Students' thinking ability is generally correct thinking, that is, from cause to effect, the analysis is logical, while reverse thinking refers to a kind of thinking that starts from the cause of the result, finds the source from the source, and starts from the opposite direction to the original problem. Strengthening the cultivation of changing from positive thinking to reverse thinking can effectively improve students' thinking ability and innovative consciousness. Therefore, it is necessary to strengthen the cultivation of students' reverse thinking ability in classroom teaching. The traditional teaching mode often pays attention to positive thinking and downplays the cultivation of reverse thinking ability. The results of classroom teaching show that many students' learning level is low, which is an important factor, that is, their ability of reverse thinking is weak, they are determined to learn formulas and theorems forward and apply them rigidly, and they lack creativity, observation, analysis and pioneering spirit. In order to comprehensively promote quality education, strengthen the cultivation of students' abilities in all aspects and break the traditional educational concept, here I talk about the cultivation of students' reverse thinking from the following aspects.

First, the thinking and training of reverse thinking in mathematics concept teaching.

Concepts and definitions in high school mathematics are always two-way. Many teachers only pay attention to the use from left to right in their usual teaching, so they form a mindset and are not used to using formulas and rules in reverse. Therefore, in concept teaching, students should not only understand the concept itself and its routine application, but also be good at guiding and inspiring students to think in turn, so as to deepen their understanding and expansion of the concept. For example, when set a is a subset of set b, the intersection of a and b is equal to a. On the other hand, if the intersection of A and B is known to be equal to A, A can be used as a subset of B. Therefore, we should pay attention to this training in teaching and cultivate students' basic skills in reverse application of concepts. Of course, in the usual teaching, teachers themselves should make clear which inverse propositions of theorems are true propositions, so as to train students in time.

Second, reverse thinking in the reverse application of mathematical formula teaching

General mathematical formulas are used from left to right, sometimes from right to left, which is the embodiment of the ability to change from positive thinking to reverse thinking. In the process of solving many mathematical exercises, it is necessary to deform formulas or use formulas and rules in reverse, but students often lack this awareness and basic skills when solving problems. Therefore, we should pay attention to this training in teaching and cultivate students' basic skills of applying formulas and rules in reverse. Therefore, after teaching a formula and its application, giving some examples of reverse application of the formula can give students a complete and full impression and broaden their thinking space. Reverse applications in trigonometric formulas abound. For example, the inverse application of the sum and difference formula of two angles, the inverse application of the double angle formula, the inverse application of the induction formula and the inverse application of the relationship formula between trigonometric functions with the same angle. It is also like the reverse application of the base power. If they think forward, this formula can only solve some problems, but it can't answer all the questions. If used flexibly and reversely, it will be surprisingly successful. Therefore, reverse thinking can give full play to students' thinking ability, which is conducive to the cultivation of broad thinking, and can also greatly stimulate students' subjective initiative in learning mathematics and their interest in exploring mathematical mysteries.

Thirdly, reverse thinking in the teaching of inverse theorem in mathematics.

Every theorem in high school mathematics has its inverse proposition, but the inverse proposition may not be true. It is proved to be an inverse theorem. Inverse proposition is an important way to discover new theorems. In solid geometry, many properties and judgments have inverse theorems. For example, the application of the three vertical theorems and their inverse theorems. Paying attention to the relationship between conditions and conclusions, deepening the understanding and application of theorems, and attaching importance to the teaching application of inverse theorems are very beneficial for students to broaden their thinking horizons and activate their thinking.

Fourth, strengthen students' reverse thinking training.

The training of a group of reverse thinking questions is to transform the known and verified questions into new ones similar to the original ones under certain conditions. In the process of studying and solving problems, students are often guided to explore in the opposite direction to habitual thinking. The main idea is: if the forward push fails, consider the backward push; If it cannot be solved directly, consider an indirect solution; If you can't solve it from the front, you can consider starting from the opposite side of the problem; If it is difficult to explore the possibility of the problem, consider exploring its impossibility; If a proposition cannot be solved, we can consider transforming it into another equivalent proposition. Correctly and skillfully using the thinking method of reverse transformation to solve mathematical problems can often make people have an epiphany, break through the mindset and make thinking enter a new realm, which is the main form of reverse thinking. Often carrying out these targeted "reverse variant" training and creating problem situations play a great role in the formation of reverse thinking.

Fifth, through the cultivation of reverse thinking, further strengthen flexible teaching methods.

The basic method of senior high school mathematics is the key content of teaching. Several important methods such as reverse analysis and reduction to absurdity can be regarded as the main ways to cultivate students' reverse thinking. For example, when proving a geometric proposition (also commonly used in algebra), teachers often ask students to start with the conclusion of the proof, combine the figure and the known conditions, and deduce it layer by layer, and the problem is finally solved. Cultivate the thinking mode of "what to prove, what to prove first, what to prove", from cause to cause, pointing to the known. Reduction to absurdity is also a common method in geometry, especially in solid geometry. Some problems are difficult to prove directly, so we can think backwards, assuming that the conclusion proved is not valid, and trying to prove this assumption is wrong through layer-by-layer reasoning, so as to achieve the purpose of proof. Through the training of these basic mathematical methods, students can realize that when a problem cannot be solved by one method, they often change their thinking direction and can think reversely, thus improving their ability of thinking reversely. In the process of studying problems, it is undoubtedly a divergent thinking to guide students to explore completely contrary to the habitual thinking method. Cultivating students' reverse thinking ability is not only conducive to improving their problem-solving ability, but more importantly, improving their thinking mode of learning mathematics, helping to form good thinking habits, stimulating students' innovation and pioneering spirit, cultivating good thinking character, improving learning effect and interest, and improving thinking ability and comprehensive quality. In fact, the "reverse" thinking method can be seen everywhere in middle school mathematics textbooks. As long as teachers have the heart to dig, they can organize teaching more effectively and improve the quality of mathematics teaching.