Meanings of Skill: Effects of Abacus Expertise on Number Representation

Research on expertise has focused on the amount and organization of domain-relevant knowledge as the key feature distinguishing experts from novices. The representations of experts are described as being more functionally organized as well as more detailed than those of novices. There are two different senses in which knowledge could become more functionally organized with expertise. The knowledge of experts could become more functionally organized with respect to the execution of skill, or their knowledge could become more functionally oriented with respect to contexts broader than their particular skill. Abacus skill provides a domain in which these two alternatives can be evaluated. The first alternative, conceptual determination by skill, implies that abacus experts' representations of numbers should emphasize the features that are functional in their calculation strategies. The second alternative, conceptual transparency, implies that experts should not emphasize abacus-specific features when judging similarity of numbers, giving less weight than novices to abacus features when judging abacus representations and no more weight than novices to abacus features when judging numerals. Conceptual transparency occurs when those features important in performing a skill are judged to be of little significance in understanding the skill. Number similarity judgments of abacus experts and novices from Taiwan and American children of comparable ages indicted that abacus skill was associated with a deemphasis of those features that are unique to the abacus. Implications of the phenomenon of conceptual transparency for models of skill development are discussed.

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