High school students' mathematical innovation ability runs through the whole process of high school mathematics teaching. In the process of mathematics teaching, teachers should pay attention to cultivating students' innovative ability, so that students can analyze, think, solve and extend problems independently, so as to achieve the purpose of drawing inferences from others. Teachers should not only impart knowledge to students, but also cultivate students' innovative ability, and the cultivation of mathematical innovative ability is conducive to students to develop good mathematical thinking quality and strict logical thinking ability.

First of all, teachers should update their teaching concepts.

Senior high school mathematics is an elastic subject, not just a few concepts, principles and formulas. Senior high school math teachers should update their educational concepts. Teachers are neither machines to impart knowledge nor containers for students to passively accept knowledge. Teachers should turn from the "commander" to the "guide" of teaching, from the "conclusion" of teaching to the "process" of teaching, and from the "teaching" of teachers to the "learning" of students. In the teaching process, teachers should guide students to discover, analyze and solve problems step by step, inspire students' thinking, and let students find the law through a problem and summarize it.

In the teaching process, teachers should establish an equal and democratic view of teachers and students. Richard Blumso, president of Dalton School in new york, USA, contacted China and the reality of American school education and pointed out that in American schools, teachers are all in the student circle, and even in class, you can't tell which one is the teacher; In China, teachers often stand in front of the whole class and become the center of the students' door. In America, most teachers always encourage students to ask questions and work together to solve problems. If the teacher is knocked down, the teacher will not be unhappy, but will praise the students. In this way, students will be encouraged to study independently and learn better. We can learn from foreign good teaching methods and advanced teaching concepts, so it is very important for teachers to establish the concept of democratization; Teachers should even learn from students and draw wisdom from them.

Secondly, teachers should attach importance to the cultivation of students' innovative ability in teaching activities.

The middle school stage is a critical period for the growth of teenagers. Students' psychological and physical development tends to be mature, with certain independent thinking and judgment ability, active thinking, large amount of information, strong thirst for knowledge and great plasticity, which provides psychological and physical basis for cultivating innovative ability. Therefore, in high school mathematics teaching, it is necessary to highlight the cultivation of students' innovative ability and activate students' thinking, thus effectively improving students' learning efficiency.

Improving students' self-study ability is the basis of cultivating innovative ability. Self-study is an important way of learning. After all, a person's life is limited, and the stage of being guided by a teacher is even more limited. A lot of knowledge can only be acquired by students' self-study, positive thinking and active learning. Therefore, teachers should advocate students' autonomous learning and give some guidance to improve students' autonomous learning ability and innovation ability, so that students can find problems in autonomous learning and solve problems independently. In the process of finding problems, teachers should also guide students to think reversely. The traditional thinking mode can't solve the problem effectively sometimes, but if we look at it from another angle, or from the opposite side, we may get a solution. Therefore, teachers should also cultivate students' reverse thinking ability, guide students to break the shackles of traditional and fixed thinking, explore and dig the essence of questions from different angles, and get correct answers.

Thirdly, teachers should create a lively and relaxed teaching environment.

Psychological research has proved that a person's perception, attention, memory, thinking, imagination and other intellectual factors are all affected by the subject's emotions. In an extremely relaxed environment, people's independent exploration and experience of the ontological state of life is the most creative and pioneering. In other words, only when the classroom is full of lively psychological atmosphere, students' spirits will be full, their emotions will be high, their interests will be strong, their thinking will be active, their acceptance will be enhanced and their learning efficiency will be improved.

In a relaxed and active teaching environment, students' thinking ability and innovation ability can be fully brought into play. Therefore, teachers should design a variety of teaching methods, optimize teaching activities and create a vivid and orderly teaching environment conducive to students' development. Teachers should make full use of inquiry activities in senior high school mathematics textbooks, so that students can cultivate their innovative ability in inquiry activities, because innovative ability is acquired in the process of practice, not by recitation and memory. Research-based learning can enable students to gain experience in research and exploration in practical activities, form the habit of being good at finding problems, being willing to think and being diligent in doing things, and stimulate students' enthusiasm for exploring innovative mathematical problems.

Finally, teachers should fully protect students' interest in learning and innovative ability.

In the teaching process, teachers should actively stimulate students' interest in learning, and the process of innovation needs interest to maintain. At the same time, teachers should design teaching according to the teaching objectives, contents and students' acceptance ability, ask questions with moderate difficulty and inspire students to think. Only in this way can we stimulate students' interest in learning and arouse a strong desire for knowledge, so as to carry out innovative thinking.

In teaching, it is not enough for teachers to improve their language expression ability and language intuition, but also to make full use of various intuitive teaching methods. Intuition has the advantages of being visible and tangible. Sometimes it can directly explain the problem, and sometimes it can help to understand the problem, which will leave a deep impression on students and make them have endless fun from learning. For example, in teaching, we should give some examples that students are familiar with, and use slides, models, objects and other teaching AIDS to guide students to observe, analyze and synthesize intuitively, stimulate students' interest in learning knowledge, and let students simplify the complex in a relaxed and pleasant environment and easily master what they have learned.

In short, the innovative ability of senior high school students runs through the whole mathematics teaching activities. We should be good at guiding students to discover, analyze, solve and summarize problems, cultivate students' mathematical innovation ability and lay a good foundation for lifelong learning.