Eugenics To Solve The Mathematical Problems Of Students With Learning Difficulties Comparative Study Of Characteristics Of Inner Psychological Mechanisms

In the 1980's, the famous American mathematical educationist, Prof. Alan H. Schoenfeld, and others compared and analyzed the difference that experts and novices had shown in the process of mathematical problem solving. Their job pushed forward the research of mathematical problem solving. On the base of their job, this article chose the students who were the same age and had similar psychological traits as interviewee, and analyzed their different internal psychological mechanism in mathematical problem solving by comparing between excellent students and low achievement students. Moreover, based on the comparison and analysis, the author put forward a series of tactics in order to raise the student's capacity to solve mathematical problems.As the experiment and research indicated, the excellent students did very well in the process of problem solving, in the time of problem solving, and at the result of problem solving as well. In fact, there were some factors such as mathematical knowledge, mathematical tactics, schema, metacognition, attitude and so on, which jointly influenced the system of internal psychological mechanism in mathematical problem solving. Finally, in good problem situation, middle school students could enhance then problem solving ability by the methods of optimizing cognitive structure, increasing tactics, developing metacognitive ability and correcting mathematical attitude.This article paid attention to integrating theory and practice, it used a few of research methodologies including documents analysis, questionnaire, case studies, comparison analysis etc. Also, it tried to study the questions dialectically.