What is the ideal in math?

Mathematics, as a basic subject, in the emotional scale of students has been wavering, love and hate. Because the current education system highlights the function of the examination, students must face, must invest enough energy to learn it well; however, it is the requirements of the college entrance examination selection, teaching, "digging deep holes, wide accumulation of food," and now it is difficult to make many students in the process of learning mathematics often have to spend more time to fiddle! Mathematics ultimately ended up in failure and "the expedition is not yet successful body first died" situation. I once sighed: it is easy to shake the mountain, but it is too difficult to improve students' performance in math. Reflecting on our math textbooks and math teaching, I feel as if I have been lost on a blind journey for a long time. How many years of unchanging textbooks, how many years of consistent teaching concepts, how many years of flip-flopping question types, how many years of a sea of unsettling questions. In the ever-changing era, how backward and lagging behind. "Development is the hard way", math teaching should also come to the "cry" time. Thus, I call for the ideal math education in my mind. Ideal math is the popular math, is the common man's math, not the elite math, learning math is every student's thing, is a life-long to keep learning math. "Popular mathematics" was first proposed by the German mathematician Damilov at the International Conference on Mathematical Education in Warsaw in 1983, and was identified as one of the main issues of current mathematical education after a special discussion at the Fifth International Conference on Mathematical Education in 1984. Mathematics, as a culture, must have the characteristic of being transmissible from a disciplinary point of view. The essence of "dissemination" is "access for all". It contains the following three meanings: First, "mathematics is necessary for everyone"; the development of society needs to have a certain degree of mathematical literacy of people, modern people, should have the necessary mathematical knowledge to modify their own, and secondly, "everyone should learn a little bit of mathematics, that is, the popular mathematics"; Different people learn different mathematics, mathematics should have a clear hierarchy, the most common level of mathematics should be necessary for everyone. Thirdly, everyone has equal opportunities to learn popular mathematics". Based on this, teachers should truly understand that "everyone learns valuable mathematics, everyone has access to necessary mathematics, and different people develop differently in mathematics". This is the basic concept of the new century mathematics curriculum, which should be implemented and embodied in our mathematics teaching materials and ideas, and then guide our front-line mathematics teachers to speed up the process of arming themselves and developing their own concepts, so that they can be implemented in mathematics education. Mathematics education in the sense of "popular mathematics" should focus on the development of human qualities, from the perspective of how students learn mathematics well, return the learning time and space to students to the maximum extent possible, and allow students to independently see, say, do and think, which not only reduces the burden on students, but also provides students with opportunities to express themselves and define their own abilities through the acquisition of mathematical knowledge. The opportunity to express themselves and determine the active position of the learners. Ideal mathematics is the mathematics of life, which should solve the mathematical problems related to students and society, and should be more practical in life and less scientific research. Mathematics is a rigorous subject, because of the rigor, so that our teaching into a misunderstanding: to cultivate the mathematician's thinking quality to require our students. Separated from the actual, become is Yangchun white snow, high and low. We should shift the focus of math research to better focus on the level of students. We should study the relationship between mathematics and our real life. To lead students to realize mathematics, from the psychological point of view, their own close relationship with things will awaken more attention. In the teaching of mathematics, we should always grasp: First, mathematics comes from life. Many places in life are rich material for mathematics. Mathematics teaching to speak of the source, speak of the usefulness, so that students feel that there is mathematics everywhere in life, and appreciate that mathematics is a visible, touchable, and useful subject, so as to cultivate students with mathematical vision to observe the surrounding things of interest, attitude and awareness. However, this kind of practical introduction is not just simply giving an example, but requires teachers to design some image and vivid life-like scenarios for students, ask questions, and let go of the students to observe, think, discover and create new knowledge. Second, mathematics serves life. The objectives of school education reflect the specifications and requirements of social and economic development for talents. Of course, in different stages of social development, due to different humanistic philosophical outlooks and differences in values, there are often different interpretations. But progressive education always keeps its eyes on the development of society. Therefore, the general value orientation of our education is the reality and future of our living space - the society. Therefore, every citizen is required to have a high level of 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 math textbooks give many problems related to life. In this way, problems that students never cared about before become hot topics for their discussion. On the one hand, it cultivates students' sense of active participation and creativity, and on the other hand, it improves their problem-solving ability. Thus, the students in turn understand the society and the value of mathematics. Ideal math is applied math, and it is the math that students learn to use. Mathematics learning has a clear direction. Less inaction, more sense of belonging. One of the reasons why students are not motivated enough to learn math is because they feel that learning math is not useful. Instead of learning useful math, in this kind of math learning without a sense of direction, of course they have to lose the direction of learning math and lose the motivation to learn math. In fact, in the second half of the 20th century, the biggest development of mathematics is its application. The wide application of computer technology makes mathematics able to create wealth and value for society directly in some aspects. It is important for students to know that mathematics creates great social wealth in society and that mathematics is widely used in all walks of life in a wide range of machines. Mathematics is a highly applied subject, and the application of mathematics has penetrated into various fields of society. However, in actual classroom teaching, the source and practical usefulness of knowledge are seldom taught. Students' sense of application is weak, and even the teaching of application problems lacks "application flavor". Many students only feel the usefulness of mathematics in the classroom and during the examination, but hardly feel the existence of mathematics after leaving these places. Mathematics learning and social practice connected to the opening of the mathematics research study course to solve a real life problem as the core, in the process of problem solving so that students appreciate the importance of mathematical knowledge and practical value, so as to take the initiative to learn to explore. For example, trigonometric functions and their graphs are very difficult for students to learn and boring content, so for this content to carry out research projects: how to cut the cuffs of the clothes, through trying and exploring, the students found with the cuffs of the clothes in the cutting of the boundary of its cut-off is a sinusoidal curve, so that the fitted sleeves to wear the right fit. Students' interest is very high. On this basis, students are induced to explore other life examples related to their knowledge of trigonometric functions, and are encouraged to put what they have learned into practice. The students found pleasure in the exploration of solving real-life problems, and thus also developed a strong interest in learning trigonometry. One aspect of mathematics teaching is to enhance students' awareness of a wide range of applications, emphasize the application of mathematics, and improve students' ability to solve mathematical problems encountered 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, and the mathematics belonging to secondary school students should be less scientific logic and more humanistic care Previous discussions on mathematics teaching have always tried to pursue the logic of natural science. From the perspective of natural science, education scholars are first influenced by positivism. Positivism only requires to solve the problem of "what" in pedagogy, not to solve the problem of "why". Under the guidance of such an idea, the methodology of mathematics teaching is characterized by induction rather than deduction. Scientific induction has played an important role in pedagogical research and will continue to play an active role in the future development of pedagogy. The focus of the natural sciences on unidirectional questioning and constructed descriptions of the world, without any emphasis on intersubjective understanding, inevitably limits the understanding of the development of pedagogy. The human sciences emphasize the search for human beings, human nature, and the care of human existence in general, in order to pursue the harmony and perfection of human nature. As well as to the whole of life and connotation as its purpose. Humanities is not only committed to exploring the inner spiritual world of man, but also attaches more importance to the extremely discursive relationship of cultural traditions as the objective expression of the inner world of man, and tries to reveal and grasp the values, ideals and pursuits of human beings in general in the unity of the three. The focus of humanistic interpretation and evaluation will shift from the care of objects to inter-subjective understanding and communication. Humanistic care takes the pursuit of meaning as a vector for humanistic interpretation, stipulation, and evaluation, focusing both on the epiphany of the self and on the mutual expression and understanding between subjects. The intersubjective character contained in humanistic research will undoubtedly help to abandon the alienated or objectified mode of thinking. This trend in the teaching of mathematics has led to a truly human place in education. With the study of ecology and values, the true value of the human being will also be realized. Ideally, mathematics is a tool to cultivate students' good interest and stimulate their desire to learn, with less utilitarian coloring and more to sex education. As long as our mathematics teaching is no longer rigidly focusing on the examination and promotion, and more life-oriented and interesting content, we can let students learn mathematics in a really easy and enjoyable way, and we can make more students like mathematics instead of being afraid of mathematics, and the value and function of this course of mathematics will be more The value and function of mathematics will be more and more y entered and rooted in the minds of students, and the unique cultural connotation of mathematics can be more integrated into the spiritual world of students and become part of their quality. Mathematics, as a discipline that takes people as the starting point and destination of research, is also a discipline that seeks for goodness and beauty. Theoretical research is a course of truth-seeking, mathematics teaching to develop, we must pay attention to the development of practice, because people can only word practice in order to achieve unity of truth, goodness and beauty. Should be explored from a variety of specific theoretical issues into the test of educational practice, seeking truth, seeking goodness, seeking beauty Ideal mathematics is the paradise of students' thinking, is the sea of students' thinking to swim, teachers and students are surfing the tide, is to enjoy the fun of mathematical surfing. The true meaning of mathematics teaching in the training of students' thinking as Kalinin said: mathematics is the gymnastics of thinking. Teaching and learning of mathematics, throughout the movement of thinking. Learning math. That is Learning to use their own brains to think, to find problems, research problems, solve problems, reflect on the problem (this is my problem-solving teaching strategies in the classroom teaching application of the steps), during which thinking pervades the entire teaching and learning process. Our role as teachers, like our students, is to be the surfers of thought. The relationship between math and thinking is like a goldfish bowl and goldfish, goldfish left the goldfish bowl, will die, the goldfish bowl left the goldfish is a pool of stagnant water, empty, no vitality. Similarly, in the teaching of mathematics, thinking away from mathematics, empty for thinking, mathematics without thinking, mathematics has lost its meaning. Our teaching should be to develop students' thinking as the goal, through problem solving, (thinking is shown through problem solving), thinking as the main line, training as the main attack, guiding students or accompanying students in the thinking of the ocean surfing, to swim, to improve their own ability. Eulogy for thinking. People, can not do without thinking. Ideal math should make the classroom full of life vitality, is a wonderful chapter in the life of teachers and students. Classroom is the interpretation of the magnificent music of life. The mind of mathematics is a living subject, reflected in the status of mathematics in the entire basic teaching full of vitality, it is mathematics because full of vitality, can be reflected in all walks of life, his vitality to a certain extent to drive the development of productivity. Mind math teaching is a process full of life activities. This is because the subjects of teaching are students and teachers, both of whom are living beings with positive meanings. In this dynamic system of teaching and learning, there are too many variable factors, there are all kinds of problems arising in the teaching and learning process, the teacher is thinking about how to interpret the teaching process better, to pass on more knowledge to the students, and to better cultivate the students' various abilities; how to make the relatively static, dead knowledge more lively, more vitality, in order to facilitate the students' better absorption, while the students will think about how to make themselves more active, and the students will think about how to make themselves more active, and the students will think about how to make themselves more active, and the students will think about how to make themselves more active, and the students will think about how to make the students more active. Students will think about how to make their own learning process more effective, more operational, more targeted, in general, more vital. The object of teaching in mind is a distinctive vigor of the students, is equal to the teacher, independent life form, is the need for more care, care of life. Give life more rights, give life more space for development, give life more autonomy. Let the classroom surge the tide of life, glowing with youthfulness. Energetic, passionate, the ideal classroom is full of the salute of life. Ideal math is that there should be a sea of tolerance, a great deal of inclusiveness, compatibility, in line with the characteristics of the development of the times. Focus on the integration of information technology and the subject of mathematics. Modern educational technology is having a profound impact on mathematics teaching. We should not only pay attention to the use of information technology to present course content, but also to the organic integration of information technology and course content. The Standard can make general use of scientific calculators and various mathematics education platforms to strengthen the integration of mathematics and information technology. In terms of content, the unique role of "algorithms" in the development of mathematics as a whole is highlighted as an important clue to understanding the development of mathematics, and efforts are made to integrate algorithms into all relevant parts of the mathematics curriculum. Integration of Mathematics Teaching with Other Disciplines: An inevitable trend of the new curriculum reform is the integration and intersection of knowledge of various disciplines. Mathematics, as a fundamental subject in the natural sciences, can only play its role by applying it to other disciplines, and the teaching of mathematics organized directly from this perspective will be more meaningful and colorful, and will attract more students. For example; such as Euler's formula in polyhedra, introduces the story of the three chemists who won the 1996 Nobel Prize in Chemistry to discover molecular structure with Euler's formula. Is a molecule composed of 60 C atoms, his structure for the simple polyhedron, with Euler's theorem students can also be solved, if anyone can be earlier than the three scientists to use Euler's theorem to solve the problem, then he is the Nobel Prize winner. The students were greatly inspired and highly motivated to learn. The math in mind is the ideal math, the math with real life. After experiencing a lot of helplessness and frustration in the life of mathematics, after experiencing the many confusions of a mathematics teacher facing the current mathematics teaching, after one learns many new theories and new insights, the image of mathematics in the mind is more and more rich and full. After reading Mayor Zhu Yongxin's dream, I can not help but follow Mayor Zhu also made a dream, no matter whether it is a daydream or a fool's dream, I also look forward to the time when the dream is complete, the dream of the city of true day. The day of the dream is really good!