Article,
Mastery of Basic Number Combinations: Internalization of Relationships or Facts?
Journal for Research in Mathematics Education, 16 (2): 83--98 (1985)
Abstract
The thesis is advanced that children do not learn and store basic number combinations as so many separate entities or bonds (as hundreds of specific numerical associations) but as a system of rules, procedures, and principles as well as arbitrary associations. In this view, "mastering the basic facts" largely involves discovering, labeling, and internalizing relationships--processes encouraged by teaching thinking strategies. Moreover, internalized rules, procedures, and principles may become routinized and may help to account for the efficient production of number combinations in adults. Given an infinitely large arithmetic system, the use of such automatic reconstructive processes would make sense--would be cognitively economical. Accessibility, which has been advanced to account for anomalous retrieval time results, could be affected by input from semantic and procedural knowledge.
