How to learn mathematics well

Mathematics is one of the compulsory subjects, so we should study mathematics seriously from the first day of junior high school. So, how can we learn math well? Here are some methods for reference:

First, pay attention to listening in class and review in time after class.

The acceptance of new knowledge and the cultivation of mathematical ability are mainly carried out in the classroom, so we should pay attention to the learning efficiency in the classroom and seek the correct learning methods. In class, you should follow the teacher's ideas closely, actively develop your thinking and predict the following steps, and compare your own problem-solving ideas with what the teacher said. In particular, we should grasp the study of basic knowledge and skills, and review them in time after class without leaving any doubts. First of all, we should recall the knowledge points the teacher said before doing all kinds of exercises, correctly master the reasoning process of various formulas, and try our best to recall them instead of turning over the books immediately if we are not clear. To finish your homework conscientiously and independently, and to be diligent in thinking, in a sense, you should not create a learning style of asking questions if you don't understand. For some problems, it is difficult to solve them for a while because of your unclear thinking, you should calm yourself down and analyze the problems carefully and try to solve them yourself. In each stage of learning, we should sort out and summarize, and combine the points, lines and surfaces of knowledge into a knowledge network and bring it into our own knowledge system.

Second, do more problems properly and develop good habit of solving problems.

If you want to learn math well, it is inevitable to do more questions, and you should be familiar with the problem-solving ideas of various questions. At the beginning, we should start with the basic problems, take the exercises in the textbook as the standard, lay a good foundation repeatedly, and then find some extra-curricular exercises to help broaden our thinking, improve our analytical and problem-solving abilities, and master the general law of solving problems. For some error-prone questions, you can prepare a set of error questions, write your own problem-solving ideas and correct problem-solving processes, and compare them to find out your own mistakes so as to correct them in time. We should develop good problem-solving habits in peacetime. Let your energy be highly concentrated, make your brain excited, think quickly, get into the best state, and use it freely in the exam. Practice has proved that when it comes to the critical moment, your problem-solving habits are no different from your usual practice. If you are casual, careless and careless when solving problems, it is often fully exposed in the big exam, so it is very important to develop good problem-solving habits in peacetime.

Third, adjust the mentality and treat the exam correctly.

First of all, we should focus on three aspects: basic knowledge, basic skills and basic methods, because most of the exams are basic topics. For those difficult and comprehensive topics, as a diversion, we should seriously think about them, try our best to sort them out, and summarize them after finishing the questions. Adjust your mentality, make yourself calm at any time, think in an orderly way, and overcome impetuous emotions. In particular, you should have confidence in yourself and always encourage yourself. No one can beat me down except yourself. No one can beat my pride if you don't beat yourself.

Before the exam, you should be prepared, practice routine questions, and spread your own ideas. Don't go before the exam to improve the speed of solving problems on the premise of ensuring the correct rate. For some easy basic questions, you should have 12 points to grasp and get full points; For some difficult problems, we should also try to score points, and learn to try to score points in the exam to make our level normal or even extraordinary.

It can be seen that if you want to learn mathematics well, you must find a suitable learning method, understand the characteristics of mathematics, and make yourself enter the vast world of mathematics.

How to learn math well

The method of learning math well is not much different from reading other subjects. The process can be divided into six steps:

1. Preview

2. Concentrate on listening

3. Practice after class

4. Test

5. Error detection and reinforcement

6. Recall <

1. preview: before class, browse the content of the unit that the teacher will teach, and pay attention to the part that you don't understand.

2. Listen attentively:

(1) There are many new definitions of terms or new ideas at the beginning of the new course. The teacher's explanation is definitely clearer than the students' reading by themselves. Be sure to listen attentively, and don't be clever and make mistakes.

if the teacher talks about the part you didn't understand in the preview earlier, you should pay special attention.

Some students think that the teacher's explanation is simple, and then they are distracted to do other things, but they don't know that they missed the most wonderful and important sentences, which may be the key to getting wrong answers in future tests.

(2) While listening to the lecture, you should memorize the key points. Definitions, theorems, formulas and other key points should be memorized by heart in class, so that the teacher can understand the essence of the teacher when giving examples.

It will only take a short time to review the lessons taught today when you get home. Get twice the result with half the effort. It's a pity that most students enjoy the teacher's performance easily in class like watching a movie, and they don't remember anything after class. It's a pity to waste a class in vain.

3. After-class exercises:

(1) Sorting out the key points

On the evening of math class, you should sort out the contents taught that day, and you must memorize the definitions, theorems and formulas. Some students think that mathematics focuses on reasoning and doesn't have to memorize anything, so this concept is not correct. Generally speaking, the so-called immortal memorization refers to the immortal memorization method, but the basic definitions, theorems and formulas are our tools for solving problems. If we don't remember these, we will not be able to use them flexibly when solving problems, just like how a doctor can save people in the first place if he doesn't memorize all medical knowledge and medication knowledge. Many students didn't do well in the math exam, that is, they didn't understand the definition clearly and didn't memorize some important theorems and formulas completely.

(2) Practice properly

After finishing the key points, practice properly. Do the examples explained by the teacher in class first, then do the textbook exercises, and spare no effort, and then do the reference books or supplementary questions issued by the teacher. If you can't solve the problem for a while, you can skip it first to avoid wasting time, and then challenge it in your spare time. If you still can't solve it, discuss it with your classmates or teachers.

(3) When practicing, you must do the calculus yourself. Many students often can't go on when they solve the problem in the middle of the exam. The reason is that he looks at it when doing exercises, and many key steps are ignored.

4. Test:

(1) Before the test, the key points within the test scope should be sorted out again, and the important questions specially prompted by the teacher must be paid attention to.

(2) In the exam, the questions you can do must be done correctly. Students who often make mistakes in calculation should try to slow down the calculation speed as much as possible, move items carefully, add, subtract, multiply and divide, and use "mental arithmetic" less.

(3) In the exam, our aim is to get high marks, not to do academic research. Therefore, if we encounter difficult questions, we should skip them first, and then use the remaining time to challenge the problems, so that we can fully show our strength and achieve the most perfect performance.

(4) There are two possible reasons for students who are easily nervous during exams:

A. Lack of confidence due to insufficient preparation. This kind of person should strengthen the preparation before the test.

B. The expectation of the score is too high. In case you can't solve several difficult problems, you can't concentrate, resulting in a lower score. Such people must adjust their mentality and don't expect too much.

5. Error detection and reinforcement:

After the test, no matter whether the score is high or low, you should revise the wrong questions again, and you must find out the mistakes and correct your ideas, so that you can learn the unit better.

6. Recall:

After learning a unit, students should recall the key contents of the whole chapter from beginning to end, paying special attention to the title. Generally speaking, the title of each section is the theme of the section and the most important. Only by focusing on the theme can we fully understand what we are learning.

how to learn mathematics well

Wu Jian of Zhangzhou No.3 Middle School

1. What is mathematics?

Engels said: "The object of pure mathematics is the spatial form and quantitative relationship in the real world." Mathematics includes pure mathematics, applied mathematics and their intersection with other disciplines. It is a knowledge that integrates rigor, logicality, accuracy, creativity and imagination, and it is also a huge intellectual resource of natural science, technical science, social science and management science. Mathematics has its own unique language system-mathematical language, and mathematics has its own unique value judgment standard-unique mathematical epistemology. Mathematics is not only an important tool for studying other natural sciences and social sciences, but also a kind of culture. Mathematics reflects the height of human intelligence development from one aspect. Mathematics has its own beauty, and some people who work in mathematics regard mathematics as art. However, with the continuous development of science, the object of mathematical research has far exceeded the general spatial form and quantitative relationship. The abstraction and application of mathematics have developed greatly to two extremes at the same time. If abstract mathematics is regarded as "root" and applied mathematics as "leaf", then mathematics has become a towering tree in natural science.

We live in the information age. One of its important characteristics is that the application of mathematics permeates all fields, and the relationship between high technology and mathematics is getting closer and closer, resulting in many new disciplines combined with mathematics. With the increasing mathematicization of today's society, some far-sighted scientists have profoundly pointed out: "The competition of high technology in the information age is essentially the competition of mathematics."

second, the application of mathematics

Mathematics is the "queen" and "servant" of science. According to the general understanding, the queen is elegant. What is authoritative and supreme is the spring snow, which only pure mathematics has in science. Simple and clear mathematical theorems, once proved, are eternal truths, extremely beautiful and impeccable. On the other hand, all branches of science and engineering use mathematics extensively to varying degrees and enjoy its contribution. At this time, mathematical science is a servant, and the word servant in the English book title means "something for people to use, a useful service tool" in English. This formulation skillfully explains the position and role of mathematics in the whole science, and it is very important to correctly understand and understand the importance of mathematical science for the development of science, economy and education.

1. Mathematics is the foundation of other disciplines

Whether it is physics, chemistry, biology, emerging disciplines such as information, economy and management, or even the study of humanities, mathematical methods are necessary basic tools. In the past, people thought that mathematics was the common language of science and engineering. If you want to describe your findings and achievements to everyone, then you must master mathematics and apply mathematics. Now, from the weather forecast to the sewage treatment, and even the cycle and quantity of supermarket purchases, the planning and design of public transportation lines must use mathematics. Mathematical modeling and related calculations are becoming the key to engineering design. Even in the fields of medicine and biology, where mathematics was rarely used in the past, there are many applications. For example, in the diagnosis of cardiovascular diseases, the basic equations of fluid mechanics are used, and the possible results in various situations can be simulated by computer before surgery as a diagnostic reference; Neurology uses mathematics to analyze various rhythms, etc. Mathematical knowledge is also widely used in the study of biological DNA, and its double helix structure is a problem related to geometry.

2. The application of mathematics in other fields

The greatest scientific achievement in the 2th century is Einstein's special and general relativity, but without Riemann geometry invented by Riemann in 1854 and the invariant theory developed by mathematicians such as Gloria, West Leviste and Nott, Einstein's general relativity and gravity theory could not have such a perfect mathematical expression. Einstein himself said this more than once.

Newton, Leibniz, Euler, and Gauss have systematically studied the skills of calculation-numerical analysis and the problem of operation speed (computer manufacturing), and they have always been an important part of mathematics. Mathematicians have played a decisive role in the development of modern computers. Mathematicians such as Leibniz and Babbage have all developed computers. In 193s, the study of symbolic logic was very active. Church, Godel, Post and other scholars studied formal languages. After their research work and Turing's research work; The mathematical concept of computability is formed. Around 1935, Turing established an abstract model of general computer. These achievements provided von Neumann and his colleagues with computers with stored programs and a theoretical framework for the invention of formal programs.

On the surface, mathematics is not closely related to humanities and social sciences. After all, there is no need for a writer to rack his brains to prove Goldbach's conjecture. A painter doesn't need to know calculus. In fact, humanities can't be separated from mathematics. As a rational basis and representative mathematical thinking method, mathematical spirit has been injected into many fields such as literature, art, politics, economy, ethics and religion.

The influence of mathematics on social science and humanities is not very intuitive formulas and theorems, but abstract mathematical methods and mathematical ideas, the most prominent of which is deductive method, that is, deductive reasoning, deductive proof, which is to deduce new propositions from recognized facts. To admit these facts as a prerequisite, we must accept the deduced new propositions. Philosophically, the study of some eternal topics, such as life and death, can not be studied by simple induction (trial and error) and analogical reasoning, but only by mathematical method-deductive reasoning. There are many similar examples. Mathematics has influenced the direction and content of many philosophical thoughts to a certain extent, which can be proved by Pythagorean philosophy in ancient Greece, rationalism and empiricism in modern times and logical positivism and analytical philosophy in modern times.

Mathematics also has a certain influence on music, painting, linguistic research and literary criticism theory.

In music, since the fact that there is a close relationship between the chord length and the tone of musical instruments was discovered, this research has never stopped, and the study of the golden section in aesthetics is also an indispensable topic. Before the Renaissance, painting was regarded as a lowly occupation like workshop workers. After the Renaissance, painters began to use mathematical principles such as plane geometry, three views, plane rectangular coordinate system and so on to guide painting art. Leonardo da Vinci's perspective theory is a prominent example (with the help of plane geometry knowledge, the visual effect pursued in painting is achieved-the distant things get closer and the small things get bigger). Since then, painting has entered the hall of human art.

From the practical application, many social sciences and humanities are also inseparable from mathematics.

when studying history and politics, the most commonly used method is statistics, which was called political mathematics at the beginning of its appearance, showing its status.

Archaeology, a branch of history, is inseparable from mathematics, such as trigonometric calculation, exponential function and logarithmic function. Archaeology is inseparable from physical and chemical methods, but these two disciplines will be useless without mathematics as a tool.

A lot of high school mathematics knowledge, such as set, mapping, addition principle, multiplication principle, etc.