Sophian, C. (2007). The origins of mathematical knowledge in childhood. Lawrence Erlbaum Associates.

The origins of mathematical knowledge in childhood contrasts the widespread assumption that mathematical knowledge begins with counting with an alternative position, the comparison-of-quantities position.  That position holds that the origins of mathematical knowledge lie in comparisons between quantities, which provide the foundation for more basic concepts on which the concept of number itself depends—among them, concepts of equivalence, less-than, greater-than, and unit.  Several lines of research are examined in relation to these alternative accounts.  These include research on infant number discriminations, on preschool children’s reasoning about numerical relations between sets, on young children’s reasoning about relations between non-numerical quantities, on whole-number addition and subtraction, on multiplicative reasoning, and on fraction learning.  Finally, ramifications of the comparison-of-quantities position both for broad theoretical accounts of cognitive development and for mathematics instruction are considered.

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