This book is centrally concerned with how mathematics education is
represented and how we understand mathematical teaching and learning
with view to changing them. It considers teachers, students and
researchers. It explores their mathematical thinking and the concepts
that this thought produces. But also how these concepts acquire cultural
layers that mediate our apprehension. The book examines some of the
linguistic and socio-cultural filters that influence mathematical
understanding. But above all it introduces some contemporary theories of
human subjectivity, in which subjectivity is seen primarily as
consequential to, rather than productive of, our attempts to represent
or categorise the world in which we live. That is, our sense of who we
are results from our attempts to see ourselves against the various
versions of the world that we encounter. Such theories trouble the very
notion of mathematical "concepts" as apprehended by "humans". And in
foregrounding this concern with subjectivity the book considers
mathematics rather differently to styles more familiar in many instances
of mathematics education research. The book proposes that mathematics
can provoke us to think differently about our world and as a result
enable our transformative capacities. Such an orientation may disturb
our understanding of what mathematics is, how it exists in an
"objective" sense, insofar as mathematical objects can be derived from
social filters being applied to the world, but also serve as filters on
the world capable of producing new social entities.
