How to learn math well

Mathematics is one of the compulsory subjects, so we should study it seriously from the first day of junior high school. So, how can we learn math well? Introduce several methods for your reference:

First, pay attention to the lecture in class and review it 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 correct learning methods. In class, you should keep up with the teacher's ideas, actively explore thinking, predict the next steps, and compare your own problem-solving ideas with what the teacher said. In particular, we should do a good job in learning basic knowledge and skills, and review them in time after class, leaving no doubt. First of all, we should recall the knowledge points the teacher said before doing various exercises, and correctly master the reasoning process of various formulas. If we are not clear, we should try our best to recall them instead of turning to the book immediately. In a sense, you should not create a learning way of asking questions if you don't understand. For some problems, because of their unclear thinking, it is difficult to solve them at the moment. Let yourself calm down and analyze the problems carefully and try to solve them by yourself. At every learning stage, 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 questions appropriately and develop good problem-solving habits.

If you want to learn math well, it is inevitable to do more problems, 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 extracurricular exercises to help broaden our thinking, improve our ability to analyze and solve problems, and master the general rules of solving problems. For some error-prone topics, you can prepare a set of wrong 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 at ordinary times. Let your energy be highly concentrated, make your brain excited, think quickly, enter the best state, and use it freely in the exam. Practice has proved that at the critical moment, your problem-solving habit is no different from your usual practice. If you are careless and careless when solving problems, it is often exposed in the big exam, so it is very important to develop good problem-solving habits at ordinary times.

Third, adjust the mentality and treat the exam correctly.

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

Be prepared before the exam, practice routine questions, spread your own ideas, and avoid improving the speed of solving problems on the premise of ensuring the correct rate before the exam. For some easy basic questions, you should have a 12 grasp and get full marks; For some difficult questions, you should also try to score, learn to score hard in the exam, and make your 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 let yourself enter the vast world of mathematics.

How to learn math well

There is not much difference between learning mathematics well and reading other subjects. The process can be divided into six steps:

1. Preview

2. Pay attention to the class

homework

test

5. Error detection and reinforcement

Think back

The following provides the precautions for each step for students' reference.

1. Preview: Before class, browse the contents of the unit that the teacher will teach, and pay attention to the parts that you don't understand.

2. Listen carefully:

(1) There are many new definitions of terms or new ideas at the beginning of the new curriculum. The teacher's explanation must be clearer than the students' own reading. Be sure to listen attentively, don't be smart and make mistakes.

If the teacher says what you didn't understand in the preview, 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 miss the most wonderful and important words, which may be the key to getting the wrong answer in the future exam.

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

After returning home, it only takes a short time to review the lessons learned today. Get twice the result with half the effort. Unfortunately, most students enjoy the teacher's performance as easily as watching a movie in class, and they don't remember anything after class. It's a pity to waste a class in vain.

3. After-class exercises:

(1) finishing points

In the evening of math class, we should sort out the contents taught that day, and memorize definitions, theorems and formulas. Some students think that mathematics focuses on reasoning and does not need to recite anything. This concept is incorrect. Generally speaking, the so-called immortal rote learning refers to the immortal rote learning method, but the basic definitions, theorems and formulas are our tools to solve problems. If we don't remember these things, we can't use them flexibly when solving problems, just as a doctor can't save people in the first place if he doesn't memorize all medical knowledge and medication knowledge. Many students didn't do well in math test, that is, they didn't understand the definition clearly and didn't recite some important theorems and formulas completely.

(2) Proper exercise

After you finish the key points, you should practice properly. In class, do the examples explained by the teacher first, then do the textbook exercises, spare no effort, and then do the reference books or supplementary questions issued by the teacher. If you can't solve it 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 calculus by yourself. Many students often can't go on when they solve problems in the middle of the exam. The reason is that he watches while doing exercises, and many key steps are ignored.

4. Test:

(1) Before the exam, it is necessary to sort out the key points within the scope of the exam, and pay attention to the important questions specially prompted by the teacher.

(2) When taking an exam, you must do the right questions. Students who often make calculation mistakes should try to slow down the calculation speed, carefully move items and add, subtract, multiply and divide, and use less "mental arithmetic".

(3) During the exam, our purpose is to get high marks, not to do academic research. So if you encounter a difficult topic, skip it first, and then use the rest of the time to challenge the problem, so as to fully show your strength and achieve the most perfect performance.

(4) There are two possible reasons for nervous students during the exam:

A. insufficient preparation leads to lack of confidence. Such people should strengthen their preparation before the exam.

B.the expectation of the score is too high. If you encounter several difficult problems and can't solve them, you won't be able to 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 exam, no matter how high or low the score is, you must revise the wrong questions again, and you must find out the mistakes and correct your thinking, so that you can learn the unit better.

6. Memories:

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 math well

Wu Jian Zhangzhou No.3 Middle School

First, 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 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 learning other natural and social sciences, but also a kind of culture. Mathematics reflects the height of human intelligence development from one side. Mathematics has its own beauty, and some people who work in mathematics regard mathematics as art, but with the continuous development of science, the object of mathematics research has gone far beyond the general spatial form and quantitative relationship. The abstraction and application of mathematics develop to two extremes at the same time. If abstract mathematics is regarded as "root" and applied mathematics as "leaf", then mathematics will become a towering tree in natural science.

The age we live in is 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 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. The authoritative and supreme is Chun Xue, which is only found in pure mathematics 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 widely use mathematics to varying degrees and enjoy its contribution. At this time, mathematical science is a servant. The word servant in the English title means "something for people, 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 to the development of science, economy and education.

1, mathematics is the foundation of other disciplines.

Whether it is physics, chemistry, biology, information, economy, management and other emerging disciplines or even humanities, mathematical methods are essential basic tools. People used to think 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 and apply mathematics. Now, from weather forecast to sewage treatment, even the cycle and quantity of supermarket purchases, the planning and design of bus lines must use mathematics. Mathematical modeling and related calculation are becoming the key to engineering design. Even in the medical and biological fields 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 to simulate the possible results in various situations by computer before operation 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 20th century is Einstein's special and general relativity, but Einstein's general relativity and gravity theory could not have such a perfect mathematical expression without Riemann geometry invented by Riemann in 1854 and invariant theory developed by mathematicians such as Gloria, West Leviste and Nott. Einstein himself said this more than once.

Newton, Leibniz, Euler and Gauss have all 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 developed computers. In 1930s, the study of symbolic logic was very active. Scholars such as Church, Godel and Persia study formal languages. After their research work and Turing's research work; The mathematical concept of computability is formed. 1935, Turing established the abstract model of general computer. These achievements provided von Neumann and his colleagues with computers with stored programs, and provided a theoretical framework for the invention of formal programs.

On the surface, the relationship between mathematics and humanities and social sciences is not close. After all, writers don't need to rack their brains to prove Goldbach's conjecture, and painters don't need to know calculus. In fact, the humanities are inseparable 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 ideas. The most prominent one is deductive method, that is, deductive reasoning and deductive proof, that is, new propositions are derived from recognized facts, and on the premise of acknowledging these facts, new propositions derived must be accepted. Philosophically, some eternal topics, such as life and death, cannot 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 string length and musical instrument timbre was discovered, the research in this field has never stopped, and the golden section research in aesthetics is also an indispensable topic. Before the Renaissance, painting was considered as a lowly occupation like a workshop worker. After the Renaissance, painters began to use mathematical principles such as plane geometry, three views and plane rectangular coordinate system to guide painting art, and 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 palace 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 are useless without the tool of mathematics.

A lot of high school mathematics knowledge, such as set, mapping, addition principle, multiplication principle, etc. It is often used in daily work and study, while problems such as probability analysis, extreme value and function derivation are not so common in people's daily life, but they play a decisive role in modern economic development.

For example, probability analysis is also a basic subject of applied mathematics. It can describe the net cash flow and economic effect index of the scheme by studying the probability distribution of various uncertain factors in different ranges and their influence on the economic effect of the scheme, so as to make a more accurate judgment on the risk of the scheme. Therefore, in practical work, if we can give various possible states and their occurrence probabilities of uncertain factors that affect the cash flow of the scheme during its life cycle through statistical analysis, then we can calculate the net present value, expected value and variance of the scheme by combining different states of various factors and finding out all possible net cash flow sequences and their occurrence probabilities.

In order to meet the needs of rapid economic development, the teaching of function content in senior high school mathematics should be strengthened accordingly, and more contents such as probability statistics, linear programming and mathematical model should be added.

(Continued from issue 75)

3. The purpose of learning mathematics

As a basic subject, you don't have to be a mathematician to learn mathematics. It is more important to cultivate people's mathematical concepts and ideas and their ability to solve mathematical problems. The importance of mathematics is not only reflected in the application of mathematical knowledge, but also in the way of thinking of mathematics. It is beneficial to cultivate people's thinking, innovation, analysis, calculation, induction and reasoning abilities. After entering the society, students may rarely use a formula and theorem in mathematics directly, but the thinking method and spirit of mathematics will benefit him for life.

The way of thinking in mathematics is very important. Anyway. Mathematics provides a way to organize and construct knowledge. Once mathematics is used in technology, it can produce systematic, reproducible and teachable knowledge. Analysis, design, modeling, simulation and application will become possible and become efficient and structured activities. That is to say, it can be transformed into productive forces. However, 50 years ago, although mathematics directly provided some tools for engineering technology, it was basically indirect. First, promote the development of other sciences, and then these sciences provide the basis of engineering principles and design. Now, mathematics and engineering interact directly on a larger scale and at a deeper level, which greatly promotes the development of mathematics and engineering science and the progress of technology.

One of the most important scientific and technological advances in the second half of the 20th century? It is the rapid development of computer, information and network technology. As far as the computing speed of the computer is concerned, the computing speed of the first computer, the electronic mathematical integration computer, publicly displayed in 1946 is 5000 times per second. Now it has reached 654.38+00 billion operator operations per second, and experts estimate that it will reach 1 trillion operations by 2065.438+00. As you can imagine, what computers can do now is nothing compared with 50 years ago. Many mathematical models have been produced to describe and study various practical problems. Some can be solved, and some can solve problems to varying degrees. However, if it can't be worked out at that time, or it can't be worked out in time, the problem will not be solved. At present, technical indicators such as calculation speed are far ahead in a sense. Mathematical modeling and its accompanying calculation are becoming the key tools in engineering design. Scientists rely more and more on calculation methods. In addition, we must have enough experience in choosing the correct mathematical and calculation methods and the accuracy and reliability of the interpretation results. What we see is that mathematics and computer technology are widely used in all walks of life to solve problems through mathematical modeling, simulation and other means, and the methods and achievements of solving similar problems are made into software (they are even quite stupid) for sale. What people see is the great development of mathematics application. More precisely, the head of the Mathematics Department of the American Science Foundation said in his comments that mathematical science has become the first of the five innovative projects. "The driving force behind this major innovation project is the mathematicization of all scientific and engineering fields." Of course, there are different understandings. Some people think that you don't need to know a lot of mathematics, as long as you can use software. Some people think that there is no need to develop basic mathematics now, and only through mathematical modeling calculation and physical intuition can we solve the problem. In particular, some people think that students nowadays don't need so much math. This is really a great misunderstanding.

Third, how to improve middle school math scores.

1, cultivate interest and learn with curiosity.

Learn math and love math. Mathematics is beautiful, its ontology is simple and clear now, and it is a kind of rational beauty and abstract beauty. Mathematics is like a garden. You can't see its beauty without entering the door, but once you enter it, you will find it really beautiful. Many mathematicians put their interest in the primary position of learning mathematics well. Secondly, curiosity, learning mathematics should have ideas, dare to guess and learn mathematics with curiosity. Find pleasure and a sense of accomplishment from the process of solving problems. As long as curiosity and thirst for knowledge become the desire to solve problems, we can consciously improve our ability to solve problems by using mathematical knowledge. Only when you are full of fun in learning mathematics can you study and study mathematics more consciously.

2. Read the book carefully and understand the mathematical language.

It is a common problem for middle school students not to like math classes. Mathematics textbooks are written in mathematics language, including written language, symbolic language and graphic language. Its language is concise, logical, rich in connotation and profound in meaning, so reading a math textbook must not be fleeting.

Mathematical concepts, definitions, theorems, etc. They are all expressed in written language, so be sure to pay attention when reading. There are five essentials to preview: ① draw the key points with wavy lines; ② Labeling formulas and conclusions; 3 Draw a question mark with a pencil where you don't understand and have questions; (4) Write the answers to simple exercises and the key points of solving problems at the back; ⑤ If there is more than one condition in the definition and theorem, the conditions should be numbered.

Symbolic language is rich in connotation, so we should write, argue and remember clearly. When reading symbolic language, we should tell its meaning and distinguish its characteristics.

Graphic language can not only reflect the relative position of elements, but also directly reflect the quantitative relationship. Therefore, when watching geometric figures, we should understand the hidden internal relations and quantitative relations between graphic elements; While looking at the image, we should glimpse the essence of the function from its shape.

If reading math books before and after class can meet the above requirements, learning math is an introduction; If we form a good reading habit from this, we can improve our grades just around the corner.

3. Listen carefully and master the thinking method.

Listen attentively and think positively with the teacher's explanation. Do you understand the seemingly understandable concept in the preview? Has the mystery been solved? The teacher's oral insights, supplementary examples and wonderful answers should be recorded quickly. Writing a good speech will not only leave valuable information, but also help you concentrate.

In class, you should constantly doubt and question, and dare to ask and answer questions. Think about whether the teacher's explanation is complete and correct, and whether the answer is rigorous and flawless. If you understand the example of blackboard writing, you should come up with a new solution; When in doubt, ask questions boldly. Contending to answer questions is by no means "graphic expression", but to elaborate one's own views and improve one's oral expression ability. Even if your answer is wrong, it is easy to book a certificate after exposing the problem. The most taboo in class is to follow blindly, go with the flow, follow the trend, and not pretend to understand.

4. Learn independently and learn to summarize.

To develop the good habit of autonomous learning, we must do the following:

(1) Finish your homework on time and consolidate your knowledge. Only by finishing homework on time can we consolidate our knowledge and minimize forgetting. In the process of completing homework, it will increase the repetition rate of knowledge, promote one's thinking ability and give play to the creativity of solving problems.

Students who study well should also pay attention to the cleaning and collection of homework, because this is not only a treasure of their own labor achievements, but also a good review material.

(2) Review lessons in time to form a knowledge network. Chapter review, unit review and exam review are indispensable parts in mathematics learning, which have the function of connecting the past with the future. When reviewing, we should sum up knowledge and methods according to a certain system to form a "latitude and longitude network" of mathematics. The "essence" here refers to the knowledge of each branch of mathematics; "Weft" refers to the application of the same mathematical method in different branches. If you want to learn mathematics well, you must weave the "latitude and longitude net" of mathematics well.

③ Attention should be paid to the standardization of writing. Mathematics is a highly specialized subject, which has strict requirements on the process of expression and narration and the rules of symbol use. Therefore, when doing exercises, homework and exams, writing should be standardized.

(4) Apply what you have learned and keep on pioneering and innovating. Mathematics has a strong correlation, and there is no insurmountable gap between old and new knowledge. Therefore, learning from books and associating can not only improve students' interest in learning, but also cultivate their creative thinking ability.

Paying attention to the above methods can not only consolidate the original knowledge, but also expand our own knowledge field and communicate the internal relations between mathematical knowledge. With good study habits, you will learn math well.