EFFECTIVE PRACTICES IN GRADE 9 APPLIED MATHEMATICS by ALISON VM MACAULAY A ...

335 Pages·2015·8.16 MB·English

EFFECTIVE PRACTICES IN GRADE 9 APPLIED MATHEMATICS

by

ALISON V. M. MACAULAY

A thesis submitted in conformity with the requirements
for the degree of Doctor of Education
Department of Leadership, Higher and Adult Education
Ontario Institute for Studies in Education
University of Toronto

© Copyright by Alison Macaulay 2015
ii

EFFECTIVE PRACTICES IN GRADE 9 APPLIED MATHEMATICS
Alison Macaulay
Doctor of Education
Department of Leadership, Higher and Adult Education
University of Toronto
2015
Student achievement in Grade 9 has been linked to both secondary and post-secondary
outcomes. Although Ontario has implemented significant curriculum and secondary
school reforms, a significant subset of Ontario Grade 9 students consistently do not attain
proficiency in mathematics. Students that take the applied mathematics course—on the
pathway to college—are more likely to not reach the provincial standard on the
provincial Grade 9 mathematics assessment than they are to reach it. This can have long-
lasting consequences. The purpose of this qualitative study was to discern practices from
the field that might contribute to better student outcomes in Grade 9 Applied
Mathematics classrooms. Mathematics education experts from across the province were
interviewed and visits were conducted at four of the province’s most successful schools
on the Grade 9 provincial mathematics assessment. The findings from this study
contribute to our understanding of the types of resources, professional development,
departmental, leadership, and teaching practices that support student achievement in
Grade 9 Applied Mathematics. The findings can be distilled into six central ideas. These
are the importance of: reform-based teaching strategies and dispositions that foster
intellectual engagement and investment in learning; instructional leadership by both the
school administrator and mathematics department head; collaboration for both the
teachers of and students in the Grade 9 Applied Mathematics course; valuing EQAO
iii

assessments at all levels of the system; mitigating the stigma around applied-level
courses; and, careful attention to the placement of teachers in Grade 9 Applied
classrooms. This study contributes to the Ontario literature on Grade 9 Applied
Mathematics and the literature on implementing mathematics reform. The findings of
this study are of relevance to policy-makers and practitioners, especially school leaders
and teachers. The study concludes with recommendations for both research and practice.
iv

Dedication

For my father,
You are never far from my thoughts.
This one is for you.
v

Acknowledgments
I have left the writing of this section of my research report as the final act of my
EdD journey. And so, I sit here with mixed emotions. Though I am incredibly thrilled to
have crossed the finish line, this also marks the tangible end to an amazing journey of
growth, discovery, reflection, and intellectual engagement. I think differently now as a
result of the journey, and I am forever transformed. There are many people to thank.
First of all, in pursuing my doctorate, I decided to go the route of the EdD cohort.
What a great decision that turned out to be! I learned so many lessons from my cohort
colleagues and from the opportunity to engage in the academic enterprise with them.
Thank you especially to Kathy, Mary, Cindy, Richard, and John who kept in touch with
me long after the courses were over, gave me encouragement to carry on, and delivered
pep talks as needed.
To the professors and staff at OISE that contributed to my EdD experience, thank
you. Whether you taught a course, played a role in, or organized one of the many
milestones (internship, comprehensive exam, proposal hearing, ethical review, and final
oral examination)… I appreciate what you did to support me along the way.
To Dr. Jane Gaskell, thank you for serving as a member of my examining
committee. I appreciate the time and energy that you gave to the cause. It was an added
bonus after your presence at my proposal hearing. I valued all your support and
encouragement on both of these occasions as well as the perspective that you brought
which pushed my thinking in new ways.
To my external committee member and reviewer, Dr. Ann Kajander, thank you. I
have followed your work for a long time, and it was a thrill that you agreed to read and
vi

give feedback on my work. Your enthusiasm and encouragement for my research is
much appreciated. I am especially grateful that you travelled from the Lakehead to
attend my examination in person. Thank you also for your thoughtful questions that
facilitated my growth as a new scholar. It was very nice to hear your thoughts and
perspective on my work and how it might be helpful to the field.
To my committee members Dr. Carol Campbell and Dr. Doug McDougall, you
have been a “Dream Team” to work with… I look up to you both as accomplished
scholars and role models, so having you on my committee is indeed a dream come true! I
appreciate the time that you both took to read my work, to prepare your thoughtful
feedback, and to share your insights. You have helped me to understand the significance
and value of the peer review process and how it can make my work and thinking that
much better. I am honoured that you believed in this work and what might be learned
from it.
To my supervisor Dr. Joe Flessa, your presence along my journey has had a
profound impact on me: from my course work, to the comprehensive exam, to the
research thesis. You have challenged me to rise to new heights and to become an
independent and confident thinker “with a cause.” Your feedback and questioning about
what I was learning helped me to consolidate my understanding and clarify my new and
emerging insights. You always gave me the perfect advice to polish my writing. I am
forever grateful to you for catching the ball in play and helping me make it to the finish
line. You so graciously honoured the work as it was and believed in me to carry on.
Thank you for the leap of faith! I am quite certain that I would not have made it without
vii

your support, inspiration, and reassurance that the end was in sight. What’s more, I could
not hoped for a better outcome in the end! Gratias tibi ago.
To everyone that participated in my study, thank you. I have learned so very
much from all of you. Thank you also to the boards and schools that permitted the
research. What I have learned from this work is a celebration of remarkable things
happening in your remarkable classrooms with your remarkable teachers and their
remarkable students. I look forward to sharing the lessons that I have gleaned from them.
To my friends and colleagues who have encouraged and supported me over the
past eight years, thank you. Thank you especially to my co-workers Sandra, Natalie, and
Beth who were such willing active listeners and sounding boards. I must also thank
Maureen for giving me the latitude to make “it” happen, for believing in this work, and
my “other” life as a researcher.
I must also extend a special thanks to Sandra for helping me at the drop of a hat,
whenever I made a random request of her. I owe Figures 7, 8, and 23 to her genius for
transforming my field note sketches to a “thing of beauty” with Geometer’s Sketchpad.
Last, but not least, I must thank my family. For the patience, the faith and the
occasional nudges that you have given, thank you. Thank you to my parents and my
sister for believing in me and celebrating my accomplishments along the way, not only
on this journey but also throughout my life. You have always supported me
unconditionally, whatever the venture, and I am so very grateful for that.
Thank you to my husband Don who never batted an eye when I first broached the
subject of pursuing my doctorate. He had barely had time to recover from the Masters
epoch! Regardless, he has been in my corner this whole time, bestowing unending
viii

support, latitude, and endurance. Eight years is a long time. It is time to turn the page
and start a new chapter. And finally to my pets Kobe and the never-forgotten Patches.
They have taken their turns in keeping me company during many a late night. There
should be lots more time now for walkies, frolics in the park, and Sunday drives!
ix

TABLE OF CONTENTS

ABSTRACT ...................................................................................................................... ii
DEDICATION .................................................................................................................. iv
ACKNOWLEDGEMENTS .............................................................................................. v
TABLE OF CONTENTS ................................................................................................. ix
LIST OF TABLES ......................................................................................................... xiii
LIST OF FIGURES ........................................................................................................ xiv
CHAPTER ONE: INTRODUCTION .............................................................................. 1
Overview ............................................................................................................................. 1
Background and Policy Context .......................................................................................... 2
Education Reform in Ontario .............................................................................................. 3
Statement of the Problem .................................................................................................... 5
Guiding Research Questions ............................................................................................. 10
Background of the Researcher ........................................................................................... 11
Plan of the Thesis .............................................................................................................. 17
CHAPTER TWO: LITERATURE REVIEW .............................................................. 19
Overview ........................................................................................................................... 19
Literature Review Search .................................................................................................. 19
The Evolution of Mathematics Curricula in Ontario ......................................................... 21
The Common Curriculum ...................................................................................... 21
The Ontario Curriculum: Mathematics .................................................................. 22
x

The Ontario Curriculum: Mathematics (revised 2005) ......................................... 29
Ontario Provincial Assessments ............................................................................ 37
EQAO Grade 9 Assessment of Mathematics ........................................................ 39
The Mathematics Reform Movement ................................................................................ 47
Reform-based Teaching Practices ..................................................................................... 51
Supports for Mathematics Reform in Ontario ................................................................... 80
Barriers to Implementing Reform-based Practices ............................................................ 84
Implementing Change in Secondary Schools .................................................................... 88
Departmental Structures .................................................................................................... 88
Teacher Autonomy ............................................................................................................ 94
Streaming ........................................................................................................................... 98
The High Stream Advantage ........................................................................................... 105
Conceptual Framework .................................................................................................... 113
Theoretical Perspective: Social Constructivism .............................................................. 116
Significance of the Study ................................................................................................. 117
Chapter Summary ............................................................................................................ 123
CHAPTER THREE: METHODOLOGY ................................................................... 126
Overview ......................................................................................................................... 126
Research Design .............................................................................................................. 126
Data Collection ................................................................................................................ 127
Data Management ............................................................................................................ 128
Phase 1: Focus Groups .................................................................................................... 133
Sample ............................................................................................................................. 135