Mathematics is an important subject in middle school, but many students often complain that high school mathematics is useless in daily life. But mathematics, as the foundation of science and engineering, can cultivate and improve people's logical reasoning ability and strengthen people's rational thinking. The real purpose of learning mathematics is not embodied in exam-oriented education, but in mental thinking.

Second, how to learn math well?

When learning mathematics, we should learn how to master mathematical knowledge, grasp mathematical skills and develop mathematical ability. How to cultivate good mathematical psychological quality, from mastering mathematical learning methods to forming comprehensive learning ability?

(A) to lay a solid foundation in mathematics

The basic knowledge of mathematics in senior high school 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: What is the maximum value of a function? If you are not familiar with the definition, you will often be confused with the demarcation of functions (required mathematics in senior high school 1 Chapter 2 Monotonicity and maximum value of functions, demarcation is a term appearing in universities, which is very similar to maximum value); What is the zero point of a function? Is the zero point the coordinate of a point? (High School Mathematics Required 1 Chapter III Functions and Equations) Many students think that the zero point is the coordinate of a point because they are unfamiliar with it. Because mathematics is a highly coherent subject, mastering the properties of functions correctly will lay a good foundation for learning trigonometric functions, functions and derivatives well. 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. Consolidate and strengthen mathematical operation ability, and develop good study habits. In high school mathematics, many questions mainly examine the ability of calculation. Poor computing ability is reflected in two aspects: (1) carelessness: mistakes caused by the formation of thinking habits, mistakes caused by skipping steps, mistakes caused by being superior to others, etc. (2) Negligence in calculation: there are too few calculations at ordinary times, which leads to difficulties in calculation, slow speed and insufficient time. This is actually a bad study habit and math skills. As long as these shortcomings are corrected, I believe that mathematics will definitely get better.

(B) cultivate the ability of logical thinking

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. These processes all require thinking activities in the mind and correctly explain one's own thoughts and viewpoints, which is the ability of logical thinking. In order to improve their logical thinking ability, we should do the following:

1. Strictly abide by the laws of thinking and develop strict thinking habits. Strictly observing the laws of thinking, rigorous reasoning and well-founded words are the core of logical thinking. This first requires us to use concepts, definitions or theorems and formulas accurately and make logical judgments. In the usual study, we should strictly follow the laws of thinking, solve problems in strict accordance with the correct way of thinking, be strict with mistakes in learning, and never be careless, and cultivate our rigorous and realistic thinking habits.

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, which is most easily overlooked by students. Many students think that as long as this theorem can be used, there is no need to know how it came about. 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 you don't pay attention to it, you will actually lose an opportunity to learn from it, exercise and develop your logical thinking ability.

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, when calculating the permutation and combination, you can directly calculate or get the total result, and then remove the unqualified result, that is, the indirect method; Binding, insertion, etc. can be used. Actually, there are many other ways. 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.

Fourth, cultivate good math habits.

The improvement of math scores and the mastery of math methods are inseparable from students' good study habits, so let's discuss math study habits at last.

Good math study habits include practicing more and thinking more.

Practice more: the knowledge of mathematics is constantly improved and perfected in practice. Let them be familiar with all kinds of knowledge points and the relationship between knowledge points. Practice makes perfect, which will speed up the problem solving and save time.

Think more: in the process of practice, we should think more about the problem and why. After the problem is solved, we should explore some new methods, learn to think from different angles, and even change conditions or conclusions to find new problems. After a period of study, you should sort out your thoughts and form your own thinking rules.

The usual exercises and exams are just to find out the defects and deficiencies, to practice and think more from them, and to constantly improve and improve in failure. Perseverance, I believe that the college entrance examination can get high marks.