George Polya's research and contribution on mathematical education was world-famous. His achievement on mathematical education mainly included theory of problem solving, theory of mathematical teaching and theory of teacher education. These three kinds of theories had great significance on the reform of modern cirrocumuli of mathematics and teachers to teaching, the cultivation and training of mathematical teachers to our country.Through the study of Polya's works, the article clears up his thinking theory of solution, and discusses it from both micro and macro phases to develop a comparatively complete system.The theory of solving problems Polya emphasizes is a kind of mathematical thinking , who regards solving problems as a means and tells people how to enlighten the students'mathematical thinking which may arrive at the aim of educating the students'ability to analyze and solve problems.The meta-cognitive construction on leaning of mathematical problem solving was an important part of the cognitive construction of mathematical problem solving. Polya gave a system for the meta-cognition that wasn't named in Psychology. The enhance of meta-cognitive capacity in mathematical problem solving relied on that the learner of problem solving was good at to apply"heuristic words"of Polya and sum up"heuristic words"In the recent years, under the guidance of the viewpoint of mathematics quality education, the research on Polya's teaching theory of mathematics problem solving has been deepened to put his theory into practice. The presentation of the education innovation not only meets the requirement of the times and social development and of cultivating the well-develop youths, but also goes with the objective problem solving thought of Polya as reference, briefly states how to cultivate the good ways of thinking and the spirit ofinnovation in the course of the teaching.The enlightening approach in teaching mathematics was proposed by Polya in 1945, which is a teaching thought on"how to solve problems". In the early 1980s, the teaching of"problems solving"was put forth in the USA.Based on a detailed illustration about the plausible inference in Polya's literatures. Its significance during the course of mathematics discovering and creative thinking is pointed out. Furthermore according to the current reform of our mathematics curriculum, the unique, advantages of plausible inference in mathematical teaching are also dealt with. |