Abstract:

PASS theory was the cognitive processing intelligence theory developed by Das and Naglieri. The theory framework was Planning- Attention- Simultaneous Processes- Successive Processes (PASS), which was based on Luria’s working of the brain. It was indicated that high correlations between the cognitive processes of PASS and mathematical ability, and regression analysis indicated the powerful predictors of mathematical achievements were at the lower levels of PASS in low grades, while higher levels of PASS had more effects on the mathematical achievements in high grades. The previous studies in which planning was found to be significantly related to mathematical tasks and the highest correlation found between planning and arithmetic problems. Attention exerted a great impact on the equation listing performance, the processing system of Simultaneous processing and successive processing were necessary in all grades. Despite the fact that studies on different cognitive processes had been found to be some significant predictor of mathematics learning, much less was known about their contribution to different types of mathematical tasks. Actually, different cognitive processes of PASS differently predicted different kinds of mathematical tasks. The purpose of this study was to examine the role of four cognitive processes in three mathematical tasks, and to know the different cognitive characteristics in different fields of mathematical learning . This study employed the Cognitive Assessment system-2B (CAS-2B), the manipulation tool of PASS theory and selected the 226 students from grade 2, grade 4 and grade 7 to explore the features of PASS in the three tasks, that is, calculation fluency, math problem-solving and mathematical reasoning. The results suggested that different cognitive processes of PASS differently in three different grades and in three different mathematical tasks. In math reasoning task, simultaneous processing played an extremely important role in all three grades, accounted for 15%~17% unique variance, attention process only in grade 2 exerted a strong predictor to mathematical reasoning. Simultaneous processing was engaged when the relationship between items and their integration into whole units of information was required, so it predicted unique variance in mathematical reasoning which was synthetic mathematical task; in math calculation fluency task, the attention process with increasing grade, which predictive power gradually diminishes, it accounted for 5%~24% unique variance, and the role of the planning function gradually outstanding, the planning function directed students to utilize calculation rules and the attention process was in charge of maintaining the whole calculating task; in mathematical problem-solving, successive processing and attention can predict grade 2 significantly, however, the functions of planning and simultaneous processing become more significant in grade 4. There are different cognitive processes for mathematical tasks with different difficulty levels, simultaneous processing and successive processing played a main role in complicated tasks such as math reasoning and math problem-solving; planning function and attention process was very important to simple tasks such as the calculation fluency task. The results provide some theoretical basis for different grades students’ targeted mathematical learning training in the future and boost students’ mathematics performance in different areas of mathematical tasks.

摘要：

PASS理论是由Das和Naglieri提出的关于智力理论的一种认知过程理论。研究采用以PASS理论为基础编制而成的认知评估系统（第二版简版，CAS-2B）为研究工具，选取226名二年级、四年级以及七年级的学生，探讨PASS过程在数学计算流畅性，数学问题解决及数学推理等不同数学任务中的作用。研究结果显示：PASS模型各过程在三个年级的不同数学任务上各有侧重。在数学推理任务中，同时性加工对三个年级的数学推理任务预测显著，解释率为15%~17%，注意过程只在二年级对学生的数学推理任务预测；在数学计算流畅性任务中，注意过程随着年级的升高，其预测作用逐渐减退，解释率为5%~24%，计划功能的作用随年级的升高而逐渐突显；在数学问题解决任务中，继时性加工与注意功能对二年级预测显著，四年级时突显了计划和同时性加工的作用。不同复杂性的数学任务具有不同的认知特点，编码加工过程对于较复杂数学任务作用明显；计划与注意过程对简单数学任务作用明显。研究结果为今后不同年级学生开展有针对性的数学学习训练提供了理论基础。