PDF Action Research in Mathematics Education

[Pages:243]ACTION RESEARCH IN MATHEMATICS EDUCATION: A STUDY OF A MASTER'S PROGRAM FOR TEACHERS

by Sarah Ultan Segal

A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics

MONTANA STATE UNIVERSITY Bozeman, Montana April 2009

?COPYRIGHT by

Sarah Ultan Segal 2009

All Rights Reserved

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APPROVAL

of a dissertation submitted by Sarah Ultan Segal

This dissertation has been read by each member of the dissertation committee and has been found to be satisfactory regarding content, English usage, format, citation, bibliographic style, and consistency, and is ready for submission to the Division of Graduate Education.

Dr. Maurice Burke Approved for the Department of Mathematical Sciences

Dr. Kenneth Bowers

Approved for the Division of Graduate Education

Dr. Carl A. Fox

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STATEMENT OF PERMISSION TO USE

In presenting this dissertation in partial fulfillment of the requirements for a doctoral degree at Montana State University, I agree that the Library shall make it available to borrowers under rules of the Library. I further agree that copying of this dissertation is allowable only for scholarly purposes, consistent with "fair use" as prescribed in the U.S. Copyright Law. Requests for extensive copying or reproduction of this dissertation should be referred to ProQuest Information and Learning, 300 North Zeeb Road, Ann Arbor, Michigan 48106, to whom I have granted "the exclusive right to reproduce and distribute my dissertation in and from microform along with the nonexclusive right to reproduce and distribute my abstract in any format in whole or in part."

Sarah Ultan Segal April 2009

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D EDICATION

I dedicate this dissertation to my father, Donald Ultan, who did not complete his dissertation, but impressed upon me the value and importance of using my mind, thinking, and obtaining my degrees. He lives on in my heart and always will. I would like to also dedicate this to my family: William Bennett, my fianc? whom I met in the 8th grade in California and discovered he too was in Montana, and to my son, Elliot Donald Segal. Both of them work so well with me. I also dedicate this to and thank my mother for putting up with me. Her love and affection stays steady. I appreciate all that she has done.

I would like to acknowledge Dr. Maurice Burke who has been a valuable role model for me in the work I have done. I have high regard for him as a person and as a thinker, and thank him for all his time! I would like to acknowledge Dr. Elisabeth Swanson who has supported me through this process with the fellowship of CLTW, making it all possible. And, deep appreciation to Jennie Luebeck for carrying to the ball the last few laps! Lastly, I thank the rest of my committee, for putting in their valuable time and effort on this dissertation, helping me complete my PhD. I think I have finally completed what I needed to do. Thank you!

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ACKNOWLEDGEMENT

This material is based upon work supported by the National Science Foundation under Grant No. 0119786. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

The Center for Learning and Teaching in the West, funded by the National Science Foundation (grant number 0119876) is a consortium of five universities collaborating with tribal colleges and public school systems in Montana, Colorado, and Oregon. The Center brings the varied expertise of scientists, mathematicians, and educators to address current challenges in understanding and improving student learning and achievement in science and mathematics from middle school through college.

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TABLE OF CONTENTS

1. STATEMENT OF THE PROBLEM..............................................................................1

Introduction.....................................................................................................................1 Context and Focus of the Study......................................................................................3 Statement of the Problem................................................................................................4 Research Questions.........................................................................................................5 Significance of the Study................................................................................................6 Limitations of the Study.................................................................................................8 Research Assumptions....................................................................................................9 Researcher's Position & Hypothesis...............................................................................10 Variables........................................................................................................................10 Definition of Terms.......................................................................................................11 Organization of the Study.............................................................................................12

2. REVIEW OF THE LITERATURE..............................................................................14

Introduction...................................................................................................................14 Description of Action Research....................................................................................14 History of Action Research...........................................................................................16 Educational Action Research........................................................................................17 Action Research for Teachers ? Definitions, Models, and Examples...........................20

Model 1.....................................................................................................................21 Example 1.................................................................................................................21 Model 2.....................................................................................................................22 Example 2.................................................................................................................23 Model 3.....................................................................................................................23 Example 3.................................................................................................................24 How Action Research Differs From Other Types of Research.....................................26 Professional Development and Action Research..........................................................28 Validity..........................................................................................................................30 Example 1.................................................................................................................30 Criticism of the Validity of Action Research...........................................................32 Suggestions For Increasing Validity From the Literature........................................34 Summary of Findings on Validity............................................................................37 Benefit...........................................................................................................................37 Example 2.................................................................................................................37 Natural Consequences of Action Research That Provide Benefit............................40 Summary of the Findings on Benefit.......................................................................42 Practicality....................................................................................................................43 Example 3.................................................................................................................43

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TABLE OF CONTENTS ? CONTINUED

Natural Consequences of Action Research that Increase Practicality......................47 Example 4.................................................................................................................49 Summary of the Findings on Practicality.................................................................50 Continued Practice........................................................................................................51 Summary of the Findings on Continued Practice.....................................................52 Conclusion....................................................................................................................54

3. METHODOLOGY.......................................................................................................57

Introduction...................................................................................................................57 Research Design............................................................................................................57 Population and Sample..................................................................................................60 Design of the Survey.....................................................................................................62

The Survey...............................................................................................................62 Pilot Survey.............................................................................................................64 The Survey.....................................................................................................................65 Plan for Rating the Capstone Projects...........................................................................68 Reliability of the Rating System...................................................................................71 Description of the Capstone Projects............................................................................72 Constructing the Interview Questions...........................................................................73 The Interviews...............................................................................................................74 Analysis of the Survey Data..........................................................................................77 Analysis of the Interview Data......................................................................................79 Results From The Pilot Survey.....................................................................................81

4. RESULTS.....................................................................................................................84

The Survey ? Schedule and Results.............................................................................84 Results of The Survey..............................................................................................85 Background Information on the Participants...........................................................86 Survey Section 1: Benefit........................................................................................99 Qualitative Data - Benefit........................................................................................99 Survey Section 2: Practicality................................................................................101 Qualitative Data - Practicality................................................................................102 Survey Section 3: Validity.....................................................................................104 Qualitative Data - Validity.....................................................................................104 Survey Section 4: Continued Practice....................................................................105 Qualitative Data ? Continued Practice...................................................................106 Survey Section 5: Change......................................................................................107 Responses to Other Questions................................................................................107

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