4. 1 A solid foundation is the source of intuition.

Intuition does not depend on "opportunity". Although the acquisition of intuition is accidental, it is by no means a fantasy for no reason, but is based on solid knowledge. Without a deep foundation, there will be no sparks of thought. Attiya said: "Once you really feel that you understand something, and you have gained enough experience in dealing with that problem through a lot of examples and connections with other things, you will have an intuition about what the development process is and what conclusions should be correct."

4.2 Strengthening philosophical and aesthetic concepts is the key to training.

Intuition is based on the overall grasp of the research object, while philosophical views are conducive to a good grasp of the essence of things. Including unity of opposites, movement changes, mutual transformation, symmetry and so on. For example, if (a+b)2=a2+2ab+b2, even if the complete square formula has not been studied, the truth of the conclusion can be judged from a symmetrical point of view. Aesthetic feeling and aesthetic feeling are the essence of mathematical intuition. Improving aesthetic ability is conducive to cultivating intuitive awareness of the harmonious relationship and order among mathematical things. The stronger the aesthetic ability, the stronger the mathematical intuition ability. 193 1 year, Dirac boldly put forward the antimatter hypothesis from the perspective of mathematical symmetry. He thinks that the antielectrons in vacuum are positrons, and he also questions Maxwell's equation. He once said that if a physical equation looks unattractive mathematically, then the correctness of the equation is questionable.

4.3 Predicting and guessing training for students is an important training form.

Teachers should try to make students make illogical direct predictions and guesses in the inference of mathematical concepts and theorems, and gradually improve students' intuitive thinking ability. Teachers should clearly put forward intuitive thinking in classroom teaching, formulate corresponding activity strategies, analyze the characteristics of problems, infiltrate intuitive concepts and develop thinking ability. Pay attention to the problem-solving research of intuitive thinking, and choose appropriate questions, such as method of substitution, combination of numbers and shapes, inductive guessing, reduction to absurdity, etc. It is beneficial to cultivate and examine students' intuitive thinking. Another example is the multiple-choice question, which only requires choosing from four options, omits the problem-solving process, allows reasonable guessing, and is conducive to the development of intuitive thinking.

4.4 Set the artistic conception and motivation induction of intuitive thinking

Fully affirm students' bold ideas, encourage their reasonable components in time, care for and support students' spontaneous intuitive thinking, and don't dampen their enthusiasm and understanding of intuitive thinking. Teachers should make use of the situation in time, eliminate doubts in students' hearts and make students happy with their intuition. "Follow your heart" is a fashionable saying. In fact, this sentence already contains the bud of intuitive thinking, but it has not risen to a thinking concept. Teachers should clearly put forward intuitive thinking in classroom teaching, formulate corresponding activity strategies and analyze the characteristics of problems as a whole; Attach importance to the teaching of mathematical thinking methods.