The basic knowledge of junior high school mathematics refers to the concepts, laws, formulas, theorems and other necessary contents in mathematics textbooks and the mathematical thinking methods contained therein, as well as the experience of learning mathematics and solving problems, which are embodied in the following aspects:

1. Correctly understand and master the basic concepts, laws, formulas and theorems learned, and master their internal relations.

For example, the score is meaningless, and the value range of x should be. Some students fill in x=3, which is wrong. Because there is a concept here, that is, the concept of meaningless fraction and a rule for calculating absolute value, only by fully understanding and mastering this concept and a rule can we know that |x|-9=0 and get the correct answer of x = 3. Moreover, because mathematics is a highly coherent subject, correctly grasping the absolute value will lay a good foundation for us to learn quadratic roots in Grade Two and irrational equations in Grade Three. Therefore, if you encounter difficulties in learning something or solving a problem, it is probably because you have not mastered some relevant and previous basic knowledge. Therefore, you should pay attention to leak detection, find problems and solve them in time, and strive to find a problem and solve it in time. Only with a solid foundation will our grades improve.

2. Cultivate mathematical operation ability and develop good study habits.

After every exam, we often hear some students say: I was careless in this exam again. One of the most careless phenomena is the error caused by skipping steps, and it is repetitive. In fact, this is the psychology of quick success with poor study habits and poor mathematical operation skills. You know, every step of a math problem is completed according to certain rules. If a step is ignored in the process of solving a problem, it will happen that the rules of this step are not applied correctly, and then a wrong solution will be produced. Therefore, the improvement of operation ability is fundamentally to understand "arithmetic", not only to know how to calculate, but also to know why, so as to master the direction, method and procedure of operation and complete it step by step in detail, thus forming accurate and fast operation ability. Students should pay attention to the fact that if you have the above-mentioned similar jumping phenomenon, you should correct it in time, otherwise in the long run, you will have a sense of fear and worry about making mistakes before you start solving problems, so the more mistakes you make. Students who feel this way must get out of the misunderstanding quickly, so that the efficiency of learning can increase.

3. Learn some necessary testing methods and cultivate your own thinking of seeking differences.

There is an old saying in China: "One hundred secrets are sparse". Omission is inevitable, and if there are multiple inspection methods, it can be foolproof. So how to master a variety of inspection methods? This requires us to consciously train our divergent thinking in our usual study. If a mathematical problem requires not a calculation result, but a method or way to solve it, then there is not only one method to use, nor is there only one way to solve it, but there are many ways to solve it, so the answers are not necessarily the same but different. This situation belongs to the application of different thinking. For example, divide a square into four equal parts. Students often use these methods when dividing it into four equal small squares or four congruent isosceles right triangles. We should ask ourselves if there is more. You can never be satisfied with finding one or two, you will think you have finished. Actually, there are many ways to do it. Can you find it? This is the thinking of seeking difference. Usually there are many problems. Although he has only one answer, it is very beneficial to the development of our creative thinking if we consider solving him in various ways.

Second, the cultivation of logical thinking ability

In mathematics, the formation of a mathematical concept, the establishment of a mathematical proposition and the solution of a topic usually go through the process of observation, comparison, analysis, synthesis, generalization, abstraction, induction and deduction of concepts, propositions or topics, which all require thinking activities in the mind to correctly explain one's thoughts and opinions. This is the ability of logical thinking. In order to improve their logical thinking ability, students should do the following:

1. Strictly abide by the laws of thinking and develop strict thinking habits.

Strictly abide by the laws of thinking, be rigorous in reasoning, and use reasonable words, which are the core of logical thinking. This first requires us to use concepts, definitions or theorems and formulas accurately to make logical judgments. We often encounter such a situation. When we prove that two angles are equal, there is a method called "equilateral equilateral angle". If we don't notice that its preconditions are all in the same triangle, then we will make mistakes, or make mistakes when we can't solve the problem, and a series of problems will appear, such as stealing propositions, wrong choice of arguments, self-contradiction, circular argument and so on. In order to prevent this phenomenon, we must strictly think about the law, solve problems in strict accordance with the correct way of thinking, be strict with mistakes in learning, and never be careless, and cultivate our own rigor.

2. Pay attention to the process of knowledge acquisition and cultivate the ability of abstract generalization, analysis and synthesis, reasoning and proof.

When teachers explain formulas, theorems and concepts in class, they usually reveal their formation process, but this process is most easily ignored by students. They think: I just need to understand the theorem itself and then use it. I don't need to know how they got it. This idea is wrong. Because the teacher is explaining the formation and occurrence of knowledge, he is explaining the thinking process of a problem and revealing a way of thinking and method to solve the problem, including the ability of abstraction, general analysis, synthesis and reasoning. If we don't pay attention to it, we actually miss an opportunity to learn from it, exercise and develop our logical thinking ability. The above are some math learning methods for students' reference.

The improvement of math scores and the mastery of math methods are inseparable from students' good study habits, so finally we will discuss math study habits together.

Good math study habits include: listening, reading, exploring and doing homework.

Listen. We should grasp the main contradictions and problems in class, think synchronously with the teacher's explanation as much as possible, and take notes when necessary. Every time after class, we should think deeply and summarize, so as to achieve one lesson at a time.

Reading. When reading, you should carefully scrutinize and understand every concept, theorem and law. For example, you should also learn from similar reference books, learn from others, increase your knowledge and develop your thinking.

Explore. We should learn to think, explore some new methods after solving problems, learn to think from different angles, and even change conditions or conclusions to find new problems. After a period of study, we should sort out our own ideas and form our own thinking rules.

Homework. You should review your homework first, think before you start writing, do a class of questions to understand a large area, do your homework carefully and write regularly. Only in this way can you learn math well and step by step.