First, the general methods of junior high school mathematics learning:

1. Highlight the word "diligent" (overcome the word "lazy")

Mathematician Hua once said: "Intelligence lies in learning, and genius lies in diligence."

"Diligence is a good training, and one point of hard work is only one point;

When we study, we should emphasize the word diligence and overcome laziness. How to emphasize the word diligence?

Cong: What kind of diligence? Literally speaking, we should do five diligence: "ear diligence" and "eye diligence" (listening with ears, seeing with eyes and receiving information)

Is it enough for "oral diligence" (discussing and answering questions instead of speaking and digesting information) and "spiritual diligence" (being good at thinking and actively thinking about problems-absorbing and storing information) to do the above four things? No. This word is still flawed. Add "hand" under the cluster.

"Hands-on" (hands-on practice, not just doing problems, courseware and models)

Is such a person smart?

To improve learning efficiency to the greatest extent, we must first do it-listen carefully in class (this is fundamental), review before doing problems at home, if you can't listen well in class, you can't digest knowledge.

2. There are two main points to learn junior high school mathematics well, which should be highly valued:

To learn math well, one must (do) and the other must (use your head).

Thinking is to learn to observe and analyze problems, learn to think, don't do it as soon as you get the problem, find out what is the connection between the known and unknown imagination, and ask more why.

Hands-on means practicing more and doing more problems, as well as "never leaving your hands" (martial arts) and "never leaving your mouth" (singing)

The students "never leave the topic". These two points should be remembered.

"Use your mind and hands to maximize the efficiency of your brain."

Step 3 do it "three times"

Have you ever heard of "failure is the mother of success" and "repetition is the mother of learning"?

Bacon (English philosopher)-"Knowledge is power"

"Repetition is the mother of learning"

How to repeat it? Let me explain it to you:

"Listen carefully in class, push and think again."

"Watch after class"

"Before the exam"

4. Pay attention to the "four foundations"

Read a textbook well-it is the main basis for teaching and senior high school entrance examination;

Take good notes-it is the crystallization of teachers' years of experience;

Do a good job of cleaning up a problem set-to broaden the knowledge;

Take a class note, and everyone had better prepare a set of wrong questions.

Second, talk about mathematics learning from three aspects: before class, during class and after class.

1. What to do before class, preview. Some students will think that previewing is a waste of time. Class is just listening to the teacher, why spend time previewing? In fact, preview not only does not waste time, but also has many benefits. First of all, preview is an exercise of self-study ability. The teacher can't teach you all the knowledge. A lot of knowledge is acquired by self-study, which requires us to have good self-study ability. Secondly, what you preview is much more impressive than what you hear from the teacher in class.

So how to preview, preview what content? First of all, we should look at textbooks, basic concepts and examples in textbooks, and understand this part of the content. Because this is the foundation, and all changes can not be separated from ancestors, any future changes can not be separated from this foundation. Second, finish the exercises after class on the basis of understanding the basic concepts. Because the only way to test whether you understand the concept is through the topic. The setting of exercises after class is a simple application after understanding the basic concepts. If you don't understand anything in the preview process, you should mark it in the book and pay attention to this part in class; If the content is simple and you can understand it yourself, then listen to the teacher's explanation in class, compare it with yourself, see if your understanding is correct, or see if there are other ideas for solving problems.

2. What to do in class and listen carefully. Listening to lectures is the most important link in learning and the key to mastering knowledge accurately. Listen carefully for ten minutes in class, and watch it for thirty minutes after class. So how to listen carefully and what to listen to in class. First, listen to the class with questions you didn't understand in the preview, concentrate and try to solve the doubts in the class.

Second, for the problems that I think I have understood in the preview, I mainly listen to whether the teacher's explanation is consistent with my own understanding and correct my one-sided understanding or misunderstanding of some knowledge in the preview.

Third, if you don't understand anything in the preview, you should write down the key points in class and ask the teacher in time after class to understand and understand.

Fourth, pay attention to not only listening to the answers to questions, but also listening to the teacher explain the problem-solving ideas of examples and understand the problem-solving ideas. You have learned to do this kind of problem, not just a problem.

Examples are to consolidate mathematical knowledge, and the role of examples is to draw inferences from one another. Someone has done such an experiment:

A teacher takes a junior one student and tests his students every week, publicly telling his students that the exam questions are all examples he talks about in class. The students began to be in an uproar, and 90% of them were confident to get full marks. Only the worst students in the class dare not say so. Soon the preliminary test results came out, with a pass rate of 48% and a perfect score of less than 8%. The second time, things got better. In the first grade, there was a difference of 12.5 points between the math scores of this class and the average scores of math special students in the same grade. Grade two is only 1.5 points worse than the average grade 10 points. After graduating from the third grade, this class is almost the same as the special math class.

Fifth, pay attention to the examples added by teachers in class, which are usually representative. Listen to the teacher's problem-solving ideas, broaden your knowledge and learn to solve such problems by yourself.

3. What should I do after class? Finish the exercises and homework. To learn math well, we must do more problems, but not the tactics of sea. It is impossible to learn math well just by reading without doing or doing less exercises. And blindly doing problems, no matter how to solve the problem, is also difficult to receive results in learning.

Do the questions carefully and independently after full preparation. The so-called full preparation means reviewing the knowledge learned today and the examples added by the teacher, and understanding the knowledge in the textbook before doing exercises. If you still don't understand the textbook knowledge, review the text first and ask your classmates or teachers before doing the exercises until you understand it.

The so-called seriousness means that you should think carefully about every exercise and think clearly about every detail of the problem. Pay attention to form the habit of thinking about problems comprehensively and carefully. Once this good habit is formed, it will be of great benefit to your life. On the other hand, we should calculate carefully and pay attention to the order of the solution expression and the standardization of the solution format. Many students often make careless mistakes in exams, and the root cause will inevitably form careless bad habits. And "carelessness" will bring long-term harm. Once this bad habit is formed, it is very stubborn and difficult to overcome.

The so-called independent homework is to rely on your own ability to complete your homework. Because the purpose of doing the problem is to consolidate what you have learned, and also to test whether your understanding of knowledge is correct, and to cultivate and improve your ability to analyze and solve problems.

Dare to solve problems. When encountering problems, we must carefully consider the conditions and think deeply. When you are at the end of your rope and your ability really can't bear it, it is ok to ask others. Don't give up when you find difficulties. Of course, it takes a long time to do difficult problems. Some students think that it is not cost-effective, so it is better to ask questions to save trouble. This idea is not comprehensive. Actually, you have to calculate two accounts. For example, because it takes a long time to solve a difficult problem, you associate a lot of knowledge and imagine many solutions, all of which fail. It seems that you have gained zero, but in fact you have gained a lot of by-products, and the value of this by-product will be far greater than the value of this topic. Because, because of the urgent need to solve the problem, I associate a lot of knowledge, which happens to be a positive review of this lot of knowledge; You've come up with many ways. Although you can't solve this problem, it is good thinking training and plays an important role in improving your thinking ability. In addition, these methods may be effective in solving other problems. Hilbert, a great mathematician, called the problem of Fermat's Last Theorem "a hen that can lay golden eggs". It is precisely because many mathematicians discovered and created many new fields of mathematics in the failure to conquer Fermat's last theorem, which greatly promoted the development of mathematics.

For the evaluation manual of mathematics: students with difficulties in learning and teaching only need to complete the basic problems, and middle school students can complete the analysis and reflection; Good students should explore and think; Students with extra learning ability can choose a good extra-curricular book, choose some exercises by themselves, consolidate their knowledge, expand their knowledge, pay attention to multiple solutions to one problem as much as possible when doing problems, and cultivate their ability to analyze and solve problems.

I hope you can digest the problems you have done for a period of time (a week or so) and master the methods to solve such problems, so as to draw inferences from others. In practice, I think "doing" is secondary and "thinking" is primary. Mistakes are also the weakest point in our study. Knowing these places and avoiding falling twice in the same place may be more effective than counting ten exercises correctly.

4. Review and summarize. Review is to consolidate and resist forgetting; Summary is to sort out knowledge, discover and master laws, accumulate experience and improve.

After each chapter, we should review the stage in time. Stage review should focus on the key points and difficulties of each section of knowledge, read textbooks, handouts and exercise books, and extract the key points and difficulties of this chapter, especially for those places that are not well understood or not deeply understood, we should focus on review and consolidation. All the questions that you can't do or make mistakes in homework or exams should be completed independently in the stage review to check whether you have mastered these questions. Some students make mistakes many times in a certain kind of questions, or they can't do the questions they didn't do, which is the result of not completing the review task. Difficult knowledge and topics are not only difficult to do, but also easy to forget. Repeated review itself is an effective way to fight forgetting. Stage summary is very necessary, and it should be greatly improved through stage review. There is a famous saying in China: "reading should be from thin to thick, and then from thick to thin." Stage summary is to complete the process from coarse to fine. To sum up, it is necessary to extract the key points and difficulties of each chapter, the relationship between the key points of each section and the key points of this chapter, and make a systematic induction and generalization, so as to accumulate experience in solving problems and improve the ability to analyze and solve problems.

5. Extracurricular self-study and research. The purpose of extracurricular self-study and research is to expand knowledge, broaden horizons, master and accumulate thinking methods and problem-solving methods, and further improve the ability to analyze and solve problems. Read some extracurricular reference books and math magazines around the progress of the textbooks you have learned, and do some fresh or difficult exercises. Extracurricular self-study should be carried out in a planned and controlled way, so as not to affect the study of the above links, not to mention the study of other subjects. In the process of extracurricular self-study, some novel and valuable exercises, some good thinking methods and problem-solving methods are found, which should be recorded for further study and mastery.

Einstein said: "Success = = efforts+correct methods+less empty talk". For students who are eager to succeed, it is easier to try to talk less, but not everyone can find the right way. ..... Learning methods vary from person to person. I hope that everyone will "choose the good and follow it, and change the bad." Make sure you have a set of learning methods that suit you.

Jushi Education pays attention to the growth of every child.