The Theory And Practice Research On Mathematical Innovation Thinking

With the development of modern time, innovative education become more and more important, while innovative idea training play a key role in it, especially for primary and secondary students in mathematics field. This paper makes theoretical and practical researches on mathematical innovation thinking and comes to conclusion below:Innovative thinking happens not naturally, which needs some necessary qualifications. Innovative consciousness cause innovative thought that bases on knowledge and experience and look the thinking method as tool, mature character as motivity.Innovative thinking is not a single thinking mode but an integration of multi-thinking modes. There are instinct thinking, divergent thinking, analogy and association of ideas, which play an important role in innovative thinking, and the improvement of whose efficiency will greatly raise the level of innovative thinking.In addition to general characteristics of innovative thinking, mathematical innovation thinking has its own peculiarities. That is, (1) invisibility of mathematical problem; (2) subjectivity of mathematical standard of value; (3) logicality of mathematical proofs; (4) accumulation of mathematical innovation. Mathematical innovation thinking education should keep to general rule of innovative thinking as well as its special characteristics. The training of mathematical innovation thinking should deal with the following points: (1) ameliorating the .postulate ; (2) holding the direction ;(3) forming problem chains; (4) practicing the logical tools; (5) exalting the mathematical sensitivity to beauty ;(6) grasping the practical opportunity.The teaching of mathematical innovation thinking should follow the following principles: (1) initiative principle ; (2) synchronization principle ;(3) symbiosis principle; (4) quiz principle ;(5) rethinking principle. The teaching mode of mathematical innovation thinking is: asking, discussing and exploring. This teaching mode's characteristics are to emphasize training students' self-asking ability, to develop their innovative thinking ability by improving their asking ability. Afterself-asking questions, students wade into the study on their own initiative. In the course of study, they discuss with teachers or other students, and then gain illumination that result in new exploring, trying and asking.After a period of teaching experience, the teaching mode of "asking, discussing and exploring" proved to be a success. The students under experiment are better than normal students in performance and study consciousness.