The so-called thinking refers to the generalization and indirect reflection of the objective reality by the human brain, reflecting the essence and internal regularity of things. In mathematics learning, the process of students solving and summarizing problems is also the process of their thinking development; The study of basic concepts, theorems and formulas is also the basis for the formation of senior high school students' mathematical thinking. In teaching, it often happens that teachers understand everything in class, but they can't start solving problems themselves; However, students often find it not difficult after the teacher has explained a topic. The reason is that their thinking forms and specific problems are different. By doing more questions, students can understand mathematical thinking in practical operation, but this is not conducive to improving students' learning efficiency. Therefore, we should try our best to cultivate students' mathematical thinking from many aspects.

First, the importance of cultivating mathematical thinking ability

When learning mathematics, students often don't apply it on the basis of understanding, but only remember some "dead" knowledge or only remember some topics. When encountering new problems, students mostly apply the previous problems, and it is difficult to use their thinking ability to analyze the solutions to the problems. None of these learning methods can learn mathematics well, let alone help students develop their thinking ability. The improvement of thinking ability can promote the establishment of good learning attitude, cultivate interest in mathematics and enable students to learn mathematics well.

The thinking problems of senior high school students are as follows:

Mathematics study is not deep enough. In the process of learning mathematics, students do not have a deep understanding of the occurrence and development of some mathematical concepts or principles, and often stay at the level of generalization of appearances, so it is difficult to grasp the essence of things. Therefore, when analyzing and solving mathematical problems, students only solve problems according to the superficial meaning of the topic, which often leads to the formation of a thinking habit of cause and effect, without mastering the transformation method of thinking and looking for ways and methods to solve problems from various aspects. At the same time, it also causes students to lack abstract thinking ability, and it is often easy to solve intuitive and common mathematical problems, but it is very difficult to solve those non-specific and abstract mathematical problems, and they don't know how to grasp the essence of the problems and transform them into known mathematical models to analyze and solve them.

In addition, each student's thinking level is different, the thinking mode is different, the mathematical foundation is uneven, and the thinking mode has its own characteristics, so different students' understanding and understanding of the same mathematical problem will not be exactly the same. If teachers don't pay attention to these differences in teaching, students' thinking development will often be ignored, and students themselves lack the regulation of their own thinking process, which makes students seldom explore the internal conditions of problems and lack multi-angle analysis and judgment when solving mathematical problems, thus affecting the solution of problems.

Ignoring the cultivation of students' thinking ability is not conducive to the improvement of mathematics scores, and it is easy for students to form mathematical thinking patterns. High school students have formed certain problem-solving habits and methods by doing a lot of problems themselves, and they are more confident in their existing problem-solving experience, so it is difficult to find solutions flexibly according to new types of questions, which leads to rigid thinking and inhibits the development of mathematical thinking.

It can be seen that if we do not pay attention to students' mathematical thinking, it will not be conducive to the further development of students' mathematical thinking, nor to the improvement of students' ability to solve mathematical problems, and will hinder students' long-term mathematical learning. Therefore, our teachers should pay attention to cultivating students' mathematical thinking and improving their thinking ability in their usual mathematics teaching.

Second, suggestions on cultivating mathematical thinking ability

First of all, teachers should understand and master students' basic knowledge before teaching, so that the contents and methods in class can conform to the characteristics of students' cognitive development and the differences of students' cognitive level, and guide students to play their subjective consciousness. At the same time, we should attach importance to the teaching of mathematical thinking methods and guide students to improve their mathematical consciousness. Mathematics consciousness refers to the method that students choose to do problems in the face of mathematics problems, instead of thinking of a formula first and imitating the previous method of doing problems, so they can't start with problems that they have never seen or have a slightly unfamiliar background. In mathematics teaching, we should not only emphasize the accuracy, standardization and proficiency of basic knowledge, but also strengthen the teaching of mathematics consciousness. Improving students' mathematical consciousness is an important link to break through students' mathematical thinking obstacles.

Teachers can guide students to understand and feel their original thinking frame and its negative influence, and arouse students' attention to changing their original thinking.

Mathematical thinking ability includes abstract generalization ability, logical reasoning ability, selective judgment ability and mathematical exploration ability, and we can take concrete measures according to its content.

Mathematical abstract generalization ability is the core of mathematical thinking ability, which is manifested in the ability to find the differences of common phenomena, to establish the relationship between various phenomena, to separate the core and essence of problems, to get rid of non-essential details, to distinguish essential things from non-essential things, and to abstract specific problems into mathematical models. Abstract generalization ability is the basis of learning mathematics, which can be cultivated from the following aspects: (1) abstract the relationship between numbers and shapes reflected in mathematical materials from specific materials, and attach importance to the teaching of "analysis" and "synthesis"; In problem-solving teaching, guide students to explore the implicit conditions and significance of the problem, find out its internal essence, and guide students to use the methods of intuitive abstraction and ascending generalization; Cultivate students' habit of summing up, so that students can sum up their essential similarities when they encounter the same type of problems.

Logical reasoning ability, mathematical operation, proof and other activities are closely related to reasoning, which can promote the flexibility, agility and creativity of mathematical thinking, promote students to think and analyze problems themselves, and gradually cultivate students' thinking ability.

The ability of selective judgment is not only the judgment of the basic process and conclusion of mathematical reasoning, but also the estimation of the rationality of mathematical propositions, problem-solving ideas and methods and the choices made on this basis. Judgment ability is actually students' self-feedback to their own thinking process. Therefore, in problem-solving teaching, students should be trained to try multiple solutions to one problem and analyze the advantages and disadvantages of various solutions.

Mathematical inquiry ability is a creative thinking ability developed on the basis of abstract generalization ability, reasoning ability and selective judgment ability. The process of exploration is manifested in a series of meaningful discovery activities in mathematics, such as asking questions, finding methods, exploring conclusions, summarizing the law of solving problems, etc. The ability of mathematical exploration mainly lies in putting forward ideas and transforming. To stimulate students' inquiry ability, we first need to stimulate students' interest in learning, let students find problems actively, and then guide students to use various thinking methods such as analysis and synthesis to cultivate students' habit of inquiry.

The improvement of mathematical thinking ability is the basis of learning mathematics well. Therefore, it is an important task to cultivate and improve students' mathematical thinking ability. In the teaching process of cultivating students' mathematical thinking ability, we should not only consider the general requirements of ability, but also deeply study the characteristics of mathematical learning and mathematical thinking to improve students' mathematical thinking ability.