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An Investigation Into Relationships Between Alternative Assessment and Pre-Service Elementary Teachers’ Beliefs About Mathematics

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An Investigation Into Relationships Between Alternative Assessment and Pre-Service Elementary Teachers’ Beliefs About Mathematics Western Michigan University ScholarWorks at WMU Dissertations Graduate College 6-2000 An Investigation into Relationships between Alternative Assessment and Pre-Service Elementary Teachers’ Beliefs about Mathematics David Charles Coffey Western Michigan University Follow this and additional works at: https://scholarworks.wmich.edu/dissertations Part of the Science and Mathematics Education Commons, and the Statistics and Probability Commons Recommended Citation Coffey, David Charles, "An Investigation into Relationships between Alternative Assessment and Pre- Service Elementary Teachers’ Beliefs about Mathematics" (2000). Dissertations. 1441. https://scholarworks.wmich.edu/dissertations/1441 This Dissertation-Open Access is brought to you for free and open access by the Graduate College at ScholarWorks at WMU. It has been accepted for inclusion in Dissertations by an authorized administrator of ScholarWorks at WMU. For more information, please contact [email protected]. AN INVESTIGATION INTO RELATIONSHIPS BETWEEN ALTERNATIVE ASSESSMENT AND PRE-SERVICE ELEMENTARY TEACHERS’ BELIEFS ABOUT MATHEMATICS by David Charles Coffey A Dissertation Submitted to the Faculty of The Graduate College in partial fulfillment o f the requirements for the Degree of Doctor of Philosophy Department of Mathematics and Statistics Western Michigan University Kalamazoo, Michigan June 2000 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. AN INVESTIGATION INTO RELATIONSHIPS BETWEEN ALTERNATIVE ASSESSMENT AND PRE-SERVICE ELEMENTARY TEACHERS’ BELIEFS ABOUT MATHEMATICS David Charles Coffey, Ph.D. Western Michigan University, 2000 The purpose of this study was to examine how including alternative assessments in a reform-based mathematics course affects pre-service teachers’ mathematical beliefs. A single section of a mathematics course designed for elementary education majors that employed three different alternative assessments was the setting for the study. A pre- and post-belief survey completed by students enrolled in the section under study represented the first level of data collection and analysis. The results of the pre-belief survey guided the selection of seven informants from the section and provided belief statements for the informants to verify during subsequent interviews. Based on the data from these interviews, it was determined that all but one of the informants believed mathematics to be a pre-existing set of facts and procedures that are passed along by some mathematical authority. Moreover, all the informants reported that they believed assessing in mathematics meant giving a paper-and-pencil test. Further data collection methods, including a card sort of assessment practices and perusing classroom vignettes, and subsequent analysis identified each informant’s previous mathematical experiences as traditional, especially regarding assessment. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A comparison of the pre- and post-belief surveys indicated that the alternative assessments had indeed affected the mathematical beliefs of almost 50% of the students so that they now held more productive mathematical beliefs. During the final informant interviews, however, it became evident that apparent shifts in beliefs were not as profound as indicated by the comparison. Although all seven informants had become more aware that tests represent only one of many ways to assess students in mathematics, most of the informants clung to their original beliefs about the nature of mathematics. The two informants who exhibited more productive beliefs credited the alternative assessments as the most influential factor from the course under study. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. 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 bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unautfiorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6” x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. Bell & Howell Information and Learning 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 800-521-0600 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number 9973047 Copyright 2000 by Coffey, David Charles All rights reserved. ___ __® UMI UMI Microform 9973047 Copyright 2000 by Bell & Howell Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. Bell & Howell 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 by David Charles Coffey 2000 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGEMENTS I wish to thank my committee members, without whom this dissertation would have never come about. Dr. Zoe Barley helped tremendously with the design of this study and offered support during the maddening data analysis. Dr. Dwayne Channell served as my second reader and kept me sane with laughter and advice. Dr. Terry Grant’s and Dr. Laura Van Zoest’s comments on the original drafts of my dissertation helped to keep me focused and challenged me to think more like a scholar. My dissertation advisor, Christine Browning, knew exactly when to be patient and when to be stubborn. Her guidance and support will always be appreciated. My family also deserves my heartfelt gratitude. Thanks to Mom and Dad for nurturing in me a love of teaching. Thanks to Hilary, John, and Andrew for reminding me what is truly important. Mostly, thanks to my wife and best friend, Kathy. Words cannot do justice to all her efforts during the past four years. In many ways, this 4 little report’ is as much hers as it is mine. Finally, I wish to acknowledge my Creator, who on a daily basis granted me serenity, courage, and wisdom - not only for this task, but also in my life in general. David Charles Coffey Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS ACKNOWLEDGEMENTS.......................................................................................... ii LIST OF TABLES......................................................................................................... x LIST OF FIGURES....................................................................................................... xi CHAPTER I. INTRODUCTION............................................................................. 1 Background .............................................................................................. 1 Significance of the Research ................................................................. 3 Research Questions ................................................................................. 4 Brief Overview of the Study’s Methodology and the Dissertation’s Organization .................................................................... 5 Closing Comments .................................................................................. 7 II. LITERATURE REVIEW........................................................................ 8 Theoretical Framework .......................................................................... 8 Philosophy of Mathematics Learning Employed in This Study .................................................................................. 9 McEntire and Kitchens’ Theory of Axioms ............................... 11 Beliefs....................................................................................................... 14 Beliefs and Belief Systems ........................................................... 14 Mathematical Beliefs..................................................................... 17 Implications of Beliefs on Instruction and Learning ................. 20 Attempts to Effect Change on Pre-service Teachers’ Mathematical Beliefs..................................................................... 23 iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table of Contents - Continued CHAPTER Assessment.............................................................................................
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