As math teachers, we are often confused by students' "learning method is dead", and the learning effect is not good for a long time. They can only solve a few problems by imitating examples, and they are helpless when they encounter new problems. In fact, this phenomenon among students is closely related to our teaching methods. We all attach great importance to the correctness and comprehensiveness of imparting knowledge and to making students remember definitions, theorems and formulas, but seldom discuss their origin and essence. We seriously and strictly prove every theorem and deduce every formula, but we ignore the thinking process of proof and deduction. It has caused many defects in our teaching, making our students only know imitation and lack the ability to analyze problems independently. Therefore, as teachers, we must always pay attention to cultivating students' scientific thinking ability and improving their thinking quality.

The following are some of my experiences in teaching, taking several mathematical thinking methods commonly used in middle school mathematics as examples to make some discussions.

First, pay attention to the training of "transformation" thinking.

"Conversion" is a common method in mathematical research. We know that mathematical knowledge is closely related, and many new problems can be reduced to problems that we already know to solve through transformation. Some problems that are difficult to solve can be classified into one that is easy to study through transformation. Then, first of all, we should pay attention to cultivating students' "transformation" thinking. Having this kind of thinking ability is of great benefit to solving new problems. For example, solving equations, when students learn how to solve a linear equation with one yuan, the basic idea of solving a linear equation with two yuan is to transform it into a linear equation with one yuan through elimination (or substitution elimination or addition and subtraction elimination). When students master this way of thinking, it is easy to think of transforming it into binary linear equations and then into unitary linear equations to solve it. It won't be strange for students to learn fractional equations and irrational number equations in the future, because although the problems have changed, they are all the same, and they are all transformed into equations or equations that have been learned. With such a clear thinking, when solving problems, we will not look at these problems in isolation and find no solution. The idea of transformation is reflected everywhere in mathematical research. If we consciously cultivate students' thinking ability, we can not only make students organically relate what they have learned, but also show higher creative thinking ability when encountering new problems.

Second, let students' thinking activities unfold and cultivate their intuitive thinking ability.

How to cultivate intuitive thinking ability in mathematics teaching. 1. Pay attention to the combination of numbers and shapes and establish an intellectual image. The quantitative relationship can be visualized, visualized and simplified with the help of the nature of graphics. Therefore, it is necessary to purposefully help students think about abstract concepts and geometric figures, fully reveal the geometric background of the relationship between concepts and quantities, and create conditions for the development of intuitive thinking. 2. Cultivate the ability to observe, guess and verify. The conclusion of some mathematical problems needs to be based on the known conditions, through observation, analyze the simplest and most special situation of the topic, guess the general conclusion of the problem, and then find the ways and methods to solve the problem. This is a meaningful intuitive thinking training. 3. Train thinking methods and develop intuition. The specific process of intuitive thinking is often unclear. But if we show this process in slow motion, we will find traces of thinking methods such as association, analogy and imagination.

Third, through classroom teaching design, cultivate students' thinking ability.

While we impart knowledge, it is more important to teach students how to "learn", that is, to train their thinking in the practice of mastering knowledge. Students often think that learning definitions, theorems and formulas is just a matter of memorization, and seldom pay enough attention to theorem proving and formula derivation. If thinking training can be infiltrated into the teaching of these basic theories, students can not only understand the basic knowledge more deeply, but also learn the thinking methods to solve problems. For example, junior high school geometry proves that the two base angles of an isosceles triangle are equal. When I am teaching, what methods can I use to guide students to prove that the two angles are equal?

Congruent triangles structure leads to three methods of making auxiliary lines. A proof method of the theorem is given in the textbook. Why do you prove it in the textbook? Is there any other proof? When studying the proof of every theorem, I guide students to discuss this problem, so that students can realize why this proof method is used in the book, and they can find other proofs. Through this kind of teaching, students' independent thinking and innovative spirit can be cultivated.

Fourth, train thinking ability in induction and summary.

Han Yu, an ancient scholar in China, advocated that books should be read thick before they are read fine. If students can sum up every part of the knowledge they have learned and sum up the methods to solve some problems, then their knowledge level will be improved and their ability to solve problems will be improved. Our teacher should instruct students to do this work in time. For example, junior high school geometry proof problems often encounter the problem of equal line segments and equal angles. After studying congruent triangles, students can draw the conclusion that the above problems can be proved by triangle congruence, and then recall and summarize several methods to prove triangle congruence. After studying the properties of isosceles triangle, we can also prove it by using the property theorem: equilateral isometric method. The definitions and theorems in the original book are arranged in the order of knowledge. After this review and summary process, students' ability to solve problems by using these definitions and theorems has been improved, and the essence of these problems has become clearer, so they are no longer worried about finding solutions. Cultivating this ability today is also conducive to their future study.

Fifth, overcome the tendency of problem-solving teaching and enlighten innovative thinking. By innovative thinking, we mean being active and unique in solving problems. The new middle school mathematics syllabus introduces the cultivation of innovative consciousness and innovative thinking ability into the teaching purpose. Therefore, we should pay attention to cultivating students' innovative thinking ability in teaching practice. First of all, we should cultivate students' interest in learning, strengthen their awareness of application and stimulate their desire for innovation. Secondly, when solving problems, guide students to break the mindset, change the thinking angle, explore from different angles and expand the broad thinking space. While paying attention to the classification of questions, try to create divergent points and improve the ability of innovative thinking. In addition, after solving the problem, we should further reflect on the characteristics of the problem, the ideas, ways, methods and conclusions of solving the problem, and further reveal the thinking process of solving the problem in mathematics from the aspects of the law, design, application scope and popularization of the variant, so as to liberate students from the sea of problems and draw inferences from others, thus achieving the purpose of training thinking.