The Study On The Relationship Between Cognitive Processes Of Pupils' Mental Calculation And Fundamental Cognitive Abilities

Calculation skill is the basic content of mathematics education in primary school, and mental arithmetic ability is important representation of calculation skill. On the one hand, cognitive research on mental arithmetic is one of the important topics in the numerical cognition domain; on the other hand, the study of children's mental arithmetic is also the point of integration between the fundamental cognition research and school applications. Therefore, the study chose pupils'mental arithmetic ability as the object, exploring the characteristics of mental arithmetic in different processing stages, the development of mental arithmetic ability and the relationship between mental arithmetic ability and those fundamental cognitive abilities.Although there are various perspectives and methods on mental arithmetic study, this study chose four arithmetic operations of integer as the object. In details, this study aimed at:1. Using different cognitive tasks, exploring the characteristics of different cognitive processing stages (representing, retrieval, executing) during mental calculation and the children's development at different stages; 2. Using mental calculation test, studying the developmental characteristics of the children's mental arithmetic ability; 3. Finding the relationship between mental arithmetic ability and those fundamental cognitive abilities (working memory, four cognitive processes in PASS model, different aspects of attention).Participants of the study are recruited from an ordinary primary school in Shanghai. Total 102 pupils come from three classes from Grade 3 to Grade 5,49 boys and 53 girls.The results indicated that:1. Mental calculation processing show different characteristics in different processing stages. In representing phase, the participants commits more operator errors than operand errors and it takes more processing time if the input information is unclear and unsharp. In retrieval phase, the participants retrieve multiplication facts better than addition facts. In executing phase, problems with carrying operation needs take more time to execute, storing the carry needs at units calculation and executing carry operation at tens calculation.2. From third grade to fifth grade, the pupils' mental calculation ability improves significantly, and this improvement is embodied in processing speed rather than accuracy. On representing phase and retrieval phase, the developmental improvement is reflected in the speed. On executing phase, the developmental improvement is reflected both in speed and accuracy.3. With regard to working memory spans, sentence span, the accuracy of complex spatial span and the speed of simple spatial span predicts mental arithmetic ability significantly. In terms of PASS model, only attention process predicts mental calculation significantly. As for various aspects of attention, they all have a certain extent predictive effect on mental calculation.