First, in inducing flexibility, cultivate students' developmental thinking ability.
Flexibility is a remarkable sign of divergent thinking. Flexibility to problems can only be realized after getting rid of the bondage of habitual thinking mode and the restriction of fixed mode. Therefore, after students have mastered the general methods well, we should pay attention to inducing students to leave the original thinking track, think about problems in many ways and think flexibly. When students' thinking is blocked, teachers should be good at scheduling prototypes, help students to contact old knowledge and experience in solving problems, make changes such as transformation, hypothesis and reduction, and produce a variety of problem-solving ideas. For example, when talking about the problem of "chickens and rabbits in the same cage": "There are 45 heads, 1 16 feet. What are the geometric figures of chickens and rabbits? " When students do mental arithmetic and written arithmetic, their faces are still reluctant. At this time, the teacher ordered: "All rabbits stand up! Lift the first two feet! " The students laughed heartily. Then the teacher said, "Now rabbits and chickens have the same number of feet. There are 45 heads above, and how many feet below? " The student replied, "45×2=90." "How many feet are missing?" "26." At this moment, the students cried happily: "There are 26÷2= 13 rabbits and 32 chickens." In addition, our teachers should try their best to design some boring teaching contents into some interesting and attractive questions, so that students can enjoy learning mathematics and create a pleasant classroom atmosphere when solving these problems.
Through these inducements, students can consciously switch from one thinking process to another, and gradually form the flexibility of freely adjusting the amount of questions, which is extremely beneficial to cultivating students' divergent thinking.
Second, teachers should fully encourage students to discover, ask, discuss and solve problems, and let students have innovative thinking, innovative personality and innovative ability through questioning and resolving doubts.
Teachers should use profound language, create situations, encourage students to break their own thinking mode and ask questions from a unique angle. In the process of classroom teaching, teachers should make all kinds of summaries in each class, and also consciously let students summarize. Summing up ability is the embodiment of comprehensive quality. Cultivating students' inductive ability, that is, cultivating students' ability to concentrate on thinking, is complementary to cultivating students' thinking of seeking differences. Centralized thinking enables students to master all kinds of knowledge accurately and flexibly, and summarize and refine their own views as the basis of differentiated thinking, thus ensuring the breadth, novelty and scientificity of differentiated thinking.
Third, in encouraging originality, cultivate students' divergent thinking ability.
In the process of analyzing and solving problems, students can creatively put forward new and different ideas and solutions, which is the performance of original thinking. Although students' originality is generally at a low level, it contains great inventions in the future. Teachers should enthusiastically encourage them to think creatively, boldly put forward different opinions and questions, and solve problems in unique ways, so that students' thinking can move forward from seeking differences and divergence to innovation. For example, students will feel bored when doing abacus addition training. If you use an interesting story, it will have a magical effect: "How many times can a piece of paper be folded, more than the thickness of Mount Everest?" Some students doubt whether it can be done, and some students say it will take at least three days. At this time, you tell the students that it can be completed in three minutes, but with the help of an abacus. At this moment, the students were in an uproar and began to work in succession. After 27 consecutive additions, they have far exceeded the highest peak in the world. There are many interesting topics in the Hundred Flowers Garden of Mathematics, such as "Hundred Chickens Problem", "Han Xin Point Soldiers" and "Three People Divide Money", which are all good materials. There is no doubt that this originality should be encouraged. Originality is often contained in seeking differences, and students' divergent thinking is often induced, which may show originality beyond the norm; On the contrary, originality enriches divergent thinking, making thinking constantly divergent horizontally and vertically.
In a word, quality education in mathematics classroom is actually a process of getting out of the misunderstanding of the ocean of problems and realizing educational transformation. Through mathematicians' ideological and psychological activities, we can realize the hardships from failure to success and explore the only way for the development of mathematical ideas and methods. Then, students will not follow the book when solving mathematical problems, but strive to break through the stereotype and strengthen the thinking of analyzing and demonstrating problem solving, so as to truly get out of the misunderstanding and realize the transition of quality education. Divergence and concentration of thinking are like the wings of a bird, which need harmonious cooperation to make students' thinking develop to a new level and improve their quality.