Contents: Preface. Cognitive Development and Mathematics Learning. Children's Counting. Quantitative Comparison Without Numbers. Understanding Units. Relations Among Quantities in Arithmetic: Additive and Multiplicative Reasoning. Understanding Fractions. Implications for Developmental Psychology. Implications for Mathematics Education.
Sophian, Catherine
"Sophian presents a tautly reasoned and compelling challenge to
schooling-as-usual, that is, to instruction that takes counting as
the basis for teaching children arithmetic... She argues for
highlighting the unit as the foundation of mathematics instruction
[and] goes on to trace the implications of unit not only for
instruction on conventional topics, such as rational number,
multiplication, and division, but also for a wider mathematics
education that knits number, measure, data, and geometry."—Richard
Lehrer
Vanderbilt University"Sophian does a masterful job of organizing
and presenting one of the major success stories of developmental
and educational research – understanding the developmental roots of
mathematical competence.... This book will interest and benefit
both those interested in understanding children's cognitive
development and those interested in developing ways of promoting
mathematical competence. Sophian's research has contributed greatly
to our understanding of both aspects of mathematical development;
her book provides a timely and accessible introduction to the state
of the art in research on children's mathematical development."
—Kevin Miller
University of Michigan
"Sophian presents a tautly reasoned and compelling challenge to
schooling-as-usual, that is, to instruction that takes counting as
the basis for teaching children arithmetic... She argues for
highlighting the unit as the foundation of mathematics instruction
[and] goes on to trace the implications of unit not only for
instruction on conventional topics, such as rational number,
multiplication, and division, but also for a wider mathematics
education that knits number, measure, data, and geometry."
—Richard Lehrer
Vanderbilt University"Sophian does a masterful job of organizing
and presenting one of the major success stories of developmental
and educational research – understanding the developmental roots of
mathematical competence.... This book will interest and benefit
both those interested in understanding children's cognitive
development and those interested in developing ways of promoting
mathematical competence. Sophian's research has contributed greatly
to our understanding of both aspects of mathematical development;
her book provides a timely and accessible introduction to the state
of the art in research on children's mathematical development."
—Kevin Miller
University of Michigan
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