Deeply understand the concept. Concept is the cornerstone of mathematics. Learning concepts (including theorems and properties) requires not only knowing why, but also knowing why. Many students only pay attention to memorizing concepts and ignore their own background, so they can't learn math well. For every definition and theorem, we should know how it comes from and where it is used on the basis of remembering its content. Only in this way can we make better use of it to solve problems. Look at some examples. Careful friends will find that after explaining the basic content, the teacher will always give us some extra-curricular examples and exercises, which is of great benefit. The concepts and theorems we learn are generally abstract. In order to make them concrete, we need to apply them to the theme. Because we have just come into contact with this knowledge, we don't have enough skills to use it. At this time, examples will be of great help to us, and we can put the existing concepts in our minds in the process of reading examples. To make the understanding of knowledge more thorough, because the examples added by teachers are very limited, we should also find some examples ourselves, and pay attention to the following points: we should not just look at the skin, but not the connotation. When we look at the examples, we really want to master their methods and establish a wider way to solve problems. If we look at something, we will lose its original meaning. Every time we look at a topic, we should clarify its thinking and master its thinking method. If we encounter similar topics or the same type of topics again, we will have a general impression and it will be easy to do, but we must emphasize one point unless we are very sure. ? We should combine thinking with observation. Let's look at an example. After reading the questions, we can think about how to do it first, and then compare the answers to see what our ideas are better than the answers, so as to promote our improvement, or our ideas and answers are different. We should also find out the reasons and sum up experience. ? Examples of various difficulties are taken into account. Looking at examples step by step is the same as "doing problems" in the back, but it has a significant advantage over doing them: examples have ready-made answers and clear ideas, and you can draw conclusions as long as you follow their ideas, so you can look at some skillful, difficult and difficult examples, such as competition problems with moderate difficulty, without exceeding what you have learned. Do more exercise. If you want to learn math well, you must do more exercises, but some students can learn it well by doing more exercises, and some students still can't learn it well after doing a lot of exercises. The reason is whether "doing more exercise" is correct or not. When we say "do more exercises", we don't mean "crowd tactics". The latter does nothing but think, and cannot consolidate concepts and broaden ideas. Moreover, it has "side effects": it confuses what has been learned, wastes time and gains little. When we say "do more exercises", we ask everyone to think about what knowledge it uses after doing a novel topic, whether it can be explained more, whether its conclusion can be strengthened and popularized, and so on. ? You must be familiar with all kinds of basic problems and master their solutions. Every exercise in the textbook is aimed at a knowledge point, which is the most basic topic and must be mastered skillfully; Extra-curricular exercises also have many basic questions, with many methods and strong pertinence, which should be done soon. Many comprehensive problems are just the organic combination of several basic problems. If you master the basic problems, you can't worry about solving them. ? In the process of solving problems, we should consciously pay attention to the thinking method reflected in the topic in order to form a correct thinking mode. Mathematics is a world of thinking, and there are many thinking skills, so every problem will reflect certain thinking methods in the process of proposition and problem solving. If we consciously pay attention to these thinking methods, after a long time, we will form a "universal" solution to each kind of problem in our minds, that is, the correct mindset, and it will be easy to solve such problems at this time; At the same time, I have mastered more thinking methods and laid a certain foundation for doing comprehensive problems. ? Do more comprehensive questions. Comprehensive questions are favored by proposers because of the many knowledge points used. Doing comprehensive questions is also a powerful tool to test your learning effect. By doing comprehensive questions, you can know your own shortcomings, make up for them, and constantly improve your math level. Do more exercise for a long time and do it several times a day. After a long time, there will be obvious effects and greater gains. How to treat exams Learning mathematics is not only for exams, but the exam results can basically reflect a person's mathematics level and quality. In order to get good grades in the exam, the following qualities are essential. ? Kung fu should be used in peacetime, and there will be no accidents before the exam. What you need to master in the exam should be mastered in peacetime, and don't be tired the night before the exam. In this way, you can have abundant energy in the examination room. When taking the exam, we should put down the burden, drive away the pressure, concentrate on the test paper, analyze it carefully and reason closely. ? Examination requires skill. After the papers are handed out, we should first look at the questions and allocate time. If you spend too much time on a problem and haven't found a way of thinking, you can put it in the past for a while and finish what you have to do. Think about it later. After one question is finished, don't rush to do the next one, read it again, because the ideas in your mind are still clear and easier to check. For the answers to several questions, you can use the conclusion of the previous question when answering the following questions. Even if the previous question is not answered, as long as the source of this condition (of course, it is required to prove the topic) can be used. In addition, you must consider the test questions comprehensively, especially the fill-in-the-blank questions. Some should indicate the range of values, and some have more than one answer. Be careful and don't miss them. ? Be calm during the exam. Some students immediately get hot heads when they encounter problems that they can't solve. As a result, when they are anxious, they can't do what they could have done. This state of mind is that they can't do well in the exam. We might as well take advantage of the psychology of self-consolation during the exam: the questions that others can't do, the questions that I can't do (commonly known as the spiritual victory method) may be able to calm down and play their best. Of course, comfort is comfort. For those problems that can't be done at once, we should think hard and do what we can. There are also some ways to do certain steps and the habit of listening carefully. In order to synchronize teaching and learning, teachers require students to concentrate their thoughts in class, listen attentively to the teacher's lectures, listen carefully to the students' speeches, grasp the key points, difficulties and doubts, think while listening, and encourage middle and advanced students to take notes while listening. 2. The habit of positive "thinking". It is an important guarantee to improve the quality and efficiency of learning to actively think about the questions raised by teachers and classmates and keep yourself in teaching activities. Students' thinking and answering questions are generally required to be well-founded, organized and logical. With the growth of age, we should gradually infiltrate mathematical ideas such as association, hypothesis and transformation when thinking about problems, and constantly improve the quality and speed of thinking about problems. 3. The habit of "taking exams" seriously. The ability to examine questions is the comprehensive embodiment of students' various abilities. Teachers should ask students to read the content of the textbook carefully, learn to master the words and correctly understand the content, carefully scrutinize and ponder the key contents such as tips, marginal notes, formulas, rules, charts and so on, and accurately grasp the connotation and extension of each knowledge point. It is suggested that teachers often carry out special training of "the difference between one word and ten thousand words" to continuously enhance the profoundness and criticism of students' thinking. 4. The habit of "doing" independently. Practice is an important part and natural continuation of teaching activities, the most basic and frequent independent learning practice of students, and the main way to reflect students' learning situation. Teachers should educate students not to blindly follow the viewpoint of eugenics in their understanding of knowledge, not to be influenced by others, and to easily change their own viewpoints; The use of knowledge does not copy other people's ready-made answers; After-school homework should be completed in good quality, quantity, time and neatly, and the best method should be achieved, and mistakes must be corrected. 5. Be good at asking questions. As the saying goes, "curious children will become great people." Teachers should actively encourage students to question and ask difficult questions, ask teachers, classmates and parents with knowledge doubts, and strongly encourage students to design their own math problems and communicate with others boldly and actively. This can not only harmonize the relationship between teachers and students, enhance the friendship between students, but also gradually improve students' communication and expression skills. 6. The habit of being brave in "arguing". Discussion and demonstration are the best thinking media, which can form multi-channel and extensive information exchange between teachers and students and between classmates. Let students express themselves in the debate, inspire each other, exchange gains, increase their talents, and finally unify their understanding of true knowledge. 7. Try to "break" the habit. The innovation ability of a nation is an important embodiment of comprehensive national strength, so the new syllabus emphasizes the importance of cultivating students' innovative consciousness in mathematics teaching. Teachers should actively encourage students to think without the limitation of conventional ideas, be willing and good at discovering new problems, be able to interpret mathematical propositions from different angles, answer questions in different ways, and creatively operate or make learning tools and models. 8. The habit of "learning" early. Judging from the cognitive law of primary school students, in order to achieve good academic performance, we must firmly grasp the four basic links of preview, listening to lectures, homework and review. Among them, previewing textbooks before class can help students understand the main points, key points and problems of new knowledge, so as to focus on solving them in class, master the initiative of listening to lectures, and make lectures targeted. With the increase of grade, the importance of preview becomes more prominent. 9. The habit of "checking" repeatedly. Cultivating students' checking ability and habit is an important measure to improve the quality of mathematics learning, a necessary process to cultivate students' consciousness and sense of responsibility, and this is also a clear teaching requirement in the new syllabus. After the exercise, students should generally check and check from the following aspects: "Whether it conforms to the meaning of the question, whether the calculation is reasonable, flexible and correct, and whether the method of solving applied and geometric problems is scientific". 10, the habit of objective "evaluation". It is a high-level learning for students to objectively evaluate the performance of themselves and others in learning activities. Only by objectively evaluating ourselves and others can we judge our own self-confidence and shortcomings, thus achieving the goal of facing ourselves squarely, constantly reflecting and pursuing progress, and gradually forming a dialectical materialist view of understanding. 1 1, the habit of "moving" frequently. Mathematics knowledge is highly abstract, and primary school students' thinking is obviously concrete, so the new syllabus emphasizes that we should pay attention to learning and understanding mathematics from students' life experience and strengthen the cultivation of practical ability. In teaching, teachers should emphasize the use of students' hands and brains to stimulate thinking, solve difficult concepts through examples, find the correct solution to complex application problems through drawing, and ask for directions through cutting vague geometric knowledge or experiments. 12, the habit of intentional "gathering". It is not terrible for students to make mistakes in learning activities. What is terrible is that they have made many mistakes on the same question. In order to avoid making the same mistakes frequently, a responsible teacher arranged an error consultation column in the classroom, and students with computing ability set up an error knowledge file to collect the wrong questions in their usual exercises or exams and repeatedly admonish themselves, which is worth promoting. 13, the habit of flexible "use". The purpose of learning lies in application, which requires students to use what they have learned in class flexibly, which can not only consolidate and digest knowledge, but also help to transform knowledge into ability, and also achieve the purpose of cultivating students' interest in learning mathematics. To truly understand the mathematical definition, don't be specious. & lt2> Cultivate logical thinking in solving problems and know where to start. Start with conditions: understand the function of conditions in the topic and its function, and quickly infer the conclusions and results that can be drawn from it. Then, combined with the parallel conditions, we can draw further conclusions and finally solve the problem. Starting with the result: when the function of the condition cannot be determined, we can consider starting with the result. First of all, we should combine the unconditional part of the topic and think of the possible necessary conditions for reaching this conclusion. Then advance to the original conditions given by the topic and solve the problem. Cultivate a good mathematical spirit First of all, on the basis of conclusions and answers, carefully understand the problem-solving process and whether you really know the conclusion. If you don't understand, don't be happy with the answer you got. You should answer it again or ask your teacher or classmates. Every step is required to have a rigorous derivation basis, or a theorem or axiom, and it is never taken for granted. If you don't ask, this is very important for learning math. To cultivate good mathematical spirit, we must ask more questions. < 4 > Choose a topic with moderate difficulty for self-training. There are two requirements for the selection of exercises: breadth and longitude. According to the textbook knowledge and the content of the teacher's lecture, it is a good time-saving method to sum up the key points of study, listen to the teacher and watch the students do it. At the same time, it is required to take care of all the knowledge points learned and practice every knowledge point. If the knowledge points are relatively simple, you can choose exercises with relatively high difficulty. Correspondingly, if it is difficult, you can choose exercises with moderate difficulty. It is unnecessary and difficult, so practice more. Classical exercises always contain more knowledge points, which requires the solvers to have strong comprehensive ability and mathematical thinking, and be good at using conditions. It's not very difficult, but it requires strong insight and decision-making ability, and at the same time, it promotes the conclusion conditions, and then meets somewhere to solve the problem. 〈5〉 Cultivate interest in mathematics. Never think that math problems are scientists, and at most they will reach the level of teachers. Actually, it's not. Anyone should look at the whole world with suspicion. Don't doubt your different opinions. If you still have objections after your own judgment, you should bravely raise them, and don't give up your opinion because of one or two mistakes. This is not only the focus of solving problems, but also the focus of cultivating good living habits. There is no doubt that there is no innovation. Many students are not interested in mathematics because they didn't do well in the exam, so they deny themselves and even give up mathematics. Therefore, we must have a correct view of examination. It's just a way for teachers and classmates to test their learning situation. Where they fail, they will stand up. Careless or not, it doesn't matter. Carelessness is generally due to the fact that good habits are not formed at ordinary times, so it is inevitable that the thinking is not concentrated during the exam and it is easy to answer without careful thinking. Another point is easier, as long as you spend more time reviewing, you can prevent it from happening again. As long as you develop good mathematical spirit and thinking, you can give full play to your skills in the exam. Learning mathematics is not only learning to solve problems, but also learning to observe and improve life. Cultivate your observation ability and interest in life, and you will benefit endlessly in your later life. The future society needs talents who can solve problems, not nerds who can only solve problems. People who can only solve problems are always backward, not creative and not competitive. Do more exercises and ask the teacher to have a good attitude. Don't give yourself too much pressure. You can also look at the review questions in high school, communicate with teachers and classmates, and increase your interest in mathematics. 1. I don't deny that being good at math is related to genius, but being good at math is not a genius's patent. 2. Mathematics examines the sensitivity of reaction, which is what we usually call mathematical consciousness. We have to think about all the relevant knowledge points in an instant before we can do a good job. This is not only the difficulty in learning mathematics, but also its bright spot. 3. To learn math well, you must first ask yourself if you really want to learn it well. If you can really do this, then you have succeeded by one fifth. 4. Put it into practice. Where there is a will, there is a way. If you burn your bridges, you will win the battle. More than 3,000 armour can swallow Wu. That is to say, from now on, I can introduce you to several methods: a. preview in advance. At least twice as fast as the teacher. At the same time, understand the exercises after class. Ask if you don't understand. B. consult the teacher and buy one or two sets of papers that suit you. Of course, if you are lucky, your teacher will give you some of his own papers. C. consciously do the questions and learn to draw inferences. Combining geometry with algebraic knowledge (mainly applying geometry knowledge to solve algebraic problems) D. Learn to take notes, not to remember every step of a math problem, but to be as simple as possible. At the same time, after remembering a question, stop to think, sum up the rules and take notes. 5. Math study is a little different from examination. The exam needs a state of excitement, but when you do the questions, you should calm your heart, calmly examine the questions and take notes.