Table Of ContentLimin Jao · Nenad Radakovic Editors
Transdisciplinarity
in Mathematics
Education
Blurring Disciplinary Boundaries
Transdisciplinarity in Mathematics Education
Limin Jao • Nenad Radakovic
Editors
Transdisciplinarity in
Mathematics Education
Blurring Disciplinary Boundaries
Editors
Limin Jao Nenad Radakovic
Department of Integrated Studies Department of Teacher Education
in Education College of Charleston
McGill University Charleston, South Carolina, USA
Montreal, Québec, Canada
ISBN 978-3-319-63623-8 ISBN 978-3-319-63624-5 (eBook)
DOI 10.1007/978-3-319-63624-5
Library of Congress Control Number: 2017953870
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Foreword
To a modern reader, the prefix trans- can evoke a range of meanings, from the
sublime to the mundane, depending on the context of its usage and the particular
word that usually follows it. It is a powerful prefix that can create opposing mean-
ings (e.g., transform vs. transgress) and situate meanings depending on the user.
For instance, the term “transcendental” colloquially connotes esoteric practices
associated with Eastern religions, where as in mathematics it refers to a very specific
type of number, one that is not algebraic. It also turns out that although specific
transcendental numbers such as π and e are most often referred to and perceived of
as exotic, as the term “transcendental” might suggest, there happen to be “as many”
of these numbers as there are real numbers, i.e., there are infinitely many! Given the
wide range of meanings possible, it is important to know that the prefix trans- comes
from Latin transcendere meaning to climb over or beyond or across. With this
meaning in mind, we can better grasp the term transdisciplinary, which is the topic
of this book in reference to mathematics education.
The editors of the book, Jao and Radakovic, delve into the etymological aspects
of the prefix trans- and clarify how this term is different from prefixes like inter- and
multi- to provide clarity to the reader. Simply put, the difference between an inter-
disciplinary approach and a transdisciplinary approach is that the former typically
involves (research) questions that can be approached via more than one discipline
and the methods used to answer the question reveal links between the disciplines
(e.g., mathematics and physics), whereas the latter suggests (research) questions
that lie outside the disciplines with methods and answers (solutions) informing new
discipline(s) and offering the possibility of unifying disciplines (e.g., the Human
Genome Project). For instance, when we ask simple questions like “What is the
cause of gravity?” or “What is the origin of matter?” the answers usually come in
the form of theories from different disciplines which have devised their own methods
for tackling such questions. These questions are also tackled outside the discipline
of science, in the humanities and in religion. Thus, these types of questions cannot
be appropriated by any discipline per se! An even simpler question is “What is a
human being?” and this as we know is the enterprise not only of entire universities and
religious organs but also that of business corporations and the marketing industry.
v
vi Foreword
Other examples are found in issues that deal with sustainable development or with the
environment, such as drilling for oil in wilderness areas, which require knowledge
from many disciplines to even understand the nature of the questions that arise.
Similarly, issues that arise in mathematics education can easily transcend disciplinary
boundaries and lead to questions that can only be answered with transdisciplinary
thinking. Such questions are as follows:
1. What are the causes of inequity in mathematics classrooms, in schools, and in
school systems?
2. Can mathematics as a school subject accommodate indigenous views not
subsumed under culture or ethno-labels?
The book takes into account such questions within mathematics education, its
genesis and subsequent evolution, into a plurality of perspectives, of theories, and
of research design that accommodate diverse groups of stakeholders, and the even-
tual transformation of these questions into transdisciplinary frameworks that require
critical and postmodern modes of thinking. To ease the reader into this progression,
the book is organized into five sections based on a cluster model of transdisciplinar-
ity, with chapters in each section that address questions requiring a particular mode
of thinking. As a whole, the book makes an excellent case for moving beyond
domain-specific thinking, particularly if the goal of mathematics education is to
address issues that are important to all its different stakeholders.
Department of Mathematical Sciences Bharath Sriraman
University of Montana-Missoula,
Missoula, MT, USA
Acknowledgments
Although the idea for an edited book on transdisciplinarity in mathematics educa-
tion came to us in the summer of 2015, the origins of our interest in transdisciplinar-
ity are much older. The transdisciplinary nature of our personal and professional
interests stems from our early experiences as students and classroom teachers strug-
gling to make sense of mathematics and to see it beyond the decontextualized
manipulation of symbols. Subsequently, we met as graduate students at the Ontario
Institute for Studies in Education of the University of Toronto, where we began our
friendship and collaboration. It was there that we were introduced to the mathemat-
ics education research community. As emerging scholars, we were inspired by fac-
ulty members who infused transdisciplinarity into their research and teaching and
conferences that pushed our thinking about the limits and scope of mathematics
education. Specifically, we are fortunate and proud to be members of the Canadian
Mathematics Education Study Group, a wonderful community of educators,
researchers, and practitioners who are advancing mathematics education in Canada
and worldwide. As we move forward in our careers, we continue to encounter indi-
viduals who enrich, transform, and transcend mathematics education through their
explorations across disciplines and cultures.
We are indebted to our previous experiences and the individuals who have
informed and shaped our thinking. Without them, this book would not have been
possible. We extend our thanks to all of the contributing authors for their dedication
and diligence throughout the writing and editing process. Thank you to Peter
Trifonas, who gave two recent graduates the confidence to embark on this adventure.
For her assistance with editing and proofreading, we thank Madison Fox, a graduate
student at the College of Charleston. Bharath Sriraman, thank you for reading our
manuscript and writing the Foreword.
We are grateful for the support of the faculty, staff, and students at our respective
institutions: the Department of Integrated Studies in Education (Faculty of Education,
McGill University) and the Department of Teacher Education (School of Education,
Health, and Human Performance, College of Charleston).
As our graduate supervisor, Doug McDougall recognized our potential, and we
are grateful for his ongoing mentorship.
vii
viii Acknowledgments
To Susan Jagger, our friend and colleague, we are so appreciative of your
friendship, encouragement, and sense of humor. We also thank Barb, for her enthusiasm
and positive energy.
Finally, we thank our families for their unconditional support and love. We dedicate
this book to you.
Contents
Part I Interdisciplinary Approaches in Mathematics Education
1 Euclidean Exploration of Geometry in Islamic Art . . . . . . . . . . . . . . . 3
Zekeriya Karadag
2 The Hidden Musicality of Math Class: A Transdisciplinary
Approach to Mathematics Education . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Song A. An, Daniel A. Tillman, and Lawrence M. Lesser
3 Using Children’s Literature to Enhance Math
Instruction in K-8 Classrooms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Melissa Luedtke and Karen Sorvaag
Part II Complexity, Difference and/in Mathematics Education
4 Complexity as a Discourse on School Mathematics Reform . . . . . . . . 75
Brent Davis
5 Opening a Space of/for Curriculum: The Learning Garden
as Context and Content for Difference in Mathematics Education . . 89
Susan Jagger
Part III Mathematics for the Common Good
6 Transdisciplinarity, Critical Mathematics Education,
Eco-justice, and the Politics to Come . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Nenad Radakovic, Travis Weiland, and Jesse Bazzul
7 Using a Mathematics Cultural Resonance Approach
for Building Capacity in the Mathematical Sciences
for African American Communities . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Terrence Richard Blackman and John Belcher
ix
x Contents
8 Still Warring After All These Years: Obstacles
to a Transdisciplinary Resolution of the Math Wars . . . . . . . . . . . . . . 151
Ilona I. Vashchyshyn and Egan J. Chernoff
Part IV Indigenous and Transformational Mathematical Knowledge
9 Echoed Rememberings: Considering Mathematics
and Science as Reconciliation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Dawn Wiseman and Lisa Lunney Borden
10 Gendered? Gender-Neutral? Views of Gender
and Mathematics Held by the Canadian General Public . . . . . . . . . . 193
Jennifer Hall
Part V Re-formulating, Re-presenting, and Re-defining Mathematical
Knowledge and the Curricula
11 Borrow, Trade, Regroup, or Unpack? Revealing How
Instructional Metaphors Portray Base-Ten Number . . . . . . . . . . . . . . 215
Julie Nurnberger-Haag
12 Mathematics and Movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
Susan Gerofsky
13 Examining the Development of a Transdisciplinary
Collaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
Limin Jao, Melissa Proietti, and Marta Kobiela
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
