Teachers who teach junior high schools often say this half jokingly: "The first day is the foundation, and the second day is the key, otherwise the third day will be over!" Junior high school mathematics knowledge is no exception. Junior high school mathematics is a complete system. Among them, the second grade is the most difficult and the third grade has the most test sites. Although there are many knowledge points of mathematics in the first grade, they are relatively simple. Therefore, many students often feel very simple when they first enter junior high school mathematics study, and even feel no difference from primary school, so they don't feel pressured. These students often don't pay enough attention to the mathematics knowledge of the first grade. At the same time, a lot of small problems have accumulated. When students enter the second grade of junior high school and encounter many comprehensive or complex problems, these problems will be quickly highlighted. At this time, students feel that they can't keep up with the teacher's progress and find it more and more difficult to learn mathematics. The fundamental reason is that these students don't pay enough attention to the mathematics knowledge of Grade One and have not laid a solid foundation.

Let me first list the main problems of first-year students in mathematics learning:

1. Can't correct learning attitude, have no interest, even have the psychology of being afraid of mathematics, and lack the intention of active learning.

2. Did not develop good study habits (preview, listen carefully, take notes, summarize, review, etc.). ).

3. In terms of knowledge, the understanding of basic knowledge points such as mathematical definitions and concepts is not accurate enough, and it only stays at the level of a little knowledge, especially the grasp of special circumstances is very vague.

4. Mathematical ability (examination ability, calculation ability, analysis method, mathematical thought, etc.). ) more or less lacking, leading to all kinds of small mistakes and unable to complete the topic completely.

In practice, you can't understand the meaning of the questioner. Simply put, we can't grasp the key to the problem and can't find the correct solution.

6. Usually, the speed of doing questions is slow, and it is impossible to finish the test paper within the specified time.

If these problems are not improved in the first stage of junior high school, it will directly lead to the sharp decline of students' mathematics scores in the polarization stage of junior high school, and even lead to greater obstacles in junior high school learning. On the contrary, if students can lay a good foundation in junior high school learning, then junior high school learning will only increase and deepen in knowledge points, but students can easily adapt to learning habits and methods.

Then, in view of the problems that the above students are prone to, how to help students lay a good foundation in mathematics in Grade One?

I think the following points are worth noting:

1) Correct learning attitude.

Every subject has its own characteristics, and mathematics is no exception. As long as we develop good study habits and master scientific and correct methods, we will certainly learn mathematics well. However, mathematics learning cannot be opportunistic, and there is no shortcut to mathematics learning. It is necessary to understand that ensuring the quantity and quality of problems is the only way to learn mathematics well.

2) Develop good study habits.

Preview before class and listen to the class with questions. Read the book twice: the first time, get a general understanding of the contents of the next lecture or chapter, branches of knowledge, important and difficult points, etc. The second time, read important concepts, properties, judgments, formulas, etc. Think over their internal relations and causality, and mark out what you don't understand, so that you can go to class with questions and ask teachers conveniently.

Listen carefully in class and take notes. Senior one students often feel uncomfortable with the increase of courses and the amount of classroom learning. A large number of students think that there are no notes to remember in mathematics, and it is unreasonable for students who have notes to remember. They think that what the teacher writes on the blackboard is listening carefully and taking notes blindly, rather than listening and thinking, which leads to a decline in the effect of listening to lectures. In the process of listening to lectures, we should pay attention to the introduction and formation of knowledge. Understand the important and difficult points in teaching, especially those you don't understand or have questions in preview; Listen to the tips (breakthroughs) and mathematical thinking methods of the key parts of the topic; Summary after class. When taking notes, you should pay attention to: take notes selectively, mainly recording the main points of knowledge, your own doubts, the contents that are not in the textbook supplemented by the teacher, the ideas for solving problems, the mathematical thinking methods, and the class summary.

Review carefully after class and summarize in time. After class, review what the teacher said, especially the classic examples, analyze, summarize and summarize them, internalize them into your own knowledge system, and improve your cognitive structure.

In addition, study should have overall planning and learn to manage your own time.

3) Study the textbook carefully.

Some students think that the content in the textbook is simple, but the exam is a difficult problem. In fact, this is because students have not really understood the textbook, and the content of the exam is basically the basic concepts and models in the textbook. Therefore, in this important stage of the first grade, it is necessary to master the basic knowledge of mathematical definitions and concepts very accurately, rather than just staying at the level of a little knowledge. For the study of basic concepts and models in textbooks, I think we should pay attention to: focus on understanding the basic concepts and special cases (special cases) of basic models, grasp the essence of definitions and concepts, give comprehensive examples, and clarify concepts and definitions. Concepts and formulas can't be memorized by rote, and they lack the connection with practical topics. Memorizing on the basis of understanding can effectively promote mathematics learning. Remember: understanding and memorizing the basic knowledge of mathematics is the premise of learning mathematics well.

4) Learn to summarize and review.

Reviewing and summarizing is not only a teacher's job, students must learn to do it by themselves. When you can summarize the topics, classify what you have learned and done, understand the basic questions of each knowledge point, and be familiar with the corresponding problem-solving methods of each question, you can truly internalize the knowledge. If you can't solve this problem well and enter the third year of high school, students will find that your grades will fall instead of rising. I am doing repeated problems every day, and many similar problems are being done over and over again, but the problems that need to be solved are not solved. Over time, the problems that cannot be solved will not be solved, and the problems that can be done will be screwed up because of the lack of grasp of the whole mathematical system. Summary is the process of thin reading, and the questions should be done less and less.

5) Establish a "revised version".

Setting wrong questions is a very efficient and targeted learning method, which is mainly used to collect your own mistakes and questions that you can't do. The mistakes that are easy to make may include careless examination, careless calculation, irregular writing format, specious understanding of concepts and formulas, unclear understanding of implied conditions, etc. Questions that can't be done are often because there is no idea, unclear ideas or no breakthrough. For the former kind of wrong questions, we should

First of all, we should think independently, reflect in time, find out the reasons for the mistakes and pay attention to them. For the questions that can't be answered, you should refer to the teacher's explanation or answer, pay attention to their thoughts and ideas, understand their truth and the law of summing up methods, and find relevant exercises to further consolidate. Establishing an error solution book can achieve the effect of making a mistake once and deepening understanding ten times.

6) If you don't understand something, ask questions and discuss it actively.

Einstein said, "It is more important to ask questions than to solve them." When you encounter problems you don't understand, you should actively and timely discuss them with your classmates and ask the teacher for advice. When asking questions, we should not only ask why, but also why, which is very beneficial to establish a good mathematical knowledge system. What I want to say here is that discussion is a very good learning method. After discussing with classmates, you may get different inspirations and learn good methods and skills from each other.

7) Pay attention to actual combat.

At ordinary times, we should ensure the practice time of about 1 hour every day. You can give yourself limited time to do your homework to improve your speed. In the actual exam, we should also consider the completion time of each part to avoid panic, and at the same time pay attention to adjusting our mentality, treating "homework" as an exam and "exam" as homework. Of course, it is also a necessary form of exercise.

The above contents are my personal suggestions on the common problems in mathematics learning of senior one students, hoping to help the students. Finally, I want to say that each student's learning method will be slightly different according to his own situation, and the most effective method that suits him is the best.