For proposal stage:
About the author
Preface
Chapter One Introduction
Chapter Two Reason to believe
Chapter Two provides a theoretical discussion of how we understand
mathematical knowledge. The theory presents rationality and belief as
mutually formative dimensions of school mathematics, where each term is
more politically and socially embedded than often depicted in the field
of mathematics education research. School mathematics then presents not
so much rational mathematical thought distorted by irrational beliefs
but rather a specific mode of activity referenced to the performance of
certain substitute skills and procedures that have come to represent
mathematics in the school context consequential to the demands of social
management. The chapter considers alternative modes of apprehending
mathematical objects derived as they are from this socially defined
space. The chapter's central argument is that rational mathematical
thought necessarily rests on beliefs set within a play of ideological
framings that within school often partition people in terms of their
proxy interface with mathematics. The challenge is then seen as being to
loosen this administrative grip to allow both students and teachers to
release their own powers to generate diversity in their shared
mathematical insights rather than being guided by conformity.
Chapter Three The social packaging of mathematical learning.
Chapter Three considers some of the arbitrary curriculum or assessment
criteria that operate in the social construction of mathematics in
educational institutions. The advance of mathematics as an academic
field is typically defined by the production of new ideas, or concepts,
which adjust progressively to new shared ways of being. That is,
mathematical concepts are created or invented to meet the diverse
demands of everyday life, and this very diversity can unsettle more
standardised accounts of what mathematics is supposed to be according to
more official rhetoric. For example, the expansion of mathematics as a
field often relies on research grants selected to support economic
priorities. In schools, economic factors influence the topics chosen for
a curriculum. In some countries, for instance, there is a shortage of
specialist mathematics teachers that limit curriculum choices and
restrict the choice of viable teaching materials, educational targets or
models of practice advocated by research in mathematics education. Our
evolving understandings of who we are and of what we do shape our use of
mathematical concepts and thus our understandings of what they are.
School mathematics has been reduced according to ideological schema to
produce its conceptual apparatus, pedagogical forms and supposed
practical applications.
Chapter Four The social administration of mathematics subject knowledge
through teacher education
Chapter Four describes some recent empirical research in university
teacher education. It considers how practices of teacher education
impact on classroom practice by new teachers and thus shape the
mathematics that takes place. The theme is explored through an extended
discussion of how the conduct of mathematical teaching and learning is
restricted by regulative educational policies that set the parameters
through which teacher education takes place. Specifically, it considers
the example of how mathematics is discursively produced by student
teachers within an employment
