Memorizing the basic number combinations, such as 9 þ 7 5 16 and 16 2 9 5 7, is a punishing and insurmountable task for children with difficulties learning mathematics. Two perspectives on such learning lead to different conclusions about the primary source of this key learning difficulty. According to the conventional wisdom (the Passive Storage View), memorizing a basic fact is a simple form of learning-merely forming and strengthening an association between an expression and its answer. The two primary reasons this simple form of learning does not occur are inadequate practice or, in cases where adequate practice has been provided, a defect in the learner. According to the number sense perspective (Active Construction View), memorizing the basic combinations entails constructing a well-structured or -connected body of knowledge that involves patterns, relations, algebraic rules, and automatic reasoning processes, as well as facts. In effect, fluency with the basic number combinations begins with and grows out of number sense. Aspects of number sense critical to such fluency begin to develop in the preschool years. According to the Active Construction View, the primary cause of problems with the basic combinations, especially among children at risk for or already experiencing learning difficulties, is the lack of opportunity to develop number sense during the preschool and early school years.

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