Mathematical Problem Solving Teaching Method

On the basis of combining problem teaching method, education psychology and constructive learning and teaching theory .The present paper defines the meaning of Mathematics problem solving teaching method (MPSTM), that is MPSTM is a teaching method that emphasize en educating the ability of creative thinking, problem posing, problem solving and reflective thinking through sruderts' cooperation and exploration with teachers'guidance. By using cognitive science, thinking theory, constructive learning and teaching theory, this paper analyses the education character and function of MPSTM that is arousing students'driving, educating their creativity,creating flexible knowlege structure, developing their higher order thinking skills and fostering their ability of communication and collaboration. At the same time, this paper put forward three phases of MPSTMs conduction that is posing problem through problem situation, solving problem through their cooperation and exploration and fostering their abffity of reflective thinking through installing teaching activity.On the basis of the theory research on MPSTM, this paper discusses emphatically the practice strategies of MPSTM in classroom that is the strategies of teaching how to pose problem and think reflectively, the strategies of teaching how to posing problem are consist of two aspects :(1)from the coursecontent and knowledge posing problem through applying "What-if-not" method, weakening the condition or concealing the condition and experimental mathematics;(2)fiom production, living and other subjects posing problem through arousing studenrs'interest, their observation and contradiction between truth and cognition, the strategies of teaching how to think reflectively consist of two aspects, yet:(1)making dear the contents of reflective thinking which is the progress of problems token, the wholeprogress of thinking and thinking strategies, etc.;(2)making dear how to think reflectively through fostering their reflective thinking sense and custom, teachers' demonstration, self posing mathematics, daily record and discussion, and so on.This paper points out the research problems and the direction of MPSTM through two aspects: to harmonize the two relationships of the subject contents and the system of subject knowledge and the degree of the truth of the problems and the structure arrangements of the teaching purpose.