Abstract: Abstract Humans and animals have a system which approximately represents the number of objects or events in a nonverbal way. This system is called the Approximate Number System (ANS), and was found to improve with age. A number of studies have shown a positive correlation between ANS acuity and mathematical ability. Recent research suggests ANS acuity's contribution to mathematics ability might be affected by individuals’ ability of inhibitory control. However, it is still unclear what role the inhibitory control plays in this relationship. With regard to this issue, there are three main purposes in this study. 1) To explore how ANS acuity develops among primary students; 2) To examine whether ANS acuity correlates with the mathematical ability in primary school stage; 3) To examine whether inhibitory control is a mediating factor between ANS acuity and mathematical ability. A hundred and seventy-two rural pupils who were in grade 1 (50 students, age 7.11 ± 0.73 years), grade 3 (55 students, age 9.00 ± 0.50 years), and grade 5 (67 students, age 11.29 ± 0.61 years) participated in this study. They were arranged to complete the Chinese Students Basic Math Ability Test Scale, Stop-signal task, and non-symbolic magnitude comparison task to measure their mathematical ability, inhibitory control ability, and ANS acuity respectively. Specifically, the mathematical ability test was a class centralized testing, and the test time was strictly controlled. Besides, the stop-signal task and non-symbolic magnitude comparison task were intensively measured in a computer class for the grade 3 and grade 5 students, while the grade 1 students were measured individually. Results revealed that 1) with age, pupils’ ANS acuity generally improved, but from grade 1 to grade 3 the improvement was relatively slower than other grades, while from grade 3 to grade 5 pupils' ANS acuity improved rapidly, p<0.01; 2) ANS acuity(w of negative sequence ), inhibition control (SSRT) and mathematical abilities were significantly correlated with each other, p<0.05; 3) after controlling age, pupils' mathematical ability was positively predicted by ANS acuity (w of negative sequence) as well as the ability of inhibitory control (SSRT) (ps<0.05); 4) the relationship between mathematical ability and the ANS acuity (w of negative sequence) was partially mediated by the ability of inhibitory control, and the mediation effect accounted for 19.53% of the total effect. The findings of the present study are consistent with previous research, which were mainly conducted among preschoolers or adults. Although some researchers claimed that the influence of ANS acuity on mathematics ability might be affected by the inhibitory control, rare empirical study testified this hypothesis. This study adopted primary school children as participants and was an extension to previous study. We investigated the development of ANS acuity and its relationship with mathematical ability, as well as the role of inhibitory control in this relationship. As the conclusion, 1) in primary school, students' ANS acuity continues to improve with age; 2) both ANS acuity and inhibitory control ability can positively predict the mathematical ability among primary school students; 3) inhibitory control ability can partially mediate the relationship between mathematical ability and ANS acuity. These findings may be helpful to improve mathematics?teaching?and learning in primary school.

Key words: primary schools students, approximate number system, weber fraction, inhibitory control, mathematical ability

摘要： 采用测量法和问卷法考察了172名小学生近似数量系统敏锐度的发展，以及抑制控制在近似数量系统敏锐度与数学能力关系中的中介效应。结果表明：(1)随着年龄增长，小学生的近似数量系统敏锐度逐渐提高；(2)近似数量系统敏锐度(负相关序列中的韦伯系数)和抑制控制均能显著正向预测小学生的数学能力；(3)抑制控制在小学生近似数量系统敏锐度(负相关序列中的韦伯系数)与数学能力的关系中起部分中介作用。

关键词: 小学生, 近似数量系统, 韦伯系数, 抑制控制, 数学能力