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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