HKIER

Abstract

Do novices and experts use the same arithmetic metaphors for negative numbers? Twenty-four participants (12 middle school children and 12 post-secondary adults) computed arithmetic expressions involving negative numbers and described their understanding of six arithmetic expressions. The children and adults used the same metaphors to understand arithmetic expressions involving negative numbers. The adults showed a more integrated understanding of arithmetic expressions through multiple metaphors and multiple uses of each metaphor. In the problem-solving task however, the children reasoned metaphorically more often to perform computations and detect errors. When the children reasoned metaphorically, they computed more accurately, but they also used more time. The adults also showed less detail in their metaphors than the children did.

Keywords: metaphors; negative numbers; theory-constitutive

摘要

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