| As is known to all, the mathematical applied problem education is one of the most hot point of Chinese mathematics education , it has been received significant attention since 1990's .Practically, a good achievement has been got in the mathematical applied problem education in china. But essentially , there is a very long way to go . Fox example , the student's performance of solving mathematical applied problem isn't promoted rapidly . Theoretically , over a long preiod of time , fewer attention is paid to the mathematical applied problem solving theory study , which has a greater or lesser extent effect upon the development of the mathematical applied problem education.In order to improve the mathematical applied problem education , this experiment study is designed to gain insights into the cognitive process for mathematical applied problem solving under the direction of the modern cognitive psychology theory, and to explore the role and peculiarity of metacognition and pattern recognition in solving mathematical applied problem by the students of two middle schools and a normal university .The results of this study are as follows :(1) The cognitive processing mechanism of the mathematical applied problem solving is a cognitive action of mathematics in which the subject must break the plot structure , establishing and processing the mathematical model structure of the appliedproblem by means of mathematical metacognition , i. e. it is a psychological process in which the subject has to transform the typicality model coming from the field of typicality models for the problem into the problem model . This ability can be improved through drills with the structure-analysis training in the mathematical applied problem solving.(2)In solving the mathematical applied problem , the pattern recognition appears mainly to be the characteristics that the subjects gradually use the mathematical model structure schemata instead of the plot structure schemata as the grade goes up .
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