Table Of ContentMATHEMATICS, CULTURE, AND QUESTIONS:
A STUDY IN THE CULTURE OF THE MATHEMATICS CLASSROOM
THROUGH A RANDOM QUESTIONING EXPERIMENT
By
PAIGE ALLISON
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2005
Copyright 2005
by
Paige Allison
This work is dedicated to
my children, Julie and Tommy,
who have been with me every step of the way;
to my Mother, Selma;
to those who motivated and inspired me to do this work;
and to all the students and teachers
who have touched my life and made this work possible.
ACKNOWLEDGMENTS
I am most grateful to all those who have been a part of this process. My first
contact with the University of Florida Department of Anthropology was with Allan
Burns, through Pat Waterman, who encouraged me to do the work that I wanted to do.
Dr. Burns said to me during our first conversation, “Don’t ever let anyone tell you that
you can’t do it.” I took his advice to heart and it has served me well. As my committee
chair, he fostered me as an anthropologist and directed me adroitly, carefully nudging me
in the right direction, even when I wasn’t sure that I wanted to go there. He stuck with
me through it all, and I am truly thankful for all of his help, support, and advice over the
years. Without Allan’s initial and long term support and encouragement I might never
have embarked on this project.
The many kindnesses I have received from Russ Bernard over the years have been
invaluable. He has always been there for me. I will never forget the thrill of learning
some clever way of counting or measuring things and the way his enthusiasm for his
work was such an integral part of his teaching. Not only did the subject matter appeal to
me; Dr. Bernard is very simply a fine teacher who is inspired by his work and passes that
inspiration on to others.
I am most appreciative of Sue Boinski, who has been my constant navigator and
reassurance that all will be well. Sue has been a mentor and helped me negotiate my way
through the maze of graduate school in such a way that she seems invisible to all but me.
iv
As professional mothers, we have shared support systems and advice when either of us
was in need. To sum it up, Sue has always had my back.
Several years ago, I had the pleasure of having dinner in San Francisco with
Catherine Emihovich. I came home from that meeting remembering her phrase, “Life is
long.” Everyone else says, “Life is too short.” I added her saying to my collection and
used it often. What a gift it was to find her moving to UF. I asked her to meet me for
lunch upon her arrival and explained to her that I was an “at risk” student. Before lunch
was over, she had me pointed in the right direction again. I appreciate her support and
her continued advice and assistance.
I extend many thanks to Thomasenia Lott Adams, who most graciously came to my
rescue when I was in need. From the day she defended her dissertation until the present,
she has always been a positive role model who conducts herself with great grace and
dignity. It is a special honor to have her, a student of Mary Grace Kantowski, as a
member of my committee.
I also want to extend my sincere appreciation to all those people who are a part of
my life who have in one way or another supported me or contributed to me making it to
this point. To those whom I have lived, loved, and laughed with, I thank them all. Many
thanks go to my extended family of dancers, drummers, musicians, and kindred spirits of
many varieties who have been my refuge and strength. Special thanks go to Julie and
Tommy who began this degree with me as little children who would come and sleep on
the couch near where I worked on late nights and who have given me their love and
support through thick and thin. To hear my daughter say to me, “You know I’m proud of
you, don’t you?” brings a big smile and tears to my eyes.
v
I wish also to thank my fellow students, friends, and neighbors who have wondered
just how long this was going to go on and who have patiently encouraged me and never
given up; and my students, who have taught me so much over the years and without
whom this project would never have come to fruition.
I wish to thank Robert, my friend of the heart, for everything!
Sincere gratitude goes to Heather McIlvaine-Newsad, who continued to pursue this
project even when I had given it up. Heather’s persistent crusade for funding and the
generosity of Western Illinois University were critical in the implementation of this
study. Additionally, I appreciate the firm but kind words of my friend Sheila Jeffers, who
said, “Just do it, Paige!” Spending a weekend with these two women made me realize
that I simply had to do this project. The invaluable, support, friendship, data analysis,
and editing contributions of Hank Green facilitated the seamless integration of qualitative
and quantitative data and the completion of this project. I extend many thanks to my
dissertation group, and to the SOR group who have always been helpful, kind, and
encouraging. An especially exuberant thank you goes to Stefany Burrowes who adroitly
talked me through the entire dissertation process and the peripheral life processes in such
a wonderfully kind, enlightening, supportive and juicy manner. Stefany’s faithful support
facilitated me completing this project sanely, and with grace and style.
A long overdue thank you is extended to the faculty, staff, and students of the UF
Department of Anthropology and the faculty, staff, and students of OGHS and the OCSB.
Without the help, encouragement, facilitation, and support of all these wonderful folks
this project would not have been possible.
vi
I would also like to thank James "Skippy" Albury for his tireless service and
devotion to the Empire, Butch and Arnold for always curling up next to me and just being
there for me as I worked, and Ernie Lado for being a really fine father to our children.
There are far too many names to remember or list, so to all those who have been a part of
this project in any way, I offer my sincerest gratitude and appreciation.
vii
TABLE OF CONTENTS
page
ACKNOWLEDGMENTS.................................................................................................iv
LIST OF TABLES............................................................................................................xii
LIST OF FIGURES.........................................................................................................xiv
ABSTRACT.......................................................................................................................xv
1 INTRODUCTION........................................................................................................1
Background...................................................................................................................1
Research Questions and Objectives..............................................................................2
Applied and Theoretical Significance of the Research.................................................6
Applied Significance.............................................................................................6
Theoretical Significance........................................................................................7
Research Site and Population.......................................................................................8
The Cultural Context of Oak Grove High School: A Sense of Place..........................9
Data Collected............................................................................................................13
Field Data............................................................................................................13
Analytic Data.......................................................................................................13
Organization of Chapters............................................................................................15
2 LITERATURE REVIEW...........................................................................................16
Theoretical Framework...............................................................................................30
Critical Race Theory............................................................................................30
Critical Pedagogy................................................................................................32
Research Objectives, Expectations, and Hypotheses.................................................39
3 RESEARCH DESIGN AND METHODOLOGY......................................................42
Introduction.................................................................................................................42
Quantitative Research Design and Methodology: The Random Questioning
Strategy Experiment................................................................................................42
Performance Measures........................................................................................45
Participation.........................................................................................................46
Attitudinal Measures...........................................................................................46
The scales.....................................................................................................46
Implementation and administration of the scales.........................................47
Teacher Perceptions and Feed Back....................................................................48
viii
Teacher Compensation........................................................................................48
Validity and Confounds.......................................................................................48
Limitations...........................................................................................................49
Qualitative Research Design and Methodology: The Focus Groups..........................50
Introduction.........................................................................................................50
Methodology........................................................................................................51
Ethnographic Methods.........................................................................................53
Variables..............................................................................................................56
Limitations...........................................................................................................56
4 RESULTS FROM QUANTITATIVE PORTION OF THE STUDY: THE
RANDOM QUESTIONING STRATEGY EXPERIMENT......................................58
Introduction.................................................................................................................58
Data Classification and Variables...............................................................................60
Academic Performance Measures..............................................................................62
National Proficiency Survey—Mathematics.......................................................62
Student Grades.....................................................................................................62
Discussion of Academic Performance Measures................................................62
Participatory Measures...............................................................................................63
Attitudinal and Belief Measures.................................................................................64
Evaluation of Survey Data...................................................................................64
Anxiety.........................................................................................................64
Math Value...................................................................................................64
Self-Concept.................................................................................................66
Enjoyment....................................................................................................67
Motivation....................................................................................................67
Beliefs...........................................................................................................68
Attitudes.......................................................................................................69
Discussion of Survey Data..................................................................................69
Between-Group Comparisons.............................................................................70
Mathematical performance—NPSS mathematics........................................71
Math anxiety.................................................................................................72
Value of mathematics...................................................................................74
Self-Concept in mathematics.......................................................................75
Enjoyment of mathematics...........................................................................76
Mathematical motivation..............................................................................77
Beliefs about mathematics...........................................................................78
Attitudes toward mathematics......................................................................79
Discussion of Between-Group Comparisons.......................................................79
Summary.....................................................................................................................86
Key Findings...............................................................................................................88
RQS.....................................................................................................................88
T1 and T2 Between-Group Comparisons............................................................88
ix
5 RESULTS FROM QUALITATIVE PORTION OF THE STUDY...........................90
The Focus Groups.......................................................................................................90
Objectives and Questions....................................................................................90
Data Analysis.......................................................................................................91
The Focus Groups................................................................................................92
Major Themes and Sub-Themes..........................................................................93
What Teachers Do...............................................................................................95
Teaching and instruction..............................................................................95
Ethnicity and gender – teacher...................................................................104
What Students Do..............................................................................................109
Student effort..............................................................................................110
The value of education...............................................................................112
Future plans................................................................................................113
Student feelings and stress.........................................................................114
Student behavior.........................................................................................116
Math rating.................................................................................................121
Textbooks...................................................................................................124
Best Practices.............................................................................................124
Ethnicity and gender – student...................................................................128
Classroom Questions and the Random Questioning Strategy (RQS)...............133
Classroom questions...................................................................................133
Focus groups RQS......................................................................................136
Teacher perceptions and feedback – surveys and comments RQS............138
Students’ perceptions, attitudes, and feedback—surveys and comments
RQS.........................................................................................................141
Follow Up RQS Questions.......................................................................................141
What Administrators Do: The School Environment........................................144
Class size....................................................................................................145
Good and bad classes.................................................................................146
Views From the Field...............................................................................................148
Outside Participant Observations......................................................................148
A Lifetime in the Field......................................................................................149
Leadership for Social Justice.............................................................................156
Teaching assignments................................................................................158
Curriculum.................................................................................................163
Suggested improvements............................................................................169
Practicing leadership for social justice.......................................................172
Discussion of Qualitative Results.............................................................................173
Key Findings.............................................................................................................177
Focus Groups and Participant Observation.......................................................177
Teachers.....................................................................................................177
Students......................................................................................................177
Administrators............................................................................................178
RQS Feedback...................................................................................................178
Focus Group Data Table....................................................................................179
x
Description:through the maze of graduate school in such a way that she seems invisible to all
but me. I came home from that meeting remembering her phrase, “Life is.
