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  • Technological Pedagogical Content Knowledge: Secondary School Mathematics

    Teachers Use of Technology

    By

    Dorian Stoilescu

    A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

    Department of Curriculum, Teaching, and LearningOntario Institute for Studies in Education of the

    University of Toronto

    Copyright by Dorian Stoilescu 2011

  • Technological Pedagogical Content Knowledge: Secondary School Mathematics

    Teachers Use of Technology

    Dorian Stoilescu

    Department of Curriculum, Teaching, and Learning

    The Ontario Institute for Studies in Education

    University of Toronto

    2011

    ABSTRACT

    Although the Technological Pedagogical Content Knowledge (TPACK) framework

    has shown a lot of promise as a theoretical perspective, researchers find it difficult to use

    it in particular environments because the requirements of the framework change in

    specific contexts. The purpose of this study was to explore and produce more flexible

    ways of using the TPACK for inservice mathematics secondary teachers. Three such

    teachers at an urban public school were observed in their classrooms and interviewed

    about their experiences of teaching mathematics and integrating computer technology in

    their day-to-day activities. Each participant had over 10 years experience in teaching

    mathematics in secondary schools in Ontario, and expertise in using computers in

    mathematics curriculum. The research questions were: 1) How do secondary school

    mathematics teachers describe their ways of integrating technology? and 2) What

    difficulties do teachers have when they try to integrate technology into mathematics

    classrooms?

    The findings from the first research question show that teachers displayed a high

    degree of integration of technology. Their activities were very clearly designed,

    ii

  • conferring clear roles to the use of integrating computer technology in mathematics

    classes. Teachers had specific approaches to integrate computer technology: a) to allow

    students opportunities to learn and experiment with their mathematical knowledge; b) to

    help them pass the content to the students in the process of teaching mathematics; and c)

    to assess and evaluate students work, and give them feedback. The findings from the

    second research question reveal that teachers had difficulties in purchasing and

    maintaining the computer equipment. They had some difficulties in trying to integrate

    new technologies as these required time, preparation, and dedication. In addition,

    teachers had some difficulties in making students use computers in a significant way.

    The implication for teacher education is that inservice teachers should have

    opportunities to update their computer and pedagogical skills, a long term perspective in

    integrating technology in mathematics education, and professional and technical support

    from teaching colleagues and administrators. Finally, the integration of computer

    technology in mathematics requires more intensive teamwork and collaboration between

    teachers, technical support staff, and administrators.

    iii

  • ACKNOWLEDGEMENTS

    There are a great number of people whose paths crossed mine at various stages of

    my doctoral program and helped me to complete it. First, I am indebted to Lawrence,

    Cecilia, and Mark, the three secondary school teachers that I interviewed, for

    participating in this research. They discussed with me their ways of integrating

    technology in mathematics classrooms and offered me fresh perspectives. Also, many

    thanks to their students, colleagues in the mathematics department, and the administration

    of the school, for facilitating my research.

    I would also like to thank my thesis committee. I am grateful to Douglas McDougal,

    my supervisor and my counsellor, for his guidance and leadership. I can never tell you

    how much I appreciate your encouragement and advice in getting me through this

    important career stage. Many thanks go to the members of the thesis committee, Rina

    Cohen and Jim Hewitt, for their insightful feedback. Also, I would like to thank the

    internal reader, Claire Brett, and the external reader, Geoffrey Roulet, who provided

    detailed and insightful comments to finalize my thesis.

    Thank you to other professors from our department: Marlene Scardamalia, Larry

    Bencze, Jim Slotta, John Wallace, and Earl Woodruff, who, at various stages, helped me

    with advice during my doctoral program. Many thanks to my peers, current and former

    graduate students: Gunawardena Egodawatte, Greta Camase, Jeff Meyers, Zekeryia

    Karadag, Hyeran Park, Joanne Nazir, Kevin Maguire, and Nenad Radakovic who

    collaborated with me on various scholar activities.

    A huge thank you to my family who supported my academic dream. My wife Paula,

    my three sons Pavel, Daniel and David, and my black Labrador Retriever, Bailey, who

    iv

  • understood me and supported me emotionally. Also, my parents, Maria and Enache, and

    my mother-in-law, Maria, who helped me and offered me support. Last, but not least,

    thank you God for the opportunity to meet all these people in the first place.

    v

  • TABLE OF CONTENTS

    Abstract................................................................................................................................ii

    Acknowledgements.............................................................................................................iv

    Table of Contents................................................................................................................vi

    List of Figures......................................................................................................................x

    List of Tables......................................................................................................................xi

    Chapter One: Introduction...................................................................................................1

    1.1 Overview...................................................................................................................1

    1.2 Research Context......................................................................................................1

    1.3 Rationale and Purpose of this Study.........................................................................4

    1.4 Research Questions...................................................................................................6

    1.5 Definitions of Terms.................................................................................................6

    1.6 Background of the Researcher..................................................................................8

    1.7 Significance of the Research...................................................................................12

    1.8 Limitations of the Study.........................................................................................12

    1.9 Structure of the Thesis............................................................................................13

    Chapter Two: Literature Review........................................................................................15

    2.1 Introduction..............................................................................................................15

    2.2 Mathematics Education in Secondary School.........................................................15

    2.3. Integrating Technology in Classrooms...................................................................20

    2.3.1 Technical Expertise Aspects in Integrating Technology in the Curriculum.....20

    2.3.2 Pedagogical Aspects of Using Educational Technology...................................22

    2.3.3 Social Aspects of the Integrating Technology in Classrooms...........................25

    2.3.4 Integrating Technology to Support Interactions and Innovations.....................27

    2.4 Integrating Technology in Mathematics Education................................................29

    2.4.1 General Challenges in Integrating Technology in Mathematics Classrooms...29

    2.4.2 Curricular Aspects in Implementing Technologies in Mathematics.................32

    2.4.3 Sociocultural Aspects in Integrating Computer Technology in Mathematics Education...................................................................................................................38

    vi

  • 2.5 Aspects of Professional Development in Mathematics Teaching...........................39

    2.5.1 Identifying Challenges for Teachers in Professional Development..................39

    2.5.2 Professional Development in Teaching Mathematics.......................................41

    2.5.3 Professional Development in Integrating Technology in Classrooms..............43

    2.5.4 Professional Development in Integrating Technology in Mathematics Education...................................................................................................................48

    2.6 Frameworks of Teaching Knowledge.....................................................................51

    2.6 Frameworks of Teaching Knowledge.....................................................................51

    2.6 Frameworks of Teaching Knowledge.....................................................................51

    2.6.1 Pedagogical Content Knowledge Model..........................................................52

    2.6.2 Other Frameworks of Teaching Knowledge Derived from the PCK................56

    2.6.3 Technological Pedagogical Content Knowledge..............................................57

    2.6.4 Technological Pedagogical Content Knowledge in Mathematics Education. . .61

    2.7 Chapter Summary...................................................................................................62

    Chapter Three: Methodology.............................................................................................64

    3.1 Overview.................................................................................................................64

    3.2 Rationale for Research Design...............................................................................64

    3.3 Research Context....................................................................................................67

    3.4 Methodological Considerations..............................................................................68

    3.4.1 The Role of Multiple Case Studies..................................................................68

    3.4.2 Selecting Participants.......................................................................................69

    3.4.3 The Role of Researcher.....................................................................................70

    3.5 Data Collection.......................................................................................................70

    3.5.1 Interviews..........................................................................................................71

    3.5.2 Observations...................................................................................................72

    3.5.3 Document Analysis...........................................................................................72

    3.6 Data Analysis...........................................................................................................72

    3.7 Ethical Review........................................................................................................73

    3.8 Validity and Credibility Issues................................................................................75

    Chapter Four: Findings......................................................................................................77

    4.1 George Goodwin School..........................................................................................77

    4.2 Lawrence.................................................................................................................80

    vii

  • 4.2.1 Background.......................................................................................................80

    4.2.2Overall Strategies of Integrating Technology in Classrooms............................82

    4.2.3 Using Technology in Teaching, Interactions, and Communications...............86

    4.2.4 Technological Knowledge in Curriculum Planning and Assessment..............87

    4.2.5 Knowledge of Students....................................................................................94

    4.2.6 Involving Technology in Math Classroom Activities......................................99

    4.2.7 Future Plans...................................................................................................107

    4.2.8 Summary........................................................................................................107

    4.3 Cecilia...................................................................................................................108

    4.3.1 Background.....................................................................................................108

    4.3.2 Overall Strategies of Integrating Technology in Classrooms........................110

    4.3.3 Using Technology in Teaching, Interactions and Communications...............112

    4.3.4 Technological Knowledge in Curriculum Planning and Assessment............116

    4.3.5 Knowledge of Students..................................................................................120

    4.3.6 Involving Technology in Math Classroom Activities....................................123

    4.3.7 Further plans..................................................................................................127

    4.3.8 Summary ........................................................................................................129

    4.4 Mark......................................................................................................................130

    4.4.1 Background.....................................................................................................130

    4.4.2Overall Strategies of Integrating Technology in Classrooms..........................133

    4.4.3 Using Technology in Teaching, Interactions, and Communications.............137

    4.4.4 Technological Knowledge in Curriculum Planning and Assessment............138

    4.4.5 Knowledge of Students..................................................................................144

    4.4.6 Involving Technology in Math Classroom Activities.....................................147

    4.4.7 Future Plans....................................................................................................156

    4.4.8 Summary.........................................................................................................158

    4.5 A Summary of the Three Case Studies.................................................................159

    Chapter Five: Discussion and Interpretation of Findings ...............................................162

    5.1 Introduction.............................................................................................

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