British students' observation is aimed at mathematics, but it doesn't extend many feelings like liberal arts. The uniqueness of mathematics lies in its strictness. Of course, in the process of learning, it is inevitable to be a bit boring. How to adjust students' enthusiasm for learning, so that students can accept this subject and achieve certain literacy is our unremitting pursuit. We can't expect every student to have a deep knowledge of mathematics, which is unrealistic, but we must find ways to let them learn how to use it in life and how to look at mathematics from a unique perspective in the real world in order to apply mathematics. In order to make students feel happy while learning knowledge.

First, analyze the causes of students' thinking disorders

Learning itself is a cognitive process, and individual learning always goes through the known internal cognitive structure. The input information is processed "from outside to inside" and stored in an easy-to-grasp form. In other words, students can extract the most effective old knowledge from the original knowledge structure to absorb new knowledge. That is, we can find the combination of old and new knowledge, so that old and new knowledge can play a positive role and contact in students' minds. This leads to the division and reorganization of the old knowledge structure, thus enabling students to acquire new knowledge. But sometimes this process is not always a one-time success. On the one hand, in the teaching process, if teachers ignore the actual situation of students, blindly instill according to their own ideas and logic, or fail to perceive the difficulties of students' thinking, students often feel at a loss when solving problems by themselves. Another point is that when the new knowledge is inconsistent with the original knowledge that students have mastered, or there is a lack of common connection between them, then these new knowledge will exclude the old knowledge, or the new knowledge will correct the old knowledge and then the students will absorb it. Therefore, if teachers' teaching is divorced from students' reality, and students can't "hand over" old and new mathematics knowledge smoothly in the process of learning high school mathematics, it will inevitably lead to students' lack of cognition and biased understanding of what they have learned, which will lead to thinking obstacles in solving specific problems and affect the improvement of students' problem-solving ability.

Second, strengthen the study of the student phenomenon plate.

Modern natural science not only studies things, but also studies the internal relations between things and phenomena. Therefore, for mathematics and physics, the real research object is an important "phenomenon". Physics itself is a phenomenon. Einstein once said: "The teaching task of physics in a broad sense is to establish some concepts about actual events and phenomena, so as to establish a regular relationship between those perceptions perceived by our senses." Constructivism holds that mathematics should first grasp the objective world qualitatively and describe it quantitatively. However, the traditional textbooks and teaching give this section a very secondary position, and sometimes formulas and theorems are given directly without saying a word, so that some people lament that they are just annoying formulas and theorems when talking about mathematics and physics. So what is the reason why we can't see the real content of mathematics and physics?

First of all, we lack the historical literacy of natural science. In the face of nature, we see a personalized artistic conception rather than the beauty of science, and paying attention to science is considered as an alarmist with abnormal nerves. Secondly, the traditional annotation thinking mode is used to treat foreign disciplines such as mathematics and physics, and the thinking mode of attaching importance to the author's intention and ignoring the content of the work is transferred to attaching importance to formula theorems and ignoring facts.

Third, teaching should not pay too much attention to tradition.

In my opinion, one of the weaknesses of traditional mathematics education in China is that it only pays attention to the answers of mathematical exercises, but ignores the relationship between mathematics and natural science, technical science, social science and humanities. Of course there are historical reasons. As a result, the teaching content of mathematics is divorced from social life, and the role of mathematics is not well understood in society. There is always a sense of mystery, and most of them stay away from it, while most people who are interested in mathematics are not tired of it.

In recent years, due to the fierce competition for further studies, especially for entering universities, and the great attention paid by society and schools to the enrollment rate, the treatment of teachers is also related to the subjects they teach. Therefore, under the pressure of society, teachers skillfully take measures to deal with the exam, so that students can do a lot of questions, and even divide the questions into various types of questions, so that students can imitate and repeat a lot. Although this compulsory indoctrination has improved students' proficiency, the side effects are also quite obvious. Students' burden is heavier, students who learn well are tired of learning mathematics, and students who learn well are afraid of learning mathematics, so that after completing the course, students will stay away from mathematics and society will become more and more ignorant of mathematics. The rest seems to be only the needs of students for further study and obtaining credits, which also shows that there are obvious shortcomings in our mathematics education.

Fourth, optimize innovation and stimulate students' innovative consciousness.

The innovation process is not a pure intellectual activity process, but also needs the drive of innovative emotion. If you have lofty ideals, firm beliefs and strong passion for innovation. In addition, personality plays an important role in innovation activities, and the difference of personality characteristics determines the difference of innovation results to a certain extent. The exertion of innovative personality is closely related to both subjective factors and internal psychological state. Therefore, in order to cultivate students' innovative ability, teachers are dominant, and teachers should create a good classroom psychological environment while imparting knowledge. Communicate with students more, create a relaxed, harmonious, equal, democratic and happy learning atmosphere, and optimize students' innovative psychology.

Innovation consciousness is a strong emotional impulse that people have to participate in under the influence of things around them. The impulsiveness of this emotion runs through every performance process, and the accumulation and continuation of impulsiveness determines the quality and results of innovative behavior. Consciousness is the guide of behavior, and ability is the guarantee of behavior. It is extremely long and arduous for people's innovative consciousness to develop from childhood to innovative talents who do great things and create great undertakings. In this process, mathematics teachers in charge of important subjects in middle schools should actively open innovative ideas in teaching, guide students to popularize research through typical examples, guide students to seek novelty and change through new knowledge, guide students to explore research intuitively through the training of thinking ability, and guide students to seek differences and differences through the training of multiple solutions to one problem to stimulate students' innovative consciousness.

Fifth, highlight key points and solve difficulties.

Every class should have a key point, and the whole class teaching is centered around this key point. In order to make students clear about the key points and difficulties, teachers can write them on the blackboard at the beginning of class to attract students' attention. The focus of teaching is the climax of a class. Teachers should use various teaching methods to stimulate students' brains through the constant changes of gestures, voices and blackboard writing, so as to make students excited, leave a strong impression on what they have learned and stimulate students' interest in learning. In order to improve students' ability to accept new knowledge. In solid geometry, we often show the geometric model to students by demonstration and observe the positional relationship between its edges and corners. Sometimes, in a class, multiple teaching methods should be used at the same time. "There is no fixed method in teaching, what is important is proper method". As long as it can stimulate students' interest in learning and improve their enthusiasm for learning, it will help to cultivate students' thinking ability and help them master and use what they have learned. This is a good teaching method.

In a word, in mathematics classroom teaching, if we want to improve students' learning efficiency and teaching quality in 45 minutes, we must think more and prepare more, fully prepare teaching materials, students and teaching methods, improve our teaching wit and give play to our leading role.