Science study focuses on weekdays and is not suitable for surprise review. The most important thing to study on weekdays is to attend class for 45 minutes. Listen attentively and keep your thoughts close to the teacher. At the same time, it should be pointed out that many students tend to ignore the mathematical thinking methods taught by teachers and pay attention to the solution of problems. In fact, thinking methods such as \ "transformation \" and \ "combination of numbers and shapes \" are far more important than solving a problem.

Second, finish the homework with high quality.

The so-called high quality refers to high precision and high speed. When writing homework, I sometimes repeat the same type of questions. At this time, we should consciously examine the speed and accuracy, and we can have a deeper thinking about this kind of problem every time we finish it, such as the content it examines, the mathematical thinking method used, the rules and skills of solving problems, etc. In addition, the thinking questions assigned by the teacher should also be carefully completed. If you don't give up easily, you must carry forward the spirit of "nailing", meditate whenever you have time, and inspiration will always come suddenly. Most importantly, this is an opportunity to challenge yourself. Success will bring self-confidence, which is very important for learning science; Even if you fail, this question will leave a deep impression on you.

Third, think hard and ask more questions.

First of all, for the laws and theorems given by teachers, we should not only know "why", but also know "why", so as to make it clear, which is the best way to understand. Secondly, we should be skeptical about learning any subject, especially science. If you have any questions about the teacher's explanation and the content of the textbook, please feel free to ask questions and discuss with the teacher. In short, thinking and asking questions are the best ways to eliminate hidden dangers in learning.

Fourth, sum up and contrast, and clear up ideas.

(1) summary and comparison of knowledge points. After learning each chapter, you should make a frame diagram of the content of this chapter or go through it in your mind to clarify the relationship between them. Similar and confusing knowledge points should be classified and compared, and sometimes they can be distinguished by association.

(2) Summary and comparison of topics. Students can set up their own question bank. I have two sets of problem sets. One is wrong and the other is accurate. Write down the mistakes in the usual homework and exams selectively, and mark the matters needing attention with a red pen on one side. Just read what is written in red pen before the exam. I also wrote down some extremely clever or difficult problems I saw, and marked the methods and ideas used in this problem with a red pen. After a long time, I can sum up some types of problem-solving rules and write them down in red notes. In the end, they will become your precious wealth and be of great help to your math study.

Fifth, do extracurricular exercises selectively.

Spare time is very precious to us middle school students, so when you do extracurricular exercises, you should be less and better. As long as you do two or three questions every day, your mind will be broadened after a long time.

It is important to learn mathematical methods, but the spirit of studying hard and improving is more important. As long as you persist in your efforts, you are sure to learn math well. Believe in yourself, math will make your wisdom shine more!

The so-called method refers to the application of mathematical methodology in mathematics teaching and education, which is included in the means, ways and behaviors people take to achieve a certain goal.

Rules or patterns of work. Through long-term practice, people have discovered many means, channels or procedures for applying mathematical ideas. The same means, channels or procedures have been used repeatedly for many times, and all of them have achieved the expected purpose, which has become a mathematical method. Mathematical method is a scientific research method with mathematics as a tool, that is, mathematical language is used to express the state, relationship and process of things, and then interpretation, judgment and prediction are formed through deduction, operation and analysis.

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Mathematical methods have the following three basic characteristics: first, they are highly abstract and generalized; The second is accuracy, that is, the rigor of logic and the certainty of conclusion; The third is the universality and operability of application.

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Mathematical method plays an important role in scientific and technological research: first, it provides a concise and accurate formal language; The second is to provide quantitative analysis and calculation methods; Third, it provides a tool for logical reasoning. The development of modern science and technology, especially the development of electronic computers, and the strengthening of the status and role of mathematical methods are exactly complementary.

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Basic mathematical methods commonly used in middle school mathematics can be roughly divided into the following three categories: (1) methods in logic, such as analysis (including reduction to absurdity), synthesis, reduction to absurdity, induction, and exhaustion (requiring classified discussion). These methods should not only follow the basic laws and rules in logic, but also have mathematical characteristics because they are used in mathematics. (2) General methods in mathematics, such as modeling, elimination, reduction, substitution, image method (also known as coordinate method, which is often called image method in algebra and coordinate method in analytic geometry we will learn later), comparison method (mainly referring to the comparison size in mathematics, which is different from multidimensional comparison in logic), scaling method, and vector method and mathematical induction to be studied in the future (and These methods are extremely important and widely used. (3) Special methods in mathematics, such as collocation method, undetermined coefficient method, addition and subtraction (elimination) method, formula method, substitution method (also called intermediate variable method) and decomposition and complement method (including adding auxiliary elements to realize reduction).

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Whether it is natural science, technical science or social science, in order to understand the quality of the studied object more deeply, it is necessary to describe it quantitatively, which requires the help of mathematical methods. For things of different nature and complexity, the requirements and possibilities of using mathematical methods are different. Generally speaking, a science is truly mature only when it can use mathematics. In modern science, the application of mathematics has become an important symbol to measure the development of a science, especially to measure the maturity of its theory. The key to the successful application of mathematical methods in scientific research is to extract a suitable mathematical model for the studied problem, which can not only reflect the essence of the problem, but also simplify the problem and facilitate mathematical derivation. Mathematical method

The establishment of mathematical model is a scientific abstract process of concrete analysis of problems. We should be good at grasping the main contradictions, highlighting the main factors and relationships, and putting aside those secondary factors and relationships. The process of establishing the model is also a process of "simplifying the complex" and "changing the difficult to the easy". Of course, simplification is not unconditional, and reasonable simplification must take into account the allowable error range of practical problems and the preconditions required by the mathematical methods used. For the same problem, different mathematical models can be established. At the same time, through continuous testing and comparison in the research process, the best model is gradually screened out, and it is continuously tested and revised in the application process, and gradually improved. The mathematical model abstracted from a special problem often has certain universality, because a special mathematical model can be developed into a mathematical model that describes similar phenomena. There are two kinds of mathematical models that have been widely used and achieved fruitful results: one is called deterministic model, which uses algebraic equations, differential equations, integral equations, difference equations and other mathematical equations to describe and study various inevitable phenomena, in which the change and development of things follow certain mechanical laws; The other is called stochastic model, which uses probability theory and mathematical statistics to describe and study various probability phenomena. In this model, the development and change of things is a random process, which follows statistical laws and has many possible results. The inevitable and possible phenomena in the objective world are not completely separated. Some things are mainly inevitable phenomena, but when the influence of random factors can not be ignored, it is necessary to introduce random factors into the deterministic model, thus forming mathematical models such as stochastic differential equations. Since the 1970s, it has been found that in some deterministic models, such as some nonlinear equations describing conservative systems or dissipative structures, random factors are not added, but they show "inherent randomness" within a certain parameter range, that is, random behaviors of bifurcation and chaos appear. The mechanism of this phenomenon and its mathematical problems have attracted the attention of mathematicians and scientists and are currently being studied.