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.
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