Table Of ContentBookID 176232_ChapID FM1_Proof# 1 - 29/07/2009
Mathematical Subjects
BookID 176232_ChapID FM1_Proof# 1 - 29/07/2009
Fiona Walls
Mathematical Subjects
Children Talk About
Their Mathematics Lives
BookID 176232_ChapID FM1_Proof# 1 - 29/07/2009 BookID 176232_ChapID FM1_Proof# 1 - 29/07/2009
Fiona Walls
James Cook University
Townsville, QLD
Australia
BookID 176232_ChapID FM1_Proof# 1 - 29/07/2009
This work is dedicated firstly to the real
subjects of this book, known here as
Dominic, Fleur, Georgina, Jared, Jessica,
Liam, Mitchell, Peter, Rochelle, and Toby,
whose unfolding mathematical learning
narratives this book captures, secondly to
all the children learning mathematics
around the world whom they represent
and on whose collective behalf they speak,
and thirdly to Otto Caspian Kulpe-Greer,
who was born while this book was in the
writing. He symbolises the next generation
of mathematical subjects for whom the
book has been created in the hope that
their stories might speak of pleasure and
fulfilment in their learning of themselves
through mathematics.
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Preface
Teaching and learning mathematics is a political act in which children, teachers,
parents, and policy makers are made visible as subjects. As they learn about
mathematics, children are also learning about themselves – who they are, who they
might become. We can choose to listen or not to what children have to say about
learning mathematics. Such choices constitute us in relations of power.
Mathematical know-how is widely regarded as essential not only to the life
chances of individuals, but also to the health of communities and the economic
well-being of nations. With the globalisation of education in an increasingly
market-oriented world, mathematics has received intensified attention in the first
decade of the twenty-first century with a shifting emphasis on utilitarian aspects of
mathematics. This is reflected in the reconceptualisation of mathematical competence
as mathematical literacy, loosely conceived as those ways of thinking, reasoning
and working “mathematically” that allow us to engage effectively in everyday
situations, in many occupations, and the cut and thrust of world economies as
active, empowered and participatory citizens.
It is no surprise then that mathematics has become one of the most politically
charged subjects in primary school curricula worldwide. We are experiencing an
unprecedented proliferation of regional and national strategies to establish
benchmarks, raise standards, enhance achievement, close gaps, and leave no child
behind in mathematics education. Industries have sprung up around the design,
administration and monitoring of standardised assessment to measure and compare
children’s mathematical achievement against identified benchmarks and each other.
Whether regional, national or international, such tests wield substantial political
power. They are used by educational policy makers to report to parents and to
education ministers, or to gauge teacher and school effectiveness, and because they
are widely believed to provide robust evidence of the mathematical strengths and
weaknesses of individual children across demographic groups, schools, and
geographical regions, standardised test results are used to justify particular
pedagogical approaches over others and to support further research. Despite these
efforts, significant disparities continue to be observed.
Somewhere in the nexus of mathematics, government, education, commerce and
industry, our children are socially constituted. Children are generally oblivious to
the wider forces that shape their everyday worlds and take it for granted that school
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viii Preface
is the place where every child must go to learn. School is also the place where,
from a very young age, children first meet formal learning of the subject we call
“mathematics.” From the outset most children have little say in how their learning
of mathematics will be presented, structured and sequenced or in the mathematical
content they will encounter. Children’s unique and individual qualities, including
their mathematical ways of seeing and interpreting the world, are seemingly of
little account as they are processed through the apparatuses of testing, grading,
grouping and mathematical instruction that reify and position them as the objects
of mathematical education.
Since the 1980s there has been an increasing global focus on human rights in the
design and implementation of social policy, of which education forms a significant
part. In documents such as the widely ratified United Nations Convention on the
1
Rights of the Child, the child is figured as an active agent with the right to participate
in decisions that affect the child’s life. Children are produced in the discourse of
human rights as valued members of their communities with legitimate if diverse
(childish?) ways of seeing, their thoughts and feelings about the world valued as
necessary and worthwhile contributions to our societies, yet studies show that
children themselves believe that adults show little concern or respect for their views
and opinions (e.g. Tucci et al. 2007).
Recognition of children’s right to inclusion in decisions about their schooling
can be seen as part of a movement towards a critical education that seeks to enhance
learners’ participation and thus reconfigure learning spaces to reflect the child not
merely as a cognising and increasingly autonomous unitary “self” but also as a
socially connected, corporeal, emotional, ethical, and aesthetic self constantly in
the process of becoming in dynamic engagement with her or his environments
(Lloyd-Smith and Tarr 2000). As such, this book is radical for its assertion that it
is in our recognition of the different and equal being of children as mathematically
active subjects whose experiences, worldviews, proclivities, passions, and aversions
are a continuously engaged and constitutive part, that the right of children to be
heard, not simply to be seen as a demographic to be researched, operated upon,
manipulated and inscribed within our educational policies and institutions, might
be enacted in a critical mathematics education that serves, rather than being served
upon, our children. In such a spirit this book acts as a mouthpiece through which
children speak about their mathematics lives.
1
Children in this convention are defined as those between the ages of 0 and 18 years. I have used
the same definition throughout this book.
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Acknowledgements
As with any constructive endeavour, books are never solely the work of their
authors. They emerge as socially contextualised artefacts and as such, bear the marks
of a multitude of contributors from forebears, family and friends to colleagues and
mentors, all of whom I acknowledge fulsomely.
I wish to make specific mention of the following people whose support over
many years, manifested through their love, inspirational ideas and intellectual
guidance, and provision of beds and breakfasts, research grants and study leave,
dwells particularly powerfully between the lines of this work:
My family Alastair Wilkinson, Manu Greer, Tara Greer, Ben Greer and Antje
Kulpe; my mathematics education mentors Jim Neyland and Megan Clark of
Victoria University of Wellington, New Zealand; my colleagues Nola Alloway,
Malcolm Vick and Jo Balatti of James Cook University, Australia; my mathematics
education soul mates Mônica Mesquita and Aléxandre Pais of Sao Paolo/Lisbon;
my accommodating (literally) friends Barbara Smythe, Nikolien Van Wijk, Gerda
Yske (late) and Joe and June Stewart, and my publishing team Kristina Wiggins-
Coppola and Marie Sheldon of Springer, USA who believed in this project when it
was but a germ of an idea.
In the interests of privacy, the children and their family members, teachers and
principals who took part in this study cannot be named, but their contributions are
particularly lovingly acknowledged. It is in their generous opening of their homes
and classrooms and their frank telling of life as they experienced it that these
remarkable everyday people have given life to this book.
Proceeds from the sale of this book will be donated to UNICEF in support of the
global Child-Friendly Schools Initiative, “a cause that helps children in education”
as suggested by the children in this study. It is hoped that this book will raise
awareness of the power that mathematics education has to make children and of
the largely unquestioned and often obscured practices that adults adopt in their
teaching of mathematics that determine who our children might become.
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Contents
Part 1 U nderstanding Children as Mathematical Subjects:
Theories and Methods
1 O f Subjects, Subjectivity and Subjectification:
Subjects Made Visible .............................................................................. 3
2 O f Archaeology and Genealogy:
Choosing Sites and Tools ......................................................................... 13
Part 2 The Art of Being Mathematical: The Primary Years
3 Children at Work ..................................................................................... 29
4 Tests and Contests .................................................................................... 67
5 Error and Correction ............................................................................... 93
6 The Emergence of Ability ........................................................................ 133
Part 3 Subjects of Choice: The Secondary Years
7 Form and Formula ................................................................................... 175
8 Measures of Success ................................................................................. 187
9 Keeping Up ............................................................................................... 207
10 The Shape of Life ..................................................................................... 217
Part 4 Mathematical Futures: Life After School
11 Girl Time and Boys’ Clubs: Mathematical Genderfication ................. 231
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xii Contents
12 Background or Foreground? Home, Social Class and Ethnicity ......... 247
13 Contemplating a Child-Friendly Mathematical Education ................. 257
Epilogue ............................................................................................................ 269
References ......................................................................................................... 271
Appendix ........................................................................................................... 281
Index .................................................................................................................. 283
