The development of mathematical competence -- both by humans as
a species over millennia and by individuals over their lifetimes --
is a fascinating aspect of human cognition.
This book explores when and why the rudiments of mathematical
capability first appeared among human beings, what its fundamental
concepts are, and how and why it has grown into the richly
branching complex of specialties that it is today. It discusses
whether the truths of mathematics are discoveries or inventions,
and what prompts the emergence of concepts that appear to be
descriptive of nothing in human experience. Also covered is the
role of esthetics in mathematics: What exactly are mathematicians
seeing when they describe a mathematical entity as beautiful ?
There is discussion of whether mathematical disability is
distinguishable from a general cognitive deficit and whether the
potential for mathematical reasoning is best developed through
instruction.
This volume is unique in the vast range of psychological
questions it covers, as revealed in the work habits and products of
numerous mathematicians. It provides fascinating reading for
researchers and students with an interest in cognition in general
and mathematical cognition in particular. Instructors of
mathematics will also find the book s insights illuminating.
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