Abstract: As a model of cognitive function, PASS has redefined intelligence in terms of four kinds of competence: planning, attention, simultaneous, and successive cognitive processes. Previous studies showed the close connection between PASS and mathematics learning. However, most of these were cross-sectional studies, and the developmental relationship between PASS and mathematical skills is not yet clear. Therefore, this study aimed to examine the longitudinal relationships among different components of PASS and different mathematical skills (numerical operation and math problem-solving) of pupils. One hundred and forty-nine children of grade one and two from a primary school in Shanghai (81 boys and 68 girls; mean age = 92.18 months, SD = 6.86 months) were followed for one year, and were assessed on the PASS processes, numerical operation, and math problem-solving. The cognitive processes were assessed by tasks from the Cognitive Assessment System-2 (CAS-2). Numerical operation task was adopted from Wechsler Individual Achievement Test-Third edition (WIAT-III) and math problem-solving was assessed with the math standard achievement test (MSAT). The results showed that: (a) attention (receptive and expressive attention: F (1,143) = 112.59, p < .001, ηp2 = .44; F (1,144) = 43.51, p < .001, ηp2 = .23), planning (F (1, 148) = 407.67, p < .001, ηp2 = .73), simultaneous(F (1,148) = 16.41, p < .001, ηp2 = .10), successive processes( number and word series: F (1,147) = 50.61, p < .001, ηp2 = .26; F (1,148) = 65.32, p < .001, ηp2 = .31), numerical operation (F (1,145) = 276.34, p < .001, ηp2 = .66) and math problem-solving (F (1,145) = 194.12, p < .001, ηp2 = .57) improved significantly within one year. (b) The Pearson Correlations between PASS and mathematical skills (numerical operation and math problem-solving) showed significant correlations between these variables and a significant stability for these cognitive processes and mathematical skills. (c) Cross-lagged regression analysis showed that, after controlling for working memory and processing speed, attention and planning both had significant reciprocal relationships with numerical operation skill within one year. There is no reciprocal relation among attention, successive processes and math problem-solving skill, but planning and simultaneous processes both had significant reciprocal relationships with math problem-solving skill. These findings indicated that the different components of PASS at the lower-grade of elementary stage had inconsistent longitudinal relationships with mathematical skills of various complexity, and that higher-level cognitive processes had closer developmental connection with complex mathematical skills. This article explored the specific cognitive processes corresponding to different mathematics tasks, and provided some theoretical basis for improving the pertinence of mathematics learning of lower grade pupils. At the beginning stage of primary school, basic cognitive processes lay the foundation for mathematics learning. With the trend of mathematics tasks changing from simple to complex, more attention should be paid to the development of children's high-level cognitive processes to further promote mathematics learning.

Key words: pupils, PASS cognitive processes, numerical operation, math problem-solving, cross-lagged regression analysis

摘要： PASS认知过程和不同数学学习任务有着密切的关系。本研究对一、二年级共149名小学生进行为期一年的跟踪测查，考察学生在PASS各认知过程、数值运算、数学问题解决任务上的表现及双向关系。在控制了工作记忆和加工速度对数学技能的作用后，交叉滞后回归结果发现：注意、计划与数值运算任务存在显著的双向作用关系；同时性加工、计划和数学问题解决任务存在显著的双向作用关系；继时性加工与数值运算、数学问题解决均不存在双向作用。结果揭示了PASS各认知过程和不同数学技能之间具有不同关系，小学低年级阶段的计划、同时性加工这两种中、高层次认知过程与问题解决的发展联系更加紧密。

关键词: 小学生, PASS认知过程, 数值运算, 数学问题解决, 交叉滞后分析