Why study math first? What are the characteristics of middle school mathematics? There are many basic knowledge and a wide range of contents. Knowledge is closely related. Strong logic and large amount of calculation. What are the problems for students with high ability to learn mathematics? For a long time, mathematics learning difficulties have become a problem faced by middle school students. What are the difficulties in learning mathematics? Through the investigation and understanding of the majority of students, we can sum up the following points: what do you know about learning mathematics? You say, I listen, you write, I copy, you let me do, you test my back. The operation error rate is high. I can't analyze problems, and I will panic when I meet something I haven't seen before. Poor reading ability, lack of common sense of life. What are the conditions for cultivating mathematics learning methods? Parents and children should be considerate of each other. Don't call yourself stupid. Knowledge is power. Learning methods are knowledge perseverance and perseverance. Learning method is habit. Method Introduction Everyone should choose the method that suits them, don't be greedy, and stick to it for a long time. 1. Focus. Can you concentrate? Be clear about your learning purpose. You should study under time pressure. Basic knowledge: definitions, theorems, formulas, axioms, rules, properties, inferences, figures, examples and exercises in bold, mathematical symbols and mathematical methods. Use your hands, eyes, mouth and brain together. Try to cultivate your concentration! 2. Learn to be a little teacher. What do you mean by "know"? Being able to explain to yourself and others is called "understanding". You guessed it. You did the right thing. Math teachers are better than students, not only in solving problems, but also in math literacy. Because they give lectures to students every day, the lectures are complete and comprehensive, and the knowledge points are systematic. If students often tell others questions and try to make them clear, then they can enter the thinking of the math teacher when doing the examination questions, and it is easy to understand the questioner's intention. 3. How to cultivate the accuracy of operation? A little view on operation The ability, habit, accuracy and self-confidence of mathematical number calculation have a very obvious influence on the ability of middle school students to demonstrate and reason, that is, to "operate" abstract mathematics. When we talk about computing power again, we mean the ability to do the right questions. After investigating students' computing ability, many students said, "The questions are easy to do, very serious, and the exam is not bad." But the final scores are not high. The reason is that I can do it, but I was wrong, anxious, careless and careless. This is not to prevaricate parents and teachers. How to solve it? Most people don't know. The teachers of the research group have done experiments and analyzed the students with 50-90 marks. The results show that about 2/3 of the points that students fail in each exam will be wrong. Analysis of the reasons for the meeting error 1. When doing a problem, do it as soon as you can, and leave some time to do something you can't do. I'm afraid I can't finish it, but I'm in a hurry. It belongs to improper strategy; 2. Mental arithmetic caused disaster. The heart of primary school is one step, and at most it is two steps. But in middle school, the operation is more complicated, and students often do mental arithmetic in several steps, which is especially easy to make mistakes; Step 3: Jump. With the increase of grade and knowledge, mathematical operations must be skipped. But some students dance too much. There is less space left in the test paper or exercise book, so you don't need draft paper, just jump hard. Over time, it's uncomfortable not to jump, and it's strange not to make mistakes. 4. Draft paper can't be used. It is difficult to find the corresponding problem in the key steps of jumping around. In fact, some math experts don't use draft paper at all when doing big problems, because they rarely skip them; 5. Lack of self-confidence; Pay attention to 1 and skip less; 2. Less mental arithmetic; 3, use less draft paper, that is, use draft paper neatly; 4. Be confident to do it right once. Don't hold the idea of "hurry up and check it a few times". In fact, when it comes to the college entrance examination or the senior high school entrance examination, there is little time to check. Therefore, we should develop the habit of "doing problems slowly and doing them right once". Real masters are the slowest. On the contrary, the fastest hand-in paper is either useless or self-righteous guy. 4. To learn mathematics well, we need to pay attention to the following links-eight-link learning method: (1) making plans, (2) previewing before class, (3) listening carefully, (4) reviewing in time, (5) working independently, (6) solving problems, (7) systematically summarizing, and (8) studying after class. This method was summed up by Li Shifa, a teacher from Wuhan, who investigated the learning experience of 200 excellent middle school students with an average score of over 90 in all subjects, 40 junior college students from Huazhong Institute of Technology and 60 college students who were admitted to Wuhan University with high scores. As long as a student can learn according to these eight links and implement them step by step, he will become the master of learning and an excellent student in his class. 5. Airborne Learning Method Yukio Noguchi of Japan wrote a book "Super Learning Method". This paper introduces the super learning method of mathematics-airborne learning method, which is specially written for students with poor mathematical foundation. Most people will think that the foundation is very important. We should start from the foundation and understand it step by step. If you don't know anything, you must return to the basics. Because of this, students with learning difficulties will give up studying mathematics, but the airborne learning method does not need to feel guilty to recognize students with poor foundation. Omitting the mountaineering process, you can enjoy the mountain scenery directly by cable car, and you can watch it on TV without knowing the semiconductor principle. Therefore, when students with poor foundation make up their minds to learn mathematics, it is not necessary to start reviewing from a very low knowledge base, and they can start from the correct central part. If people who can't learn math well think that they have to fully understand the basics first, it is equivalent to waiting for the Yellow River to clear. The foundation is the most difficult part in mathematics. What people who are not good at math have in common is to learn from the basics. As a result, after learning a few pages, they feel bored and surrender. In fact, what they should do is to try their best to understand what they are learning at present, because as long as they understand this place, the difficulties ahead will naturally be understood. Airborne learning method, as long as you land in "the place where you are currently studying" by skydiving. The reason is that as long as you understand what you are learning now, you will understand what you didn't understand before. For high school students, if the junior high school mathematics foundation is poor, but the senior high school set, function and solid geometry are carefully studied, the junior high school mathematics content will be easy to understand. Therefore, students with learning difficulties don't have to feel inferior because they don't learn well. Instead, we should use the idea of "airborne learning" and concentrate on understanding every problem we face. If they do encounter the confusion of previous knowledge, then consult teachers and classmates or consult relevant materials, and fall on the level of the required basic knowledge and make up this foundation at any time. 6. Set your mind on the wrong questions. Students often make mistakes on the same or similar questions, and they often take such questions in exams. As long as you screen out such error-prone topics in your usual homework and exams, summarize and sort them out, record the comparison between the wrong solution and the correct solution, and write down your own reflections or experiences, watch them every day and deepen your impression, you can lose less points and get high marks in the exam. 7. Cultivation of memory habits Memory classification: instantaneous memory, short-term memory and permanent memory. Ebbinghaus's Law of Forgetting: A person's memory will be forgotten 80% after one night. This is the self-protection function of the brain. Because it doesn't know what really useful knowledge is unless we deliberately strengthen our memory. 1, 10 Minutes before going to bed, sort out the important things of the day, and repeat them 5 minutes after getting up, then your memory will be effectively consolidated; 2. Reciting ability: Don't expect to memorize it once, try it three times every morning, noon and evening, and strengthen it repeatedly; Review what you have learned in time and regularly. The so-called review the past and learn the new. I hope students can learn to study, cooperate and survive. I wish the students to learn knowledge, cultivate methods and form abilities! Being admitted to an ideal university will be more sustainable! I. What is Mathematics Engels said: "The object of pure mathematics is the spatial form and quantitative relationship in the real world." Mathematics includes pure mathematics, applied mathematics and their intersection with other disciplines. It is a knowledge that integrates rigor, logic, accuracy, creativity and imagination, and it is also a natural science and a technical science. Social science, management science and other huge intellectual resources. Mathematics has its own unique language system-mathematical language, and mathematics has its own unique value judgment standard-unique mathematical epistemology. Mathematics is not only an important tool for learning other natural and social sciences, but also a kind of culture. Mathematics reflects the height of human intelligence development from one side. Mathematics has its own beauty. Some people who work in mathematics regard mathematics as art, however, with the continuous development of science, the object of mathematics research has gone far beyond the general spatial form and quantitative relationship. The abstraction and application of mathematics have developed greatly at the same time. If abstract mathematics is regarded as "root" and applied mathematics as "leaf", then mathematics will become a towering tree in natural science. We live in the information age. One of its important characteristics is that the application of mathematics permeates all fields, and the relationship between high technology and mathematics is getting closer and closer, resulting in many new disciplines combined with mathematics. With the increasing mathematicization of today's society, some far-sighted scientists profoundly pointed out: "The competition of high technology in the information age is essentially the competition of mathematics." Second, the application of mathematics Mathematics is the "queen" and "servant" of science. According to the general understanding, the queen is elegant, authoritative and supreme, just like Chun Xue. In science, only pure mathematics has such characteristics. Simple and clear mathematical theorems have been proved to be eternal truths, extremely beautiful and impeccable. On the other hand, all branches of science and engineering use mathematics extensively to varying degrees and enjoy its contribution. At this time, mathematical science is a servant, and the word servant in English titles has something for people to use in English. The meaning of "useful service tools". This expression skillfully illustrates the position and role of mathematics in the whole science. It is very important to correctly understand and understand the importance of mathematical science to the development of science, economy and education. 1, mathematics is the foundation of other disciplines, whether it is physics, chemistry, biology, information, economics, management and other emerging disciplines or even humanities. Mathematical methods are all necessary basic tools. In the past, people used to think that mathematics was the common language of science and engineering. If you want to describe your findings and achievements to everyone, then you must master and apply mathematics. Now, from weather forecast to sewage treatment, and even the cycle and quantity of supermarket purchases, the planning and design of public transport lines need mathematics, mathematical modeling and related calculations. It is becoming the key of engineering design. That is, medicine, biology and other fields that rarely used mathematics in the past have many applications. For example, in the diagnosis of cardiovascular diseases, the basic equations of fluid mechanics are used to simulate the possible results in various situations by computer before operation as a diagnostic reference; Neurology uses mathematics to analyze various rhythms, etc. Mathematical knowledge is also widely used in the study of biological DNA, and its double helix structure is a problem related to geometry. 2. The greatest scientific achievement of mathematics in other fields in the 20th century was Einstein's special and general relativity, but Einstein's general relativity and gravity theory could not have such a perfect mathematical expression without Riemann geometry invented by riemann sum Gloria in 1854 and the invariant theory developed by mathematicians such as Silvis and Nott. Einstein himself said this sentence more than once. Newton, Leibniz, Euler, and Gauss all made a systematic study of computing skills-numerical analysis and computing speed (computer manufacturing). They have always been an important part of mathematics. Mathematicians have played a decisive role in the development of modern computers. Mathematicians such as Leibniz and Babbage have developed computers. In 1930s, the study of symbolic logic was very active. Scholars such as Church, Godel and Persia study formal languages. After their research work with Turing; The mathematical concept of computability is formed. 1935, Turing established the abstract model of general computer. These achievements were later Feng? 6? 1 Neumann and his colleagues made computers with stored programs, which provided a theoretical framework for the invention of formal programs. On the surface, the relationship between mathematics and humanities and social sciences is not close. After all, writers don't need to rack their brains to prove Goldbach's conjecture, and painters don't need to know calculus. In fact, the humanities are inseparable from mathematics. As a rational basis and representative mathematical thinking method, mathematical spirit has been injected into many fields such as literature, art, politics, economy, ethics and religion. The role of mathematics in social science and humanities is not very intuitive formulas and theorems, but abstract mathematical methods and ideas, among which deductive reasoning and deductive proof are the most prominent, that is, new propositions are derived from recognized facts. To recognize these facts as a premise, we must accept the new proposition derived from them. Philosophically, to study some eternal topics, such as life and death, we can't use simple induction (trial and error) or analogical reasoning, but only resort to mathematical method-deductive reasoning. There are many similar examples. Mathematics has influenced the direction and content of many philosophical thoughts to a certain extent, from Pythagorean philosophy in ancient Greece to rationalism in modern times. Empiricism can prove this until modern logical positivism, analytical philosophy and so on. Mathematics also has a certain influence on music, painting, linguistic research and literary criticism theory. Musically, since the fact that there is a close relationship between the chord length and timbre of musical instruments was discovered, the research in this field has never stopped, and the study of the golden section in aesthetics is also an indispensable topic. Before the Renaissance, painting was considered as a low-level occupation as a factory worker. After the Renaissance, painters began to use mathematical principles such as plane geometry, three views and plane rectangular coordinate system to guide painting art, and Leonardo da Vinci's perspective theory is a prominent example (with the help of plane geometry knowledge, the visual effect pursued in painting is achieved-the distant things get closer and the small things get bigger). Since then, painting has entered the palace of human art, and from the practical application, many social sciences and humanities are also inseparable from mathematics. When studying history and politics, the most commonly used method is statistics, which was called political mathematics at the beginning of its appearance, showing its status. Archaeology, a major branch of history, can not be separated from mathematics, such as trigonometric calculation, exponential function, logarithmic function and so on. Archaeology is inseparable from physical and chemical methods, but these two disciplines are useless without the tool of mathematics. Many high school mathematics knowledge, such as drawing, addition principle, multiplication principle, etc., are often used in daily work and study. For example, probability analysis, extreme value and derivative of function are not so common in people's daily life, but they play an important role in the development of modern economy. For example, probability analysis is also a basic subject of applied mathematics. It can describe the net cash flow and economic effect index of the scheme by studying the probability distribution of various uncertain factors in different ranges and their influence on the economic effect of the scheme, so as to make a more accurate judgment on the risk status of the scheme. Therefore, in practical work, if we can give various possible states and their occurrence probabilities of the uncertain factors that affect the cash flow of the scheme in the life cycle of the scheme through statistical analysis, it is possible to calculate the net cash flow sequence and its occurrence probability of all possible schemes by combining different states of various factors, and then calculate the net present value, expected value and variance of the scheme. In order to meet the needs of rapid economic development, high school mathematics should strengthen the teaching of function content and increase the contents of probability statistics, linear programming, mathematical models and so on. (Continued from issue 75) 3. The purpose of learning mathematics as a basic subject, learning mathematics does not have to be a mathematician. What is more important is to cultivate people's mathematical concepts and ideas and their ability to solve mathematical problems. The importance of mathematics is not only reflected in the application of mathematical knowledge, but also in the way of thinking of mathematics. It is beneficial to cultivate people's thinking, innovation, analysis, calculation, induction and reasoning abilities. After entering the society, students may rarely use a formula and theorem in mathematics directly, but the way of thinking and the spirit embodied in mathematics have been used by him all his life. The way of thinking in mathematics is very important. In short, mathematics provides a way to organize and construct knowledge. Once mathematics is used in technology, it can produce systematic, reproducible and teachable knowledge. Analysis, design, modeling, simulation and application will become possible and become efficient and structured activities. That is to say, it can be transformed into productive forces. However, fifty years ago, although mathematics directly provided some tools for engineering technology, it was basically indirect. First, it promotes the development of other sciences, and then these sciences provide the basis of engineering principles and design. Now, mathematics and engineering interact directly in a wider range and at a deeper level, which greatly promotes the development of mathematics and engineering science. It also greatly promoted the progress of technology. The most important technological progress in the second half of the 20th century is the rapid development of computer, information and network technology. As far as the computing speed of the computer is concerned, the computing speed of the first computer, the electronic mathematical integration computer, which was publicly displayed in 1946 is 5000 times per second. At present, it has reached 654.38+00 billion operator point operations per second. According to experts' estimation, it will reach 1 trillion operations by 2065.438+00. As you can imagine, what computers can do now is far from what they did 50 years ago. Many mathematical models have been produced to describe and study various practical problems. Some of them can be solved, and all problems can be solved to varying degrees. However, they could not be worked out at that time or in time. It can't solve the problem. At present, technical indicators such as calculation speed are far ahead in a sense. Mathematical modeling and its accompanying calculation are becoming the key tools in engineering design. Scientists rely more and more on calculation methods. In addition, they must have sufficient experience in choosing correct mathematics and calculation methods and in explaining the accuracy and reproducibility of the results. What we see is that mathematics and computers are widely used in all walks of life. Solve problems through mathematical modeling, simulation and other means, and make the methods and results of solving similar problems into software (they are even quite stupid) for sale. What people see is this great development in the application of mathematics. In other words, when commenting that mathematical science has become the first of the five innovative projects, the director of the Mathematics Department of the American Science Foundation said, "The driving force behind this major innovative project is the mathematization of all scientific and engineering fields." Of course, there are different understandings. Some people think that you don't need to know a lot of mathematics, as long as you can use software. Others think that you don't need to develop basic mathematics now, but you can solve the problem through mathematical modeling and calculation plus physical intuition. In particular, some people think that students nowadays don't need so much math. This is really a great misunderstanding. Third, how to improve math scores 1 and cultivate interest in middle school and learn with curiosity. Learn math and love math. Mathematics is beautiful, and its ontology is simple and clear now. It is a kind of rational beauty and abstract beauty. Mathematics is like a garden. You can't see its beauty without entering the door, but you will find it really beautiful as soon as you enter the door. Many mathematicians are interested in learning mathematics well. The second is curiosity. You should have ideas, dare to guess and learn math with curiosity. Find a sense of accomplishment. As long as curiosity and thirst for knowledge become the desire to solve problems, we can consciously improve our ability to solve problems by using mathematical knowledge. Only when we are full of fun in the process of learning mathematics can we study and study mathematics more consciously. 2. Read carefully and understand the language of mathematics. It is a common problem that middle school students don't like watching math classes. Mathematics textbooks are written in mathematics language, including written language, symbolic language and graphic language. Its language is concise. Because of its strong logic, rich connotation and profound meaning, we must not read a math textbook in an instant and read ten lines at a glance. Mathematical concepts, definitions, theorems, etc. They are all expressed in written language, so be sure to pay attention when reading. Five essentials should be achieved in preview: ① draw the key points with wavy lines; ② Labeling formulas and conclusions; (3) draw a question mark in an incomprehensible and doubtful place with a pencil; (4) Write the answers to simple exercises and the key points of solving problems at the back; ⑤ If there is more than one condition in the definition and theorem, the conditions should be numbered. Symbolic language is rich in connotation, so we should write, argue and remember it firmly. When reading symbolic language, we should say its meaning and distinguish its characteristics. Graphic language can not only reflect the relative position of elements, but also directly reflect the quantitative relationship. Therefore, when looking at geometric figures, we should understand the hidden internal relations and quantitative relations between graphic elements. While looking at the image, we should glimpse the essence of the function from its shape. If reading math books before and after class can meet the above requirements, learning math is an introduction; If you form a good habit of reading from this, then improving your grades will be just around the corner. 3. Listen carefully and master the thinking method. Listen attentively and think positively with the teacher's explanation. When previewing, you can understand concepts you don't understand and solve the mystery of the teacher's dictation. Supplementary examples and wonderful solutions should be recorded quickly. Write a good speech, not only leaving a valuable material. And it will help you concentrate. Be suspicious, question, dare to ask questions and answer when attending classes. Think about whether the teacher's explanation is complete and correct, and whether the answer is rigorous and flawless. If you understand the example of blackboard writing, you should think of a new solution. When in doubt, ask questions boldly. Contending to answer questions is by no means "digital expression", but to elaborate your own views and improve your oral expression ability. Even if your answer is wrong, it is easy to book a certificate after exposing the problem. The most taboo in class is to follow blindly, go with the flow, follow others and not pretend to understand. 4. Learn independently and learn to summarize. To develop the good habit of autonomous learning, we must do the following: ① Finish your homework on time. Consolidate what you have learned. Only by finishing homework on time can we consolidate our knowledge and minimize forgetting. In the process of completing homework, you will increase the repetition rate of knowledge, promote your thinking ability and give full play to your creativity in solving problems. Students who study well should also pay attention to the cleaning and collection of your homework, because this is not only a good way to cherish the fruits of their own labor, but also a good way to review the materials. ② Review homework in time to form a knowledge network. Chapter review, unit review and preparation review are an indispensable part of mathematics learning and play a role in connecting the past with the future. When reviewing, we should sum up knowledge and methods according to a certain system to form a "latitude and longitude network" of mathematics. The "essence" here refers to the knowledge of various branches of mathematics; "Weft" refers to the application of the same mathematical method in different branches. If you want to learn mathematics well, you must weave the "latitude and longitude net" of mathematics well. ③ Pay attention to the standardization of writing. Mathematics is a highly specialized subject, which has strict requirements on the process of expression, narration and the use of symbols. Therefore, writing should be standardized in practice, homework and exams. ④ We should apply what we have learned and innovate constantly. Mathematics is very important. There is no insurmountable gap between old and new knowledge. Therefore, borrowing knowledge from books and associating can not only enhance learning interest, but also cultivate one's creative thinking ability. Pay attention to the above methods, which can not only consolidate the original knowledge, but also expand your own knowledge field and communicate the internal relationship between mathematical knowledge. With good study habits, one will certainly learn math well.