It's not necessarily a paper. Clean yourself up.

How to learn math well

First, the principle of learning mathematics

Mathematics is a highly systematic and closely related subject. As far as teaching materials are concerned, the previous content is often the necessary basis for later learning. If you don't learn well in the front, it will definitely affect the learning of knowledge in the back. Therefore, learning mathematics must follow the principle of starting from the foundation, step by step and gradually expanding.

Second, the method of learning mathematics

When learning mathematics, you must think more and practice more, and use your hands and brains. Common methods are

1, summarized in time to make knowledge networked.

Mathematics is rich in content. At every stage of learning, we should summarize and sort out the knowledge and methods we have learned in time, make clear the backbone of knowledge and its connection with related knowledge, and make it form a clear network, so as to understand the application of memory.

2. Transfer deduction method

Mathematics is full of reasoning and calculus from beginning to end. When learning mathematics, we must pay attention to reasoning. "It's better to wear it with your hands than with your eyes for a thousand times." The teacher has deduced reasoning and calculus from books, so he should do it himself. This is conducive to digesting and absorbing knowledge, and at the same time, we should think about whether we can draw any new conclusions from the existing deduction process and results and whether we can adopt other deduction methods.

3. Chart method

The advantage of charts is that they are intuitive and helpful for thinking and memory. When studying mathematics, we should use charts as much as possible. When solving problems, people who are related to graphics or may use graphics should draw graphics or images in order to get inspiration from them. When summarizing and sorting out knowledge, try to systematize knowledge in the form of tables so as to understand the application of memory.

4. Contrast method

In order to avoid confusion and mistakes, comparative research is often used to compare related knowledge. Positive and negative contrast, positive and negative contrast, right and wrong contrast, extended contrast, and understanding the connections and differences between knowledge are helpful for correct application.

Third, to deal with the relationship between learning mathematics

1, the relationship between difficult and easy

Don't underestimate the easy-to-learn content, and don't be careless about the easy-to-do questions. Analyze difficult problems, don't rush for success and don't give up easily. We should have perseverance.

2. The relationship between conclusion and process

When studying mathematics, don't emphasize the conclusion and ignore the process. It is necessary to remember mathematical conclusions, but the process of drawing these conclusions can not be ignored in particular. Because many deduction processes permeate and imply common mathematical thinking methods, it is very meaningful to understand and master the thinking methods of studying mathematical problems for analyzing and solving practical problems with mathematical tools. For example, logical thinking methods in mathematics (classification and analogy, induction and deduction, analysis and synthesis, proof and rebuttal); The illogical thinking methods in mathematics (imagination and association, intuition and inspiration). The basic forms of transformation in mathematics (special and general, whole and part, concrete and abstract, number and shape, high and low, positive and negative, known and unknown, infinite and finite).

3, the relationship between quality and quantity

The transformation from mathematical knowledge to ability must go through systematic and strict training. Learning mathematics is inseparable from practice. Mathematics exercises should pay equal attention to quantity and quality. Stress quality, that is, not only the answers should be accurate and standardized, but also the process should be as concise and reasonable as possible, and the habit of testing should be formed. In addition, the representative questions should be reviewed and summarized after sorting out, so as to find out the law of answering such questions and do some flexible and developmental thinking, so as to improve their mathematical ability.

Fourth, the problems that should be paid attention to in learning mathematics

1, Several Direct Motives of Mathematical Development

Mathematical problems, mathematical concepts, mathematical symbols and mathematical aesthetics are the direct reasons for the development of mathematics. Now, computers bring new challenges to mathematics.

2. Modern development trend of mathematical methods.

The abstract method of mathematics presents new characteristics, the comprehensive method is more and more powerful, the unconventional method will dominate, and the infiltration method will make mathematics become attached everywhere; A variety of opposing mathematical theories coexist independently, and the role of computers in promoting mathematics is immeasurable.

About junior high school, see the picture below:

How to learn junior high school mathematics well

The new curriculum standard for learning mathematics describes the basic knowledge in junior high school mathematics as follows: "The basic knowledge in junior high school mathematics includes concepts, laws, properties, formulas, axioms, theorems and so on. Algebra and geometry in junior high school, as well as the mathematical ideas and methods reflected in their contents. "

Mathematical definitions, rules, properties, formulas, axioms, theorems, etc. Be sure to memorize it. It's catchy. We often say that we should remember on the basis of understanding. But some basic knowledge, such as definition, is unreasonable. For example, the definition of a linear equation with one unknown quantity, whose highest degree is 1 and whose coefficient cannot be 0, is called a linear equation with one unknown quantity. In this definition, why there is only one unknown instead of two or three, why the highest number of unknowns is 1 instead of 2 or 3, why the coefficient of unknowns cannot be 0, and so on. These questions are of little value, or the definition is just a prescribed or inherent meaning for a certain thing or phenomenon. And some basic knowledge, such as laws, formulas, theorems, etc. Know not only why, but also why. For example, the nature of parallel lines: two parallel lines are parallel, the same angle is equal, the inner angle is equal, and the inner angles on the same side are complementary. We should not only remember, but also be able to use what we have learned to explain why two parallel lines have such properties. This is what we call memory based on understanding. In the process of learning, it is inevitable that you will not understand some basic knowledge for a while. In this case, remember even by rote. After remembering it, you will gradually understand it in the learning process of the post-thread. In addition, some important mathematical methods and ideas also need to be remembered. Only in this way can you solve mathematical problems with ease, so as to experience the aesthetic value of mathematics and cultivate confidence in learning mathematics well.

Third, talk about "method" and "thought", and guide "method" with "thought". The two complement each other.

The so-called mathematical thought is an essential understanding of mathematical knowledge and methods, a rational understanding of mathematical laws, and an abstract thing belonging to mathematical concepts. The so-called mathematical method is the fundamental procedure to solve mathematical problems, the concrete embodiment of mathematical thought and the means to implement mathematical thought. Mathematical thought is the soul of mathematics, and mathematical method is the behavior of mathematics. The process of solving problems by mathematical methods is the process of accumulating perceptual knowledge. When the accumulation of this quantity reaches a certain procedure, it produces a qualitative leap and thus rises to mathematical thought. If mathematical knowledge is regarded as a magnificent building built by a clever blueprint, then mathematical methods are equivalent to architectural means, and this blueprint is equivalent to mathematical thoughts.

In the study of junior high school mathematics, we need to understand the mathematical ideas: equation function, combination of numbers and shapes, reduction, classified discussion, implicit condition, whole substitution, analogy and so on. The methods of "understanding" are: classification, analogy and reduction to absurdity; The methods that require "understanding" or "being able to use" include: undetermined coefficient method, elimination method, reduction method, collocation method, method of substitution method, image method and special value method. In fact, thoughts and methods cannot be completely separated. All kinds of methods used in junior high school mathematics reflect certain thoughts, and mathematical thoughts are rational understanding of methods. Therefore, it is an effective way to understand mathematical thoughts through the understanding and application of mathematical methods.

In the process of mathematics learning, we must fully infiltrate mathematical thinking methods, learn a knowledge point or do a problem, and seriously think about what mathematical thinking methods are used. Although the mathematical thinking method is different, it is limited after all. Correct use of mathematical ideas and methods to learn mathematics or solve problems is conducive to the comparison and classification of knowledge. Only in this way can we learn what we have learned systematically and flexibly, and truly integrate what we have learned into your knowledge structure and become your own wealth.

In addition, due to the abstraction of mathematical thought, although the mathematical method is more specific, the method itself is a science, a more important knowledge, and it is still more difficult. Therefore, when you first come into contact, it is inevitable that you can't sort out the clue. This is normal, you don't have to be afraid. In particular, mathematical thought is a gradual infiltration process, which should be understood in combination with specific mathematical knowledge or topics in the gradual learning process.

For example, when learning rational numbers, triangles, quadrilaterals, the proof of the theorem of circle angle and tangent angle, and the derivation of the root formula of quadratic equation in one variable, the idea of classified discussion will be involved. The principle of classified discussion is: unify the standard, and don't weigh or leak. Its advantage is that it has obvious logical characteristics and can train a person's thinking order and generality.

The idea of equation has realized the transformation from the arithmetic method in primary school to the algebra method in junior high school, which is a substantial leap in mathematical thought. The idea of equation refers to the relationship between unknown quantity and known quantity in mathematical problems, which can be solved by constructing equations. We will find that many problems can be solved easily if they are solved by the method of column equations.

The idea of combining numbers and shapes is conducive to visualizing abstract knowledge. In junior high school mathematics learning, "number" and "shape" are inseparable. For example, the concept and operation of rational numbers can be well understood with the help of the number axis. Many problems in solving application problems of series equations can easily find out the equal relationship between quantities by drawing the meaning of the questions, and function problems can not be separated from graphs. Often with the help of images, the problem can be clearly explained, and it is easy to find the key to the problem, thus solving the problem.

The idea of transformation is embodied in the transformation from unknown to known, from general to special and so on.

These mathematical ideas and methods will also run through the teaching process of teachers. Pay attention to the lectures, learn from the teachers and learn from the classroom. Bruner pointed out that mastering mathematical thinking methods can make mathematics easier to understand and remember. It fully illustrates the importance of mathematical thinking methods.

Fourthly, forming good thinking quality is the basis of understanding mathematical problems.

Mathematics, as a discipline to cultivate people's thinking ability, is fascinating with its rational thinking. Unlike sightseeing in the mountains, it is pleasing to the eye because of its charming scenery and lingering. Mathematics learning is to study the spatial form and quantitative relationship of things through thinking and reflection, so that the spatial form and quantitative relationship of things can be presented. Only by forming a good thinking quality and pulling away the appearance of things with the sharp blade of good thinking quality can we "see" the essence of things.

So what is a good thinking quality? Let's take the phenomenon of "visiting" in our life as an example to illustrate. Many people have this kind of life experience, let others take it to others' homes once, twice, maybe many times. One day you have to go to someone else's house by yourself. When you walk near someone's house, facing the same building, you are at a loss and don't know where someone is.

In the process of learning, we often have such a phenomenon. In class, the teacher made it very clear, and the students just nodded, which made me feel very clear. And let the students do the questions themselves, and they don't know where to start. The main reason is that students do not think deeply about what they have learned and do not understand the essence of what they have learned. Just like on the way, every time we go to other people's homes, we should remember the geographical environment around them, especially the special signs. To understand the characteristics of what you have learned and what you need to remember, especially what mathematical ideas and methods are involved in this part of knowledge, you need to master it in time. The content of this kind of memory should be carefully remembered, and only by remembering the necessary knowledge can thinking be based. In addition, pay attention to taking notes. Bacon said in On Knowledge: "Taking notes can make knowledge accurate. If a person is unwilling to take notes, his memory must be strong and reliable. " Pay attention to the key points the teacher said, especially some empirical and regular knowledge summarized by the teacher, so as to review in time after class. After-class review, we should think about which problems have been passed and which problems have not been passed, and do a good job of checking and filling gaps in time.

The above talks about how to learn junior high school mathematics well from four aspects. In order to learn junior high school mathematics well, in addition to the above, the key to learning mathematics well is hard study spirit, serious and careful study attitude and good study habits. In the classroom, we should not only learn new knowledge, but also subtly learn the teacher's way of thinking to solve problems. In the face of a problem, we should think ahead, find out our own way of thinking, and then compare our own way of thinking with the way of thinking of teachers, learn from each other's strengths and form our own way of thinking. Change "I want to learn" into "I want to learn", cultivate the initiative of learning and overcome the situation of passive learning. Really master the essentials of mathematics learning. The test of whether you can learn math well is whether you can solve problems. Understanding and memorizing the basic knowledge of mathematics, mastering the ideas and methods of learning mathematics is only the premise of learning mathematics well, and the ability to solve problems independently and correctly is the symbol of learning mathematics well.

For senior high school, see below:

How to learn the new outline of senior high school mathematics _ Mathematics thesis

1. Features of the new syllabus 1. On the premise of laying a good foundation, the selected content further simplifies the second important and useless content in traditional elementary mathematics, such as deleting exponential equation, logarithmic equation, identical deformation of some trigonometric functions, trigonometric equations, polar coordinates, power functions, inverse trigonometric functions, parametric equations, and the calculation of area and volume in solid geometry. At the same time, it reduces the requirements of some contents, such as deleting some complicated proofs of theorems and eccentric exercises.

2. Update some knowledge, teaching methods and teaching means. This new syllabus adds some new knowledge, such as vector, probability, statistics and calculus. This knowledge is the basis of further study, and it is also widely used mathematical knowledge. To update the presentation of traditional content and some mathematical languages, we should use set language, logical conjunctions and vector tools to deal with some traditional content more widely. If vector is introduced, the traditional way of dealing with solid geometry by synthesis can be changed. Updating teaching methods is also an important issue in the new syllabus. High school mathematics should use modern teaching methods such as computers.

3. Increase flexibility and attach importance to teaching application according to students' different destinations and learning abilities after graduation. The new syllabus has three different requirements. The teaching content and requirements of Grade One and Grade Two are the same, which is the basis of * * * *, and there are three different levels of liberal arts, practice and science, laying a good foundation for the diversion.

Applying the new syllabus to increase mathematics knowledge. For example, increase the widely used probability statistics, arrange internship assignments after learning relevant content, promote students to participate in mathematics activities, select mathematics application topics in any elective course, and increase students' awareness and ability to apply mathematics.

Two, learn the "new outline" to deal with several relations. 1. "the relationship between infrastructure and application" laying a good foundation is the advantage of mathematics education in China, but we can't ignore the application and separate the foundation from the application for the sake of "laying a good foundation". "Laying a good foundation is for application, but we can't ignore the foundation of application (back to the Cultural Revolution). We should keep in mind the lessons of the past, link mathematics with practical problems, solve practical problems with mathematics, establish mathematical models of practical problems, and cultivate students' awareness of using mathematics.

To study and implement the New Outline, we should also have a deep understanding and understanding of "laying a good foundation". How to "lay a good foundation" needs to be improved on the basis of our past advantages. We should master some basic mathematical thinking methods in basic knowledge; In terms of basic skills, you must be able to draw charts and use computers to process data; On the basic ability, we should also have the ability to solve practical problems with mathematics and some creative thinking ability.

In studying and implementing the new syllabus, we should attach great importance to the application of mathematics. Judging from the scores of mathematics application questions in the college entrance examination in recent years, students' ability to apply mathematics is still relatively weak, which requires everyone to change their concepts and establish the consciousness of applying mathematics, especially the examples of mathematics application in daily life. Such as "calculation of index and interest", "data change and function image", "prize sale and simple probability" and so on.

2. The relationship between unity and diversity

To cultivate and develop the ability to acquire knowledge independently, we should allow the specific requirements of teaching to be different in different degrees on the basis of the unified teaching purpose, that is, teaching students in accordance with their aptitude under the unified purpose.

To study and implement the new outline, we should fully understand the relationship between unity and diversity. In other words, we should not only pay attention to compulsory courses, but also pay attention to elective courses and activity courses. Otherwise, we will go back to the old ways and fail to show diversity.

3. The relationship between inheritance and development is to seek development on the basis of inheritance. To study and implement the new outline, we should not only inherit the traditional advantages, but also adapt to the needs of the development of the times and update the concept of education and teaching. Don't understand the modernization of mathematics education as formalism that simply increases the content of modern mathematics, which will cause students to have an excessive learning burden. It should be understood as laying a solid foundation for the four modernizations.