers was purposefully selected to participate in Phase Two of the study, which consisted of a qualitative data collection through a semi‐structured interview. Quantitative results indicated that the study sample had relatively low levels of mathematics anxiety and a relatively high degree of alignment with reform‐based mathematics beliefs promoted by the NCTM. Qualitative results expanded upon the quantitative results of Phase One of the study and indicated that the beliefs of the sub‐sample participants could be categorized according to beliefs common to general education mathematics teachers. Subject/Keywords: Mathematics teaching, special education, National Council of Teachres of Mathematics Standards, mathematics anxiety Document Type: Paper Document Archive Number: 0021cdeco2012 THE BELIEFS AND ATTITUDES OF SPECIAL EDUCATORS: MATHEMATICS, MATHEMATICS TEACHING, AND MATHEMATICS LEARNING by Melissa L. Colsman B.A., University of Northern Colorado, 1988 M. A., University of Northern Colorado, 1994 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Educational Leadership and Innovation 2012 This thesis for the Doctor of Philosophy degree by Melissa L. Colsman has been approved for the Educational Leadership and Innovation Program by Dr. Deanna Sands, Chair Dr. Karen Koellner Dr. Nancy Leech Dr. Bonnie Utley Date: November 26, 2012 ii Colsman, Melissa, L. (Ph.D., Educational Leadership and Innovation) The Beliefs and Attitudes of Special Educators: Mathematics, Mathematics Teaching, and Mathematics Learning Thesis directed by Professor Deanna Sands ABSTRACT The purpose of the study was to explore the beliefs and attitudes of special education teachers have about the discipline of mathematics, teaching mathematics, and learning mathematics. The study utilized a mixed method design that was conducted in two phases. Forty-eight in-service special education teachers participated in Phase One of the study, which consisted of quantitative data collection through surveys related to mathematics anxiety level and alignment of beliefs with the National Council of Teachers of Mathematics (NCTM) Standards. A sub-sample of seven teachers was purposefully selected to participate in Phase Two of the study, which consisted of a qualitative data collection through a semi-structured interview. Quantitative results indicated that the study sample had relatively low levels of mathematics anxiety and a relatively high degree of alignment with reform-based mathematics beliefs promoted by the NCTM. Qualitative results expanded upon the quantitative results of Phase One of the study and indicated that the beliefs of the sub-sample participants could be categorized according to beliefs common to general education mathematics teachers. The form and content of this abstract are approved. I recommend its publication. Approved: Deanna Sands iii DEDICATION I dedicate this work to my husband, Mark Colsman, whose support, encouragement, and love allowed me to persevere through this long marathon. I also dedicate this work to my father, Bill Bunney, and grandmother, Angela Bunney. Dad and Grandma, your love and faith in me are a constant source of strength and are the foundation for all of my successes. iv ACKNOWLEDGMENTS I would like to thank my EDLI program advisory committee and dissertation committee for their support and encouragement. I especially wish to thank my dissertation chair, Dr. Deanna Sands, and my program advisory, Dr. Karen Koellner. Karen, I began this journey with you, an amazing advisor, colleague, and friend. Deanna, you brought me through to end. You challenged me to become a better researcher and writer and provided the encouragement I needed. Thank you both! v TABLE OF CONTENTS CHAPTER I. INTRODUCTION ........................................................................................................... 1 Statement of the General Problem .................................................................................. 1 The Context of the Problem ............................................................................................ 2 Purpose and Significance of the Study ........................................................................... 6 Design ............................................................................................................................. 7 Conceptual Framework ................................................................................................... 8 The Relationship Between Teachers’ Beliefs and Instructional Practice ................... 9 Mathematics Anxiety as a Mediating Factor in Instructional Practice ..................... 11 Conclusion .................................................................................................................... 14 II. REVIEW OF THE LITERATURE ............................................................................. 15 The Context of the Problem .......................................................................................... 16 Mathematics Achievement in the United States ....................................................... 16 Overview of Issues within Special Education .......................................................... 21 Overview of Issues within Mathematics Education .................................................. 26 The Affective Domain: Emotions, Attitudes, Beliefs, and Values ............................... 31 Mapping the Affective Domain ................................................................................ 32 Emotions ................................................................................................................... 33 Attitudes .................................................................................................................... 34 Beliefs ....................................................................................................................... 35 Values ....................................................................................................................... 36 Emotions and Mathematics Anxiety ............................................................................. 37 vi Mathematics Anxiety: Definition and Impact ........................................................... 37 Causes of Math Anxiety............................................................................................ 41 Teacher Affect Towards Mathematics ...................................................................... 47 Beliefs ........................................................................................................................... 51 Characteristics of Beliefs .......................................................................................... 51 Beliefs of Teachers ................................................................................................... 52 Rationale for Studying Beliefs: Links to Instruction ............................................... 53 Conceptual Frameworks: Relating Beliefs to Instructional Practice ........................ 55 The Nature of Mathematics: Perspectives and Implications ..................................... 56 Limitations of Conceptual Frameworks .................................................................... 73 Special Educators and Beliefs about Mathematics ................................................... 74 Conclusion .................................................................................................................... 75 III. METHODS ................................................................................................................. 77 Study Design ................................................................................................................. 79 Sampling Design ....................................................................................................... 82 Participants .................................................................................................................... 84 Recruitment ............................................................................................................... 84 Demographic Information ......................................................................................... 85 Measures ....................................................................................................................... 87 Mathematics Anxiety ................................................................................................ 88 Mathematics Beliefs .................................................................................................. 89