The Effectiveness Of The Mathematical Problem Situation Created By Research

Problem is the heart of mathematics and mathematics don't exist without problem. Mathematical problem results from mathematical contexts and mathematical contexts is the fertile land of mathematical problem . With the reforming of middle school curricula educators take the study of mathematical problem contexts more and more seriously.Problem contexts is the psychological condition that a man has perceived it but don't know how to reach it when he don't solve new problem with the previous knowledge. The aim of designing mathematical problem contexts is to discover contradiction and to break up the balance state that exists in one's mind and to stimulate his inner strength .And then the student will go into the state of studying. Designing mathematical problem contexts is not only the need of creating knowledge but also the need of carrying out new mathematical curricula. It is not only favorable to stimulate the motive of learning mathematics but also to cultivate the questionary consciousness and to raise the mathematical level and ability of the students.On the basis of situational learning theory , this research analyles the classic examples of mathematical problem contexts and elaborates the characteristics of effective mathematical problem contexts. They include the following principles: (1) adaptive principle; (2) attractive principle; (3) intuitive principle; (4) gradational principle; (5) opening principle;(6)continuous principle, designing mathematical problem contexts may follow the following teaching tactics: (1) designing problem contexts that have little distance between them and paying attention to their gradation; (2) designing variform problem contexts and paying attention to their divergence; (3) designing delicate problem contexts and paying attention to their tactics;(4) designing problem contexts that have much more knowledge inner them and paying attention to their reality; (5) designing problem contexts that have some error inner them deliberately and paying attention to their confusion; (6) designing many-faceted problem contexts and paying attention to their exploration. I have made an experitment to test the effectivity of the above teaching tactics. Real research indicates that designing reasonable and proper mathematical problem contexts can raise the student's interesting and stimulate their enthusiasm for learning mathematics. It can also raise the mathematical level and ability of the students, and it has put forward a higher requirement to the mathematical teachers at the same time.