The common theme that links the six contributions to this volume
is the emphasis on students' inferred mathematical experiences as
the starting point in the theory-building process. The focus in
five of the chapters is primarily cognitive and addresses the
processes by which students construct increasingly sophisticated
mathematical ways of knowing. The conceptual constructions
addressed include multiplicative notions, fractions, algebra, and
the fundamental theorem of calculus. The primary goal in each of
these chapters is to account for meaningful mathematical learning
-- learning that involves the construction of experientially-real
mathematical objects. The theoretical constructs that emerge from
the authors' intensive analyses of students' mathematical activity
can be used to anticipate problems that might arise in
learning--teaching situations, and to plan solutions to them. The
issues discussed include the crucial role of language and symbols,
and the importance of dynamic imagery.
The remaining chapter complements the other contributors'
cognitive focus by bringing to the fore the social dimension of
mathematical development. He focuses on the negotiation of
mathematical meaning, thereby locating students in ongoing
classroom interactions and the classroom microculture. Mathematical
learning can then be seen to be both an individual and a collective
process.
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