"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 LehrerVanderbilt 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 MillerUniversity of Michigan

• 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 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 LehrerVanderbilt 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 MillerUniversity of Michigan

• 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 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 LehrerVanderbilt 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 MillerUniversity of Michigan

• 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.