关键词: 数学认知, 加法运算, 语义整合, 类比映射

Abstract: Recently, more and more researchers are interested in the relation between arithmetical cognition system and other cognitive function systems, especially the relation between arithmetical cognition system and the semantic concept system. A study done by Bassok, Pedigo, & Oskarsson (2008) showed that proper semantic context facilitated the processing of arithmetical cognition, whereas improper semantic context blocked the processing of arithmetical cognition. This result implied that people had the strong inclination to integrate the arithmetical knowledge with semantic knowledge. They believed that the integration was processed through the analogical mapping mechanism. This study aimed to further investigate the following questions based on Bassok et al. (2008): 1) mathematical cognition is affected by cultural cognitive activities (Tang, Zhang, Chen, Feng, Ji, Shen, Reiman, & Liu, 2006). However, whether the integration processing mode of arithmetical knowledge and semantic knowledge was cultural universal? 2) Whether the cognitive mechanism which integrated arithmetical knowledge and semantic knowledge was analogical mapping mechanism, or whether it was the necessary condition of analogical mapping mechanism? 3) Whether the factors which influenced semantic processing could influence the arithmetical cognition processing? Four experiments were engaged in the present study by using the revised version of semantic priming number matching task (Experiment 1 and 2) and the original semantic priming number matching task used by Bassok et al. (Experiment 3 and 4), in which the addition operation and categorical semantic relation were taken as objects, and the sum effect was taken as index.
The findings were mainly consistent with the study of Bassok et al. (2008). It suggested that the integrating process of the two kinds of knowledge is cultural universal. In addition, the categorical concept as well as the symmetry of the addition operation and categorical relation could influence the processing of addition operation. Moreover, it should be noted that Sum effect affected mainly by restraint of the neutral numbers in Experiment 1 and 2, whereas by activity of the sum numbers in Experiment 4. Therefore, the essence of Sum Effects was also discussed according to the recent results. Activity of the sum numbers can be considered as failure of restraint. Thus, the essence of Sum Effects was failure of restraint: although people tried to restrain two kinds of numbers, they can only restrain one of those (fail). These failures of restraint were mainly influenced by the pattern of the task. And the Sum effects can be representated by either of these failures. In short, results suggested a strong influence of semantic relation on arithmetical cognitive processing. The factors which could influence categorical processing could also influence addition operation processing.

Key words: arithmetical cognition, addition facts, semantic integration, analogical mapping