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This book contrasts the widely held view that counting is the starting point for mathematical development with an alternative comparison-of-quantities position. According to the comparison-of-quantities position, the concept of number builds upon more basic concepts of equality, inequality, and less-than and greater-than relations, which derive from comparisons between unenumerated quantities such as lengths. The concept of number combines these basic comparative concepts with the concept of a unit of measure, which allows one quantity to be described as a multiple of another. It is intended for researchers, professionals, and graduate students in developmental psychology, educational psychology, and mathematics education.
Sophian, Catherine
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.
