As a basic subject, mathematics has been wavering on the emotional balance of students, with love and hate. Because the current education system highlights the function of examination, students must face the examination and put enough energy into it to learn well; However, it is also the requirement of college entrance examination selection, and the difficulty caused by "digging deep into accumulated food" in teaching makes many students often have to spend more time fiddling with mathematics in the process of learning mathematics, and finally end in failure and "die in the battlefield." I once lamented that it is too difficult to improve students' math scores. Reflecting on our math textbooks and math teaching, I feel as if I have been lost in the blind road for a long time. How many years of unchanged textbooks, how many years of teaching philosophy, how many years of repeated questions, how many years of calm questions. In the ever-changing era, it seems so backward, so backward. "Development is the last word", so it's time for math teaching to "shout". Therefore, I call for my ideal mathematics education. The ideal mathematics is the mathematics of the masses, the mathematics of ordinary people, not the mathematics of elites. Learning mathematics is a matter for every student, and it is a mathematics that needs lifelong continuous learning. "Popular Mathematics" was first put forward by German mathematician Damilov at the Warsaw International Mathematics Education Conference on 1983. The 5th International Conference on Mathematics Education from 65438 to 0984 was identified as one of the main problems in current mathematics education through special discussion. From the perspective of discipline, mathematics, as a culture, must have the characteristics of communication. The essence of "communication" is "everyone has a share". It contains the following three meanings: first, "mathematics is necessary for everyone"; The development of society needs people with certain mathematical literacy, and modern people should have the necessary mathematical knowledge to decorate themselves. Second, "everyone should learn a little mathematics, that is, popular mathematics"; Different people learn different mathematics, mathematics should have distinct levels, and the most common level of mathematics should be necessary for everyone. Third, everyone has equal opportunities to learn popular mathematics. Based on this, teachers should really understand that "everyone learns valuable mathematics, everyone can get the necessary mathematics, and different people get different development in mathematics". This is the basic idea of mathematics curriculum in the new century, which should be embodied in our mathematics teaching materials and ideas, and then guide our front-line mathematics teachers to accelerate their armed forces and develop their own ideas, which can be implemented in mathematics education. Mathematics education in the sense of "popular mathematics" should focus on the development of people's quality. From the perspective of how students learn mathematics well, we should give students the time and space to study as much as possible, so that students can see, speak, do and think independently, which not only reduces the burden on students, but also provides them with opportunities to express themselves, and determines the active position of learners through the acquisition of mathematical knowledge. . Ideal mathematics is the mathematics of life. In life, we should solve some mathematical problems related to students and social precision, do more life practice and less theoretical research. Mathematics is a rigorous subject, because of its rigor, our teaching has fallen into a misunderstanding: our students are required to cultivate the thinking quality of mathematicians. Divorced from reality, it became a Chun Xue, a high song, and several people. We should shift the focus of mathematics research to pay more attention to students. We should study the relationship between mathematics and our real life. Guiding students to understand mathematics, from a psychological point of view, things that are closely related to themselves will attract more attention. In mathematics teaching, we should always grasp: first, mathematics comes from life. There are abundant mathematical materials in many places in life. Mathematics teaching should pay attention to the source and use, make students feel that there is mathematics everywhere in life, and realize that mathematics is a visible, tangible and useful subject, so as to effectively cultivate students' interest, attitude and consciousness in observing things around them from a mathematical perspective. However, this practical introduction is not just a simple example, but requires teachers to design some vivid life scenes for students and ask questions so that students can observe, think, discover and create new knowledge. Second, mathematics serves life. The goal of school education reflects the specifications and requirements of social and economic development for talents. Of course, at different stages of social development, there are often different interpretations due to different humanistic concepts and values. But progressive education always pays close attention to the development of society. Therefore, the general value orientation of our education is our living space-the reality and future of society. Therefore, every citizen is required to have high mathematical literacy, be good at application and dare to create. Teachers should create opportunities for students to apply what they have learned to real life. For example, many reading materials and research materials in high school mathematics textbooks provide many problems related to life. In this way, problems that students never cared about before have become hot topics for their discussion. On the one hand, cultivate students' awareness of active participation and creation, on the other hand, improve students' ability to solve problems. Let students understand the society and the value of mathematics. The ideal mathematics is applied mathematics, which is used by students. Mathematics learning has a clear direction. Less disorientation, more sense of belonging. One reason why students lack motivation in the process of learning mathematics is that they think it is useless to learn mathematics. Instead of learning useful mathematics, in this kind of mathematics learning without a sense of direction, of course, the direction and motivation of learning mathematics will be lost. In fact, in the real life of mathematics in the second half of the 20th century, the greatest development of mathematics is its application. With the wide application of computer technology, mathematics can directly create wealth and value for society in some aspects. Let students know that mathematics has created great social wealth in society, and mathematics has been widely used in all walks of life. Mathematics is a highly applied subject, and its application has penetrated into all fields of society. However, in the actual classroom teaching, there is little talk about the source and practical application of knowledge. Students' application consciousness is weak, and even the teaching of application problems lacks "application flavor" Many students think that mathematics is only useful in class and exams. Without these places, they can hardly feel the existence of mathematics. Linking mathematics learning with social practice, setting up mathematics research learning course, centering on solving a practical problem in life, let students realize the importance and practical value of mathematics knowledge in the process of solving problems, so as to actively study and explore. For example, trigonometric functions and their images are difficult and boring for students to learn, so a research topic is launched for this content: how to cut the cuffs of clothes. Students try to explore and find that the boundary between cuffs and clothes cuffs is a sine curve when cutting, so that sleeves can be worn properly. Students are very interested. On this basis, induce students to explore other life examples related to trigonometric function knowledge, and encourage students to apply what they have learned. Students find pleasure in solving practical problems, and thus have a strong interest in trigonometric functions. One aspect of mathematics teaching is to enhance students' extensive application consciousness, attach importance to mathematics application and improve students' ability to solve mathematics problems in life and production, which is the fundamental purpose of mathematics teaching and the basis of innovative education. Ideal mathematics should not be filled with cold mathematical symbols and mathematical terms everywhere. Mathematics, which belongs to middle school students, should have less scientific logic and more humanistic care. For the previous discussion on mathematics teaching, it always tries to pursue the logic of natural science. From the perspective of natural science, educators are first influenced by positivism. Positivism only requires solving the problem of "what" in pedagogy, not "why". Under the guidance of this idea, the methodological feature of mathematics teaching is induction, not deduction. Scientific induction has played an important role in the theoretical research of pedagogy and will continue to play an active role in the future development of pedagogy. Natural science pays attention to the one-way questioning and structured description of the world, but ignores the understanding between disciplines, which will inevitably limit the understanding of the development of pedagogy. Humanistic science emphasizes the exploration of human, humanity and human existence in general, in order to pursue the harmony and perfection of human nature. And take the whole and connotation of life as the purpose. The humanities not only devote themselves to exploring the inner spiritual world of human beings, but also attach importance to the dialectical relationship between cultural traditions as the objective expression of the inner world of human beings, trying to reveal and grasp the overall value, ideal and pursuit of human beings in the unity of the three. The focus of humanistic interpretation and evaluation will shift from caring for objects to understanding and communication between subjects. Humanistic care takes the pursuit of meaning as the dimension, carries out humanistic interpretation, adjustment and evaluation, not only pays attention to self-epiphany, but also devotes itself to mutual expression and understanding among subjects. Undoubtedly, the intersubjectivity contained in the research of humanities will help to discard the alienated or objectified way of thinking. This trend of mathematics teaching has really made people's position in education. With the study of ecology and value science, the true value of human beings will also be realized. Ideal mathematics is a tool to cultivate students' good interest and stimulate their desire to learn, with less utilitarian color and more sex education. As long as our mathematics teaching is no longer centered on exams and further studies, more life-oriented and interesting content will make students really relaxed and happy to learn mathematics, and more students will like mathematics rather than be afraid of it. The value and function of mathematics will be more deeply rooted in students' hearts, and the unique cultural connotation of mathematics will be able to. Mathematics, as a discipline with people as its starting point and destination, is also a discipline that pursues goodness and beauty. Theoretical research is a process of seeking truth. To develop mathematics teaching, we must attach importance to the development of practice, because only in writing practice can people achieve the unity of truth, goodness and beauty. It is necessary to discuss various specific theoretical issues and put them into educational practice for testing. Seeking truth, goodness and beauty is the ideal mathematics for students' thinking paradise, the sea for students' thinking to roam, and teachers and students are surfers, enjoying the fun of mathematics surfing. The essence of mathematics teaching is to cultivate students' thinking, as Kalinin said: Mathematics is gymnastics of thinking. The teaching and learning of mathematics runs through the movement of thinking. Learn math. It is to learn to think with my own brain, find problems, study problems, solve problems and reflect on problems (this is the step of applying problem-solving teaching strategies in classroom teaching). During this period, thinking permeates the whole teaching process. Our teacher's role is the same as that of students, who are thinking surfers. The relationship between mathematics and thinking is like a goldfish bowl and a goldfish. If the goldfish leaves the goldfish bowl, it will die. The goldfish bowl leaves the goldfish bowl, which is a stagnant pool, empty and lifeless. Similarly, in mathematics teaching, without mathematics, thinking is empty, and without thinking, mathematics loses its meaning. Our teaching should aim at developing students' thinking and solving problems (thinking is manifested by solving problems), take thinking as the main line and training as the main attack, and guide students or accompany them to surf, roam and improve their abilities in the ocean of thinking. Eulogize for thinking. People can't live without thoughts. Ideal mathematics should make the classroom full of vitality, which is a wonderful chapter in the life of teachers and students. The classroom is a place where the magnificent music of life is played. Mathematics in my mind is a living subject, which is reflected in its vital position in the whole basic teaching. It is precisely because mathematics is full of vitality that it can be reflected in all walks of life, and its vitality has promoted the development of productive forces to a certain extent. Mathematics teaching in my mind is a process full of life activities. Because the main body of teaching is students and teachers, both of which are active life bodies. In this dynamic teaching and learning system, there are too many variables, and various problems will appear in the process of teaching and learning. What teachers think about is how to better interpret the teaching process, impart more knowledge to students and better cultivate students' various abilities. How to make relatively static and lifeless knowledge lively, so as to help students absorb it better, and students will think about how to make their learning process more effective, more operable, more targeted, and more vivid in general. In my mind, the teaching object is a student with bright vitality, a life that is equal and independent with the teacher, and a life that needs more care. Give life more rights, give life more development space and give life more autonomy. Let the classroom surge with the upsurge of life and glow with the breath of youth. Full of energy and passion, the ideal classroom is full of praise for life. The ideal mathematics should have a broad mind, great inclusiveness and compatibility, and conform to the characteristics of the times. Pay attention to the integration of information technology and mathematics. Modern educational technology is having a far-reaching impact on mathematics teaching. We should not only pay attention to the use of information technology to present the course content, but also pay attention to the organic integration of information technology and course content. Standards can generally use scientific calculators and various mathematical education platforms to strengthen the combination of mathematics and information technology. In content, highlighting the unique role of "algorithm" in the whole development of mathematics has become an important clue to understand the development of mathematics, and strives to integrate the algorithm into all relevant parts of mathematics curriculum. The integration of mathematics teaching with other disciplines is an inevitable trend of the new curriculum reform. Mathematics, as a basic discipline in natural science, can only play its role if it is applied to other disciplines. If we organize mathematics teaching directly from this angle, it will be more meaningful, colorful and attract more students. For example; For example, the Euler formula in polyhedron introduces the story that three chemists who won the Nobel Prize in chemistry discovered the molecular structure from 65438 to 0996. It is a molecule composed of 60 carbon atoms. Its structure is a simple polyhedron, which can be solved by euler theorem. If anyone can use euler theorem to solve the problem earlier than the three scientists, he is the Nobel Prize winner. The students are deeply encouraged and enthusiastic about learning. Mathematics in my mind is ideal mathematics, and it is mathematics with real life. After experiencing many frustrations and frustrations in mathematics in life, and appreciating many puzzles that a mathematics teacher faces in current mathematics teaching, and after learning many new theories and viewpoints, the image of mathematics in one's mind is more and more full and substantial. After seeing Mayor Zhu Yongxin's dream, I couldn't help dreaming with Mayor Zhu, whether it was a daydream or an idiotic dream. I also look forward to this dream coming true. It's good to have a dream!