ISSN 1671-3710
CN 11-4766/R

心理科学进展 ›› 2021, Vol. 29 ›› Issue (9): 1607-1616.doi: 10.3724/SP.J.1042.2021.01607

• 研究前沿 • 上一篇    下一篇


刘炜1, 郑鹏2, 谷淇3, 王春辉1, 赵亚军4()   

  1. 1云南民族大学教育学院, 昆明 650031
    2昭通学院职业技术教育学院, 云南 昭通 657000
    3大理大学教师教育学院, 云南 大理 67100
    4西南民族大学教育学与心理学学院, 成都 610225
  • 收稿日期:2020-12-28 发布日期:2021-07-22
  • 基金资助:

Three number processing systems: Different features and parallel activation

LIU Wei1, ZHENG Peng2, GU Qi3, WANG Chunhui1, ZHAO Yajun4()   

  1. 1School of Education, Yunnan Minzu University, Kunming 650031, China
    2College of Vocational and Technical Education, Zhaotong University, Zhaotong 657000, China
    3School of Teacher Education, Dali University, Dali 671003, China
    4School of Education and Psychology, Southwest Minzu University, Chengdu 610225, China
  • Received:2020-12-28 Published:2021-07-22


数值加工的机制是数量认知领域的核心科学问题之一。三数值加工系统假说从新的角度阐释了各种数值加工机制的关系, 它认为认知系统通过三种不同的机制来快速分析非符号刺激的数值:感数(subitizing)机制精确地分析1~4个刺激的数值; 数量(numerosity)机制分析密度适中的刺激点阵的数量, 加工误差正比于被分析的数量, 符合韦伯定律; 当刺激的密度超出一定范围时, 密度(density)机制通过分析刺激密度来推断刺激的数量关系, 加工误差正比于被加工数值的平方根。一系列研究证实, 这三种数值加工机制具有不同的行为规律和脑电特征。未来研究需要探讨数量机制是否分别与感数机制、密度机制存在平行激活, 从而阐明三种数值加工机制的作用关系。

关键词: 感数机制, 数量机制, 密度机制, 平行激活


Clarifying the relationship among mechanisms underlying nonsymbolic numerical cognition is one of the most critical questions in the numerical cognition field. From a novel perspective, the hypothesis that three-number processing systems exists provides a plausible explanation for this relationship. According to this hypothesis, distinct mechanisms are involved in the number processing of nonsymbolic stimuli within different number ranges. Small numbers (1~4) can be appraised rapidly and errorlessly based on the activation of subitizing system. Moderate numbers are proposed to be processed spontaneously with a constant error rate of about 20% due to the activity of numerosity system. Typically, Weber’s law of number perception is demonstrated in this number range. For large numbers, the stimulus number relationship is suggested to be inferred indirectly via density analysis, and number processing, which is fast and has an error rate proportional to the square root of the stimulus number, is mediated by the activity of density system.

A series of studies have revealed different behavioral features, as well as distinct Event-related potentials (ERP) features, among number tasks based on these three systems. For subitizing and density systems, better processing efficiency is demonstrated by a shorter reaction time and a lower error rate, whereas a higher dependence on attention resources is also a characteristic of these two mechanisms. Neither subitizing nor density mechanisms are correlated with math ability for children in school. For the numerosity mechanism, on the contrary, lower efficiency and independence of attention are shown, and the accuracy of numerosity comparisons is suggested to be significantly correlated with math scores for school children. ERP features are also suggested to be distinguishable for these three mechanisms. An early component related to attention is typically found under a subitizing mechanism rather than under numerosity or density mechanisms. P2p showed a distance effect, namely, higher P2p amplitude correlates with more errors in comparison tasks, as the ratio of the numbers to be compared approaches “1”, under both numerosity and density mechanisms. In general, the amplitude of P2p (about 200 ms after the onset of stimuli) is larger for the density mechanism compared with that for the numerosity mechanism, whereas the P2p component is more sensitive to the change in number within the numerosity range than within the density range.

There are two major challenges for the three-number processing hypotheses. First, as proposed by some researchers, even when the numerosity and density mechanisms are distinguished by different modes of Weber fractions, more direct evidence is still needed to demonstrate that the processing bases of these two mechanisms are numerosity and density, respectively. Second, the narrow range described in the original hypothesis may induce discontinuity between the three-number processing hypotheses and the classical hypothesis, for example, the approximate number system hypothesis or ANS hypothesis. To solve these problems, it is proposed that the cause for switching from numerosity to density should be reanalyzed and that the hypothesis that the numerosity mechanism is activated in a wider number range should be considered.

Some experimental evidence indicates parallel activation between subitizing and numerosity systems as well as between density and numerosity systems. The parallel activation hypothesis is also noteworthy. Multiple number processing systems could be activated simultaneously, and cognition relies on the system whose processing result is more precise to achieve the best processing results.

Key words: subitizing system, numerosity system, density system, parallel activation