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.