A Psychological Cognition Studying Of The Combination Of "Shu" And "Xing"

This thesis is entitled Choose the Combination of "Shu"and "Xing", which is a widespread idiom in the field of mathematics education in China. The thesis is not restricted in the practical and macroscopic research, but focuses on the dimensionality of the cognitive psychology of the Combination of "Shu"and "Xing", and regards analysis and distilling as the research metaphor of the thesis, from the easy to the abstract, from superficial to essence, from theory to practice as it develops the research tactics, So as to analyze fully the Combination of "Shu"and "Xing". The thesis begins with the existing study and idea in terms of culture, and interprets the "Shu"and the "Xing"from the perspective of representation; meanwhile it analyzes the intension of the combination and points out the trend of the subsequent research. And then, the thesis dates back to the brief history of expansion and combination of the concept of "Shu"and "Xing"from cognitive angle .The thesis excavate out the double implications of the Combination of "Shu"and "Xing"——Target and Functionality, the target combination displays in the conversion of knowledge, functional combination concentrates on being reflected by thinking . Subsequently, the thesis description develops from peripheral to positive. First, it put forward the following idea from the perspective cognitive psychology: the Combination of "Shu"and "Xing"are one of psychological characteristics of math study. In virtue of the theory of mental representation, it further distinguishes the "Shu"and "Xing", expands them to the mental representation, and points out that "combination"actually includes two kinds of information processing Selection and Transformation. Secondly the domestic and international mathematics study confirms the importance of the practical research while signifying the comparison studying, and the necessity of shrinking studying area. Supported by these theoretic conclusions, the thesis shows investigations correlated with the Combination of "Shu"and "Xing"from different angles. On the basis of quality analyzing from student'and teacher'thinking passage, the thesis puts forward information processing analytical chart of the Combination of "Shu"and "Xing",and establishes it 3 main cognitive factors that include "Shu"operation , "Xing"operation and the schema of "Shu"and "Xing". On this basis, it proves the conclusion by quantized method: In analytic geometry study, it is correlated with the behavior of the Combination of "Shu"and "Xing"to the ability of "Shu"operation. The following research achievements can be used in mathematics teaching for reference: ①Emphasize excessively the target combine of the Combination of "Shu"and "Xing", pay little enough attention to functionality combine at present, namely the teaching ideas of paying attention to knowledge is still deep-rooted . ②On functionality combination, teachers and students approve of the ocular auxiliary function of the figure , but avoiding counting , and frightened the operation of "Shu"or operating "Shu"no proficiency at the low level. ③Because In analytic geometry study , it is correlated with the behavior of the Combination of "Shu"and "Xing"to the ability of "Shu"operation , it is very important going on purposeful training among actual teaching of analytic geometry.