Guided by the theory of cognitive psychology ,PME of instruction and combined with the characteristic of mathematics function of problem of high school,the thesis make an elementary exploration on the strategy of solving mathematics function of basic problem. Based on this, the thesis adopts the function of basic problems as tasks , and analyses the problem-solving process of top students and secondary students by using protocol analysis, By using quantitative analysis of oral code and qualitative analysis of oral material, we conclude that the top students do much better than secondary students on digging out latent information, distinguishing the mode, and analyze or study object by using symbolic-graphic combination,however, the difference in reasoning between the two is not so distinctive as that in past research .And also, the top students are good at self-regulating.Besides, according to the analysis of the thesis, the factors such as basic skills one masters, the experience one processes, the way the knowledge organized in one's mind, and abstract knowledge one has have an important impact on the problem-solving strategy one adopts.
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