Mainly refers to reading math textbooks carefully. Many students have not developed this habit and regard textbooks as exercise books; Some students can't read, which is one of the main reasons why everyone can't learn math well. Generally speaking, reading can be divided into the following three levels:

Preview reading before class. When previewing the text, you should prepare a piece of paper and a pen, write down the key words, questions and problems that need to be considered in the textbook, and simply repeat the definitions, axioms, formulas and laws on the paper. Key knowledge can be approved, marked, circled and marked in textbooks. Doing so not only helps us to understand the text, but also helps us to concentrate on listening in class.

2. Read books in class. When previewing, we only have a general understanding of the contents of the textbooks to be learned, and not all of them have been thoroughly understood and digested. Therefore, it is necessary to read the text further in combination with the marks and comments made in the preview and the teacher's teaching, so as to grasp the key points and solve the difficult problems in the preview.

3. Review reading after class. After-class review is an extension of classroom learning, which can not only solve the unresolved problems in preview and classroom, but also systematize knowledge, deepen and consolidate the understanding and memory of classroom learning content. After a class, you must read the textbook first, and then do your homework; After learning a unit, you should read the textbook comprehensively, connect the content of this unit before and after, summarize it comprehensively, write a summary of knowledge, and check for missing parts.

Second, think more.

It mainly refers to forming the habit of thinking and learning the method of thinking. Independent thinking is an essential ability to learn mathematics.

In terms of lectures:

The relationship between "seeing", "listening", "thinking" and "remembering" should be properly handled in class.

"Look" means paying attention to observation in class, observing the process and content of the teacher's blackboard writing, and understanding what the teacher said.

"Listening" means directly accepting knowledge with the senses. In the process of listening, make it clear: (1) Listen to the learning purpose and learning requirements of each class; (2) Listen to the introduction of new knowledge and the formation process of knowledge; (3) Understand the teacher's analysis of the key points and difficulties of the new lesson (especially the problems in preview); (4) Listen to the reflection of problem-solving ideas and mathematical thinking methods;

"Thinking" means thinking about problems. Without thinking, students can't play the main role. The ancients said, "Learning without thinking is useless." Students are the masters of learning. In class, students should not only give explanations by teachers, but also think often. In the guidance of thinking methods, students should be made clear: (1) think more, think diligently and think with listening; (2) Think deeply, that is, trace back to the source, and be good at asking questions boldly, such as: Why did the teacher say this in this class? What is this road called? Wait; (3) Good thinking refers to association, conjecture and induction through listening and observation; For example: 23 * 27 = 62138 * 32 =121646 * 44 = 202473 * 77 = 5821What are the calculation rules of these numbers? How should I calculate it? How to define the law? How to verify? (4) Establish dialectical consciousness and learn to reflect. Such as: 73*33=2409, what is the law? It can be said that "listening" is the basis of "thinking", and "thinking" is a deep grasp of "listening" and the core and essential content of learning methods. Only when you think can you learn.

"Taking notes" means taking class notes. Generally, senior one students don't take good notes. They usually copy what the teacher wrote on the blackboard, and often use "notes" instead of "listening" and "thinking". Although some notes are well written, they are of little use. Therefore, when taking notes, you should: (1) take notes to obey the lecture, combine with the teaching materials, and grasp the recording opportunity; (2) Remember the main points, questions, mistakes, ideas and methods of solving problems, and what the teacher added; (3) Remember to summarize and think after class. Make it clear that "remembering" serves "listening" and "thinking". Taking notes helps to simplify, deepen and systematize knowledge. When studying, students should think while listening (class), reading (book) and doing (topic). Through their own positive thinking, they can deeply understand mathematical knowledge, summarize mathematical laws and flexibly solve mathematical problems, so as to turn what teachers say and what they write in textbooks into their own knowledge.

Third, do more.

Think and summarize while doing, and deepen the understanding of knowledge through practice. There are many advantages of doing homework, but if you blindly do homework, take shortcuts and copy homework, these benefits will disappear. So, how to do homework more scientifically?

(1) Review before you do your homework.

When many students do their homework, they usually pick up the topic and do it. Once they encounter difficulties, they turn to check their notes. This is a bad habit. The first step in doing homework should be to review the relevant knowledge first. When reviewing, you can take the way of "watching movies", search for the knowledge that the teacher explained in class in your mind, and try to recall what you have learned. If you really can't remember, then open your textbooks or notes to see the comparison, and review what you have learned in this way before doing your homework.

(2) Carefully examine the questions.

Examining a question is to analyze and understand the meaning of the question, find out the known conditions and unknown conditions in the question, and ask to understand the question and its relationship, so as to form and maintain a clear impression on the question in your mind. Many students often ignore the examination of questions when doing their homework, and take a casual attitude towards the examination of questions. Try to solve the problem, guess at random and try blindly before understanding the meaning of the problem and analyzing the relationship between the conditions and the problem. Although some students can examine the questions, they are not careful enough, and their observation and analysis of the questions are not comprehensive and in-depth, thus ignoring the implied but important conditions. Some students' impression of the topic is not clear enough when reviewing the topic, and the result becomes more vague or even forgotten in the process of solving the problem, so that they don't know how to continue. So we must learn to examine the questions carefully. When examining a question, we should first read through the whole question and relate the meaning of the whole question. If you don't have a clear impression after reading it once, you can read it several times. Secondly, we should pay attention to the specific language in the topic and explore the implied conditions. For example, the words "increase" and "increase to" in the title have completely different meanings, so we should distinguish them carefully to avoid mistakes due to misunderstanding.

(3) Do the problem independently

On the basis of examining the questions, we should use our hands and brains to finish our homework independently. When encountering difficulties, don't rush to ask teachers and classmates, think more about yourself and try to overcome the difficulties through your own efforts. Never deceive yourself and copy other people's homework. If you can't solve the problem after thinking hard for a long time, ask a teacher or classmate. After getting advice, we should seriously think about the crux and turn it into our own knowledge.

(4) Check and modify

After you finish the problem, you should read it carefully from beginning to end to check whether the steps and ideas of solving the problem are correct and whether there are any mistakes in some places. Correct problems in time when they are found. Homework is not finished until it is checked and revised.

Fourth, review the consolidation methods after class.

(1) Do more problems appropriately and develop good problem-solving habits.

To learn math well, it is necessary to do a certain amount of problems. First of all, we should start with the basic problems, practice repeatedly according to the exercises in the textbook, lay a good foundation, and then find some extracurricular exercises to help us develop our ideas, improve our ability to analyze and solve problems, master the general problem-solving rules, and be familiar with various types of problem-solving ideas. For some error-prone topics, you can prepare a set of wrong questions, write your own wrong thinking and correct problem-solving process, and compare them together to find out your own mistakes so as to correct them in time. We should develop good problem-solving habits at ordinary times. Let your energy be highly concentrated, your thinking be agile, you can get into the best state and use it freely in the exam. Practice has proved that at the critical moment, your problem-solving habit is no different from your usual practice. If you are careless and careless when solving problems, it will often be exposed in the big exam, so it is very important to develop good problem-solving habits at ordinary times.

(2) Carefully excavate concepts and formulas.

Many students pay insufficient attention to concepts and formulas. This problem is reflected in three aspects: first, the understanding of the concept only stays on the surface of the text, and the special situation of the concept is not paid enough attention. For example, in the concept of monomial (the algebraic expression of the product of numbers and letters is a monomial), many students ignore that "a single letter or number is also a monomial". Second, concepts and formulas are blindly memorized and have nothing to do with practical topics. The knowledge learned in this way can't be well connected with solving problems. Third, some students do not pay attention to the memory of mathematical formulas. Memory is the basis of understanding. If you can't memorize the formula, how can you skillfully use it in the topic?

My advice to you is: be more careful (starting from observing special cases), go deeper (knowing the common test sites in the topic), and be more skilled (no matter what it looks like, we can use it freely).

(3) Summarize similar topics.

When you can summarize the topics, classify the topics you have done, know which types of questions you can do, master the common methods of solving problems, and which types of questions you can't do, you will really master the tricks of this subject and truly "let it change, I will never move." If this problem is not solved well, after entering the second and third grades, students will find that some students do problems every day, but their grades will fall instead of rising. The reason is that they do repetitive work every day, and many similar problems are repeated, but they can't concentrate on solving the problems that need to be solved. Over time, the problems that can't be solved have not been solved, and the problems that can be solved have also been messed up because of the lack of overall grasp of mathematics.

My advice to you is that "summary" is the best way to do fewer and fewer problems.

(4) Collect your typical mistakes and solve the problems that you can't solve.

The most difficult thing for students is their own mistakes and difficulties. But this is precisely the problem that needs to be solved most. There are two important purposes for students to do problems: First, to practice the knowledge and skills they have learned in practical problems. The other is to find out your own shortcomings and make up for them. This deficiency also includes two aspects, mistakes that are easy to make and contents that are completely unknown. However, the reality is that students only pursue the number of questions and deal with their homework hastily, rather than solving problems, let alone collecting mistakes. We suggest that you collect your typical mistakes and problems that you can't do, because once you do, you will find that you thought you had many small problems before, but now you find this one is recurring; You thought you didn't understand many problems before, but now you find that these key points have not been solved.

My advice to you is: doing problems is like digging gold mines. Every wrong question is a gold mine. Only by digging and refining can we gain something.

In short, learning methods are flexible and varied, and vary from person to person. Being able to constantly improve your learning methods is a manifestation of your continuous improvement in learning ability. Xiaodele