摘要
近年来,来自认知发展、比较认知、跨文化认知和神经生物学的研究证据都表明近似数量系统的存在,并且相较于一般认知能力,它更可能是决定个体数学能力差异最为重要的因素。本文综述了有关近似数量系统敏锐度与数学能力相互关系的横断研究、纵向研究、训练研究及认知神经科学的研究成果,分析了影响二者关系的因素,包括个体年龄、数学能力高低、抑制控制等,并总结了多种理论对二者间显著正相关关系的解释。未来研究需要在确定更具信效度的测量范式的基础上探讨近似数量系统敏锐度与数学能力各维度的关系,以及这种相互关系背后的原因,并将研究结论运用于数学教学及计算障碍个体的干预。
Number symbols play a very important role in our daily life, we use them to count and label, and we rely on them to develop superior mathematical skills. But there is wide variety in the levels of mathematical difference among us. Over the past decades, evidences from cognitive development, comparative cognition, cross-cultural cognition and neurobiology have proved that numerical skills or number symbols we used in our daily life build on the Approximate Number System（ANS）, which represents numbers in a nonverbal and noisy way. It encodes the numerosities of discrete objects or events as analog magnitudes that can be modeled as overlapping the Gaussian distributions of activations. In recent years, evidences from the normal people of different ages or children with mathematical learning disability have revealed that the acuity of ANS may be a more important factor to determine the individuals’ differences in math ability compared with general cognitive ability during our life span. These studies held that the ANS is instrumental in the acquisition of symbolic numerical skills like arithmetic. People with greater precision in the ANS are more likely to acquire the counting sequence and other subsequent symbolic numerical skills more easily in their childhood, and this may lead to a better symbolic number representation. This article first reviewed the studies about the relationship between the acuity of approximate number system and math ability, including cross-sectional studies, longitudinal studies, training studies and cognitive neuroscience studies. Then we analyzed factors that impact this relationship, including age, math ability and inhibitory control. However, from these studies we could not conclude when and how ANS representations integrated with math ability. Therefore, we summarized various different hypotheses to explain this relationship. The first hypothesis was that better precision of ANS representations may lead to increased engagement in number-related activities, which may lead to a decrease in math anxiety and an increase in math ability. The second interpretation of this relationship was that participation in mathematical tasks allowed children an opportunity to engage their ANS in a context in which the ANS was likely to be of particular benefit, participating in mathematical activities that engaged the ANS may facilitate further development of the ANS and increase the likelihood that children rely on their ANS to learn new mathematical concepts. The third hypothesis held that the symbolic number knowledge mediated the relation between ANS acuity and arithmetic competence, knowledge of symbolic number included the mapping of symbolic number, numerical ordering ability and so on. Though many kinds of evidence have been proposed to support these hypotheses, they could not have a conclusion about which one is right. Future research needs to investigate not only the relationship between the acuity of approximate number system and different dimensions of mathematical ability on the basis of more reliable and valid paradigm, but also to clarify the theoretical explanation of this relationship using other kinds of experiment design like training study. Besides, the research conclusions could be applied to math teaching and the intervention targeted at children with mathematical learning disability.
出处
《心理科学》
CSSCI
CSCD
北大核心
2016年第3期580-586,共7页
Journal of Psychological Science
基金
浙江省教育厅高等学校访问学者专业发展项目(FX2013032)的资助
关键词
近似数量系统
数学能力
心理数字线
数量比较任务
韦伯系数
approximate number system
mathematics ability
mental number line
non-symbolic magnitude comparison task
weber fraction
