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Exploring the Relationship Between Teachers' Beliefs in Mathematics and Their Instructional Practice

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Exploring the Relationship Between Teachers' Beliefs in Mathematics and Their Instructional Practice UNLV Retrospective Theses & Dissertations 1-1-2006 Exploring the relationship between teachers' beliefs in mathematics and their instructional practice Michelle Vander Veldt University of Nevada, Las Vegas Follow this and additional works at: https://digitalscholarship.unlv.edu/rtds Repository Citation Vander Veldt, Michelle, "Exploring the relationship between teachers' beliefs in mathematics and their instructional practice" (2006). UNLV Retrospective Theses & Dissertations. 2688. http://dx.doi.org/10.25669/3e0l-04ko This Dissertation is protected by copyright and/or related rights. It has been brought to you by Digital Scholarship@UNLV with permission from the rights-holder(s). You are free to use this Dissertation in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s) directly, unless additional rights are indicated by a Creative Commons license in the record and/or on the work itself. This Dissertation has been accepted for inclusion in UNLV Retrospective Theses & Dissertations by an authorized administrator of Digital Scholarship@UNLV. For more information, please contact [email protected]. EXPLORING THE RELATIONSHIP BETWEEN TEACHERS’ BELIEFS IN MATHEMATICS AND THEIR INSTRUCTIONAL PRACTICE by Michelle Vander Veldt Bachelor of Science University of Nevada, Las Vegas 1996 Master of Education Curriculum and Instruction University of Nevada, Las Vegas 1999 A dissertation submitted in partial fulfillment of the requirements for the Doctor of Philosophy Degree in Curriculum and Instruction Department of Curriculum and Instruction College of Education Graduate College University of Nevada, Las Vegas August 2006 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 3244005 Copyright 2006 by Vander Veldt, Michelle All rights reserved. INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. UMI UMI Microform 3244005 Copyright 2007 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Copyright © 2006 by Michelle Vander Veldt All Rights Reserved Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UNIV Dissertation Approval The Graduate College University of Nevada, Las Vegas June 9 ^20 06_ This Dissertation prepared by Michelle Vander Veldt Entitled Exploring the Relationship Between Teachers' Beliefs in Mathematics and Their Instructional Practice is approved in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Curriculum and Instruction___________ ination Committee Co-Chair Examination Commiiteo Co-Chair ean o f the Graduate College Examination Committee Member Graduate College Facaulty Representative 11 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT Exploring the Relationship Between Teachers’ Beliefs in Mathematics and Their Instructional Practice by Michelle Vander Veldt Drs. Linda Quinn and Jeffrey Shih, Examination Committee Chairs Professors of Currieulum and Instruction University of Nevada, Las Vegas This study explored the relationship between teachers’ beliefs about mathematics and their instructional practices. The personal epistemology of the ease study elementary mathematies teachers was doeumented and analyzed to provide evidence of the eonnection between teachers’ beliefs and practiee in an elementary sehool setting. This study was grounded in a theoretical framework of epistemologieal world views, particularly the comparison of belief across three epistemologieal world views: 1) the realist, 2) the contextualist, and 3) the relativist. Three areas of beliefs are addressed in this study: 1) beliefs about curriculum, 2) beliefs about pedagogy, and 3) beliefs about assessment. Through analysis of these beliefs speeific to mathematics, this study identified which world view the case study teachers espouse and how this influenced each teacher’s mathematical classroom practice. This study sought to answer the following research questions: 1. What are teachers’ beliefs about currieulum, pedagogy, and assessment? Ill Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2. What practices provide evidence of teacher beliefs? 3. What is the relationship between teaehers’ beliefs in mathematics and their instructional practices? This design of the study was a qualitative case study. Participants in this study were three third grade teachers from different schools in the same school district located in the southwestern United States. These teachers provided the unit of analysis for the study. The schools were selected beeause they support a standards-based approach to mathematics mandated by state and district standards. The teachers selected for the study use similar third grade resourees to implement standards-based mathematies curriculum in the elementary classroom. The participants’ perspectives are shared through interviews, observations, doeuments, and audio-visual materials. In this study, the teachers’ epistemologieal world view was examined and compared to their implementation of mathematies practices. From the domain analysis, many faetors supported and hindered practiee based on the world view of the teachers. The researcher categorized these domains based on broad external factors to narrow internal factors. The following domains were examined based on the data: 1) domain one: school district factors, 2) domain two: school culture factors, 3) domain three: physical classroom factors, and 4) domain four: individual teacher beliefs. Implications from this study included a need to: 1) provide teachers with an understanding of mathematic content and an understanding of beliefs about eurrieulum, pedagogy, and assessment, 2) provide eourses for pre-service teachers and teachers that incorporates a comparison of world views into the mathematics coursework, 3) support IV Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. collaborative efforts between teaeher edueators and sehool districts in designing a shared vision for world views, and 4) inform the mathematics domain in regards to world views to improve teaching. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS ABSTRACT................................................................................................................................. iii LIST OF TABLES.................................................................................................................... viii ACKNOWLEDGMENTS...........................................................................................................ix CHAPTER 1 INTRODUCTION................................................................. 1 Purpose of the Study...................................................................................................................2 Background.................................................................................................................................3 Statement of the Problem..........................................................................................................6 Questions Guiding the Study.................................................................................................... 7 Signifieance of the Study..........................................................................................................7 Theoretical Framework ............................................................................................................. 7 Descriptions of Subject and Setting...................................................................................... 13 CHAPTER 2 LITERATURE REVIEW.................................................................................14 Epistemology.............................................................................................................................14 Literature Review Procedures................................................................................................ 19 Mathematies Education...........................................................................................................29 CHAPTER 3 METHODOLOGY........................................................................................... 42 Research and Design............................................................................................................... 42 Setting and Partieipants...........................................................................................................43 Instrumentation and
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