Mathematical problem solving has become a hot topic in the world mathematical educational reform and research. China has witnessed rapid development in this area, though starting late. One of most important objects of mathematical education is to help mold the students into a person who is effective in tackling mathematical problems, and come up with useful and novel ways of solution when new problems crop up. Therefore, it is essential that the abilities to raise, analyze, and solve questions should be rendered in the students. Particularly, one of important topics in want of further research in mathematical education is how to correctly analyze the reasons and take effective measures to get through the problems encountered. At present, quality education is in full swing, and examination-oriented education has firmly taken hold, which has been reflected in the practical teaching process. Consequently, the focus has been put on the teaching results, the knowledge chain, and the conventional problems, whereas the process-based knowledge, and ability chain, and non-conventional problems have been neglected. As a result, the students tend to be predictable, lacking in creativity, and poor in mathematical problems solving. The students seldom thoroughly analyze the reasons for the problems, not to mention finding the right way to solve them. It is urgent that teachers and students be saved from the agony of being buried in mathematical problems.The major methods adopted in the research are reference to literature, and survey method. Survey method intends to analyze the reasons for barriers in the problem solving process, which can be classified into subjective factors and objective factors. The subjective factors include, students'intrinsic knowledge and cognitive, their metacongnitive abilities, their habitual thinking mode, and non- intellectual factors. The objective factors contain the setting of the mathematical problems, the mathematical problem representation, and the teaching theory and methodology taken by the math teachers.Proper measures should be employed, according to the reasons that cause the barriers in problems solving, and under the guidance of modern educational theories. The educational theories adopted in this paper are, the cognitive theory by Gagne, the congregating-Structure Theory by Jean Piaget, and the Meaning Learning Theory and Transference Theory by Ausubel, etc. The author suggests constructing a robust mathematical cognitive structure, laying emphasis on developing students'cognitive abilities, improving their positive transference, adjusting and bettering their learning... |