an examination of the integration of graphing calculators in formal assessments that accompany ...

225 Pages·2005·0.56 MB·English

AN EXAMINATION OF THE INTEGRATION OF GRAPHING CALCULATORS
IN FORMAL ASSESSMENTS THAT ACCOMPANY
HIGH SCHOOL MATHEMATICS TEXTBOOKS

by
Kimberly Joy Graham

A dissertation submitted in partial fulfillment
of the requirements for the degree

of
Doctor of Philosophy
in
Mathematics

MONTANA STATE UNIVERSITY
Bozeman, Montana

April 2005
©COPYRIGHT
by
Kimberly Joy Graham
2005
All Rights Reserved
ii

APPROVAL
of a dissertation submitted by
Kimberly Joy Graham

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

Maurice J. Burke

Approved for the Department of Mathematical Sciences
Kenneth L. Bowers

Approved for the College of Graduate Studies
Bruce McLeod
iii
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 non-
exclusive right to reproduce and distribute my abstract in any format in whole or in part.”

Kimberly Joy Graham
April 14, 2005
iv
ACKNOWLEDGEMENTS

I would like to express my gratitude to my advisor, Maurice Burke, for his
invaluable guidance and efforts on my behalf throughout the course of my Ph.D. studies.
I would also like to thank Ted Hodgson for his help in selecting a topic and putting
together the research proposal for my dissertation. Many thanks to Betsy Palmer for her
suggestions and statistical advice, and thank you to Linda Simonsen and Jennifer
Luebeck for their helpful input.
I would like to thank the publishing company representatives from
Glencoe/McGraw-Hill, Holt, Rinehart, & Winston, Key Curriculum Press, McDougal
Littell, Prentice Hall, Saxon, SIMMS (Gary Bauer), and South-Western Educational
Publishing (ARISE) for their cooperation and generosity in donating the curricular
materials examined in this study.
Finally, I cannot thank my husband Shane enough for his steadfast love, patience,
encouragement, and support. I want to thank and express my appreciation to my parents,
Ken and Beverly, for their encouragement in the pursuit of this endeavor and for being
great role models. Also, thank you to my mother-in-law, Marilyn, for her love and
support.
v
TABLE OF CONTENTS

LIST OF TABLES...........................................................................................................viii
LIST OF FIGURES...........................................................................................................ix
ABSTRACT.......................................................................................................................xi

1. PROBLEM STATEMENT AND SIGNIFICANCE OF STUDY`..............................1

Introduction...................................................................................................................1
Assessment and Graphing Calculators.....................................................................2
Textbooks................................................................................................................5
Statement of the Problem..............................................................................................6
Purpose of the Study.....................................................................................................6
Research Questions.......................................................................................................7
Definition of Terms......................................................................................................8
Significance of the Study............................................................................................10

2. REVIEW OF THE LITERATURE............................................................................12

Introduction.................................................................................................................12
Curricular Implementation and Standards..................................................................13
Graphing Calculator Technology...............................................................................17
Graphing Calculator Benefits................................................................................17
Topics Most Amenable to Graphing Calculator Use.............................................18
Graphing Calculator Complications......................................................................20
Curriculum Issues Related to Graphing Calculators.............................................21
Teacher Beliefs......................................................................................................22
Appropriate Classroom Use...................................................................................23
Assessment.................................................................................................................24
Graphing Calculator Technology and Assessment................................................25
Test Item Assessment............................................................................................29
Mathematics Textbook Evaluation.............................................................................31
The Use of Technology in Mathematics Textbooks..............................................31
The Use of Graphing Calculator Technology........................................................32
Textbook Assessment Materials............................................................................36
The Influence of the Standards..............................................................................37
Research Methods.......................................................................................................43
Standards-Based Instruments.................................................................................43
Mixed Methodologies............................................................................................45
Methodological Framework...................................................................................46
Summary.....................................................................................................................47
Theoretical Framework...............................................................................................47
vi
TABLE OF CONTENTS – CONTINUED

3. METHODOLOGY.....................................................................................................50

Research Design.........................................................................................................50
Textbook Sample...................................................................................................50
Formal Assessment Sample...................................................................................54
Measures................................................................................................................58
Categories in the Rubric........................................................................................60
Methodology...............................................................................................................64
Research Question 1..............................................................................................64
Research Question 2..............................................................................................65
Method of Data Collection for Research Questions 1 and 2.................................65
Method of Data Analysis for Research Questions 1 and 2....................................66
Research Question 3..............................................................................................69
Method of Data Collection for Research Question 3.............................................70
Method of Data Analysis for Research Question 3...............................................71

4. RESULTS...................................................................................................................72

Introduction.................................................................................................................72
Results for Research Question 1............................................................................72
Results for Research Question 2............................................................................79
Results for Research Question 3..........................................................................108
Part 1 of Research Question 3.............................................................................108
Saxon...................................................................................................................108
Key Curriculum Press..........................................................................................109
Glencoe................................................................................................................110
Holt, Rinehart, & Winston...................................................................................111
McDougal Littell.................................................................................................112
Prentice Hall........................................................................................................113
UCMSP................................................................................................................114
Core-Plus.............................................................................................................116
IMP......................................................................................................................117
SIMMS................................................................................................................118
Part 2 of Research Question 3.............................................................................120
Goals for Graphing Calculator Use................................................................120
Extent of Graphing Calculator Use.................................................................120
Request for Justification in Graphing Calculator Problems...........................121
Graphing Problems Set in a Real-World Context...........................................121
Use of Graphing Calculator for Computation or Visualization......................122
Translation between Different Representations..............................................122
Teaching Notes...............................................................................................123
Miscellaneous.................................................................................................124
vii
TABLE OF CONTENTS – CONTINUED

Summary of Results.........................................................................................................124
The Ten Curricula................................................................................................125
Comparison of NSF-Funded Group to Non-NSF-Funded Group.......................132

5. CONCLUSIONS......................................................................................................134

Introduction...............................................................................................................134
Conclusions..........................................................................................................134
Implications for Curriculum................................................................................138
Curriculum Alignment.........................................................................................142
Other Observations..............................................................................................145
Summary of Conclusions.....................................................................................146
Limitations...........................................................................................................147
Delimitations........................................................................................................148
Recommendations for Research..........................................................................148

BIBLIOGRAPHY............................................................................................................150

APPENDICES.................................................................................................................158

APPENDIX A: GRAPHING CALCULATOR USE RUBRIC...............................159
APPENDIX B: INSTRUCTIONS FOR GRAPHING
CALCULATOR USE RUBRIC....................................................163
APPENDIX C: SENK, BECKMANN, AND THOMPSON’S
“ITEM CHARACTERISTICS AND
CATEGORIES” CODING SCHEME...........................................177
APPENDIX D: TABLE TO COLLECT DATA WITH
GRAPHING CALCULATOR USE RUBRIC...............................180
APPENDIX E: QUANTITATIVE DATA..............................................................182
APPENDIX F: QUALITATIVE DATA.................................................................193
viii
LIST OF TABLES

Table Page
1. Example of data collected from the ARISE curriculum..........................................67

2. Outcomes.................................................................................................................68

3. Percent frequency of occurrence scale
defined by researcher...............................................................................................69

4. Indication of graphing calculator use (explicit or implicit).....................................75

5. Graphing calculator technology level (active).........................................................76

6. Cognitive level (transitional/higher-order thinking skills)......................................85

7. Reason for graphing calculator use (visualization)..................................................86

8. Request for justification...........................................................................................88

9. Real-world context...................................................................................................89

10. Role of graph (interpret/make)...............................................................................90

11. Simplification (no).................................................................................................91

12. Active items that require transitional/higher-order
thinking skills.......................................................................................................107
ix
LIST OF FIGURES

Figure Page
1. Stages in the backward design process....................................................................49

2. Venn diagram illustrating the states of Texas, Florida,
and South Carolina and publishers most common to the
textbook adoption lists of these states......................................................................52

3. Percentages for indication of graphing calculator use
as explicit or implicit...............................................................................................75

4. Percentages for graphing calculator technology level
as active....................................................................................................................76

5. Scatterplot of indication of graphing calculator use
(explicit or implicit) and graphing calculator technology
level (active).............................................................................................................78

6. Active items as a portion of explicit or implicit items.............................................79

7. Percentages for cognitive level as transitional/higher-order
thinking skills...........................................................................................................85

8. Percentages for reason for graphing calculator use as
visualization.............................................................................................................86

9. Percentages for request for justification as yes........................................................88

10. Percentages for real-world context as yes..............................................................89

11. Percentages for role of graph as interpret or make................................................90

12. Percentages for simplification as no......................................................................91

13. Saxon’s extent and quality of use, taking into account
pool sizes................................................................................................................93

14. Key’s extent and quality of use, taking into account
pool sizes................................................................................................................94