Mathematical Problem Solving Tacit Knowledge Formation Process

To study math problem solving is an important task in mathematics teaching activity. Therefore, it is of great significance to research on the processes how students solve math problems. Nowadays, the researches on math problem solving commonly are on the basis of explicit knowledge and few people pay attention to tacit knowledge of them. Tacit knowledge is unspeakable knowledge that can only be realized and understood. American psychologist, Sternberg suggested that tacit knowledge is an important form of practical intelligence. And it has played an irreplaceable role in the process of individual intelligence formation. It is under such circumstances that I have started my research.This paper mainly studies the patterns and internal structure how the students get the tacit knowledge about math problem-solving. The main methods used in the research are documentation, survey, interview and experiment.The sequence of the research: By first, this paper provides an overview of the teaching about math problem solving and it analyzed the focal point and disadvantage of the current study on teaching of math problem solving through it. In the second place, the concept of tacit knowledge in math problem-solving process is given by assigning its general connotation, eight important characteristics are summed up, at the same time the knowledge is classified according to different ways. Thirdly, by the way of investigation and personal interview, the author put forward the three ways of formation of students'tacit knowledge on math problem-solving, and put forth that there are three levels of psychological structure of tacit knowledge about math problem-solving process and how they was set up, and the author also analyzed the factors affecting the formation of such knowledge. Fourth, based on the above survey and analysis, the author gave four suggestions and three teaching strategies about teaching tacit knowledge for solving math problem. In the end, through an experiment on the formation of a tacit knowledge about math problem-solving, the author verifies the validity of the above suggestions and strategies.The main conclusions of this paper: Firstly, the three ways of formation of tacit knowledge about math problem-solving: from teacher language, setting up their Language by observation, gaining the knowledge by observation. Secondly, the forming process of tacit knowledge about math problem-solving is that students encode the message to their way by their cognition structure, and their psychological set is eventually created after so much adjustment in practice. Thirdly, students' tacit knowledge in math problem-solving can be roughly classified into three kinds, and the forming process of each kind of tacit knowledge is quite different from the other on some details. Fourthly, the author find that there are many influence factors of formation of such tacit knowledge and the most important of them are the new old knowledge characteristics and the teaching ways of their teacher.