Obstacles Of Thought In Solving Mathematical Problems And Their Teaching Countermeasures

The problem-solving information-processing view is considered to be the theoretical foundation of the thesis. From the angle of the thinking activity, the thesis undertakes a study of students'obstacles of thought in solving mathematical problems. Meanwhile, a detailed analysis is made on the causes of the obstacles of thought. Under this foundation, according to the constructivism theory, the author puts forward some teaching countermeasures to overcome the obstacles of thought. To be more specific, the main contents of this thesis are in the following:The thesis firstly discusses the background, significance and purpose of the research. Pushed by America and international mathematical education meetings, many countries launched a high tide of mathematics education reform and research on the topic of how to solve the mathematical problems. In the past few years, the solving of the mathematical problems has been considered to be an important part of education of for all-round development. Many mathematics educators conduct a great deal of explorations on it in theories and practice. Some investigations concerned, indicate that it is very common for Chinese students to have a poor level of solving the mathematical problems. The obstacles of thought really exist in the process of students'solving of mathematical problems. However, few researches are carried out on this topic. A research on the obstacles of thought and its teaching countermeasures in solving the mathematical problems is not only significant in theory but also in practice.The main focus of the thesis is put on the different kinds of the obstacles of thought in the process of solving the mathematical problems. In history psychologists and educators have undertook many studies of how to solve the mathematical problems from various perspectives, and put forward different theoretical models. In any research of the models, it is certain that the problem-solving process cannot get away from thinking and need a lot of mental activities to take part in. The problem-solving core of mathematics can be summed up in scientific thinking. In this sense, we can depend on mathematical thinking to solve the mathematical problems. Active mathematical thinking activities can make the problem-solving process develop smoothly. If the thinking activities are interfered or hindered, the process will not go on normally. Information processing psychologists often divide the problem-solving process into four stages: problem characterization, a design for the problem-solving plan, a tentative performance and evaluation. A survey was made on the teachers and students and found that during the above four stages, students have different degrees of one-sided, selective, logic and monitor-thinking and other nine obstacles. We conclude from the comprehensive analysis of the results of investigation that the female students'obstacles of thought are more serious than male students'; female students and male students both have selective obstacles but no differences; their monitor-thinking obstacles are different but not remarkable; the rest are of remarkable differences. Moreover, according to the performance of different students, their obstacles are remarkably different. The better the performance of students is, the lower the degree of the obstacles of thought is than that of the students with poor performance.On the basis of a research of different obstacles of thought, an emphasis is put on the subjective causes of the formation of the obstacles of thought. In order to directly overcome the different obstacles of thought, it is very necessary to take a serious study of their producing causes so that we can improve our teaching level and enhance the ability of prediction and directness and virtually correct the students'different departure and mistakes on the thinking. The obstacles mainly come from two negative impacts: one is the outer factor, such as culture, social background, the context of the problems; the other is internal factor, such as the individual concept system, cognitive system, etc. It is hardly possible to control the objective factors for the individuals, therefore, the thesis mainly discusses the subjective factors, which are mainly as follows: lack of experience and knowledge, incomplete cognitive system, the interference of perception, the form of thinking without multiplicity, changeless thinking and functional fixedness, a bad ability of meta-cognition, etc.In order to effectively eliminate the students'obstacles of thought, the thesis is based on the constructivism and puts forward the teaching countermeasures to overcome the obstacles. The study of how to solve problems is an advanced one. It requires the students to grasp the complexity of the definition and flexibly apply them into the specific situations. The constructivism stresses that the leaning and knowledge construction of the learners is an active process; teacher should be students'instructor and assistant; the teaching activities are represented in the way of cooperation and exploration; students should be instructed to take an active part in the study. Influenced by the understanding of the learning and teaching theory coming from constructivism and combined with the researches and analyses on the different obstacles of thought, the author puts forward the following countermeasures: (1) teach the students to form a good mathematical cognitive structure; (2) pay more attention to the display and regulation of the process of thinking; (3) construct a feasible problem system; (4) instruct and illustrate the major problem- solving strategies.