★ How can I learn math well?

The answer to this question seems simple: just remember theorems and formulas, think hard and ask questions, and do more questions.

Actually, it's not. For example, some students can recite the bold words in the book word by word, but they can't use them. Some students do not attach importance to the process of knowledge and methods, and memorize conclusions mechanically; Some students are too arrogant to think and speak, but when it comes to writing and calculation, they are full of loopholes and mistakes. Some students are too lazy to do the problem, thinking that it is too difficult, too boring and too heavy a burden; Some students did a lot of exercises and read a lot of counseling books, but their grades just couldn't get up. Some students failed to review, learned a paragraph and lost a paragraph.

There are two reasons: First, the problem of learning attitude: some students are ambiguous in learning, unable to tell whether they are enterprising or retreating, insisting or giving up, maintaining or improving, their determination to study hard is often shaken, their learning energy is also very limited, their thinking is usually passive, shallow and extensive, and their academic performance is always stagnant. On the contrary, some students have clear learning goals and strong learning motivation. They have indomitable will, the spirit of hard study and the consciousness of independent study. They always try their best to solve the difficulties encountered in their studies and take the initiative to consult their classmates and teachers. They have good self-awareness and the ability to create learning conditions. Second, the problem of learning methods: some students don't ponder the learning methods at all, passively follow the teacher, take notes in class, do homework after class, cope mechanically, and have average grades; Some students try this method today, and try that method tomorrow. They are "in a hurry to see a doctor", and they never seriously understand the essence of learning methods, nor will they integrate various learning methods into their daily learning links to develop good study habits. More students have a one-sided or even wrong understanding of learning methods, such as what is "knowing"? Is it "understandable" or "able to write" or "able to speak" This kind of evaluative experience is very different for different students, which affects their learning behavior and its effect.

Thus, the correct learning attitude and scientific learning methods are the two cornerstones of learning mathematics well. The formation of these two cornerstones can not be separated from the usual mathematics learning practice. Let's talk about how to learn mathematics well on some specific problems in mathematics learning practice.

First, mathematical operations.

Operation is the basic skill to learn mathematics well. Junior high school is the golden age to cultivate mathematical operation ability. The main contents of junior high school algebra are related to operations, such as rational number operation, algebraic operation, factorization, fractional operation, radical operation, solving equations and so on. The poor operation ability of junior high school will directly affect the learning of senior high school mathematics: judging from the current mathematical evaluation, accurate operation is still a very important aspect, and repeated mistakes in operation will undermine students' confidence in learning mathematics. From the perspective of personality quality, students with poor computing ability are often careless, unsophisticated and low-minded, which hinders the further development of mathematical thinking. From the self-analysis of students' test papers, there are not a few questions that will be wrong, and most of them are operational errors, and they are extremely simple small operations, such as 71-kloc-0/9 = 68, (3+3)2=8 1 and so on. Although mistakes are small, they must not be taken lightly, let alone left unchecked. It is one of the effective means to improve students' computing ability to help students carefully analyze the specific reasons for errors in operation. In the face of complex operations, we often pay attention to the following two points:

① Emotional stability, clear arithmetic, reasonable process, even speed and accurate results;

Have confidence and try to do it right once; Slow down and think carefully before writing; Less mental arithmetic, less skipping rope, and clear draft paper.

Second, the basic knowledge of mathematics

Understanding and memorizing the basic knowledge of mathematics is the premise of learning mathematics well.

★ What is understanding?

According to constructivism, understanding is to explain the meaning of things in your own words. The same mathematical concept exists in different forms in the minds of different students. Therefore, understanding is an individual's active reprocessing process of external or internal information and a creative "labor".

The standards of understanding are "accuracy", "simplicity" and "comprehensiveness". "Accuracy" means grasping the essence of things; "Jane" means simple and concise; "All-round" means "seeing both trees and forests", with no emphasis or omission. The understanding of the basic knowledge of mathematics can be divided into two levels: first, the formation process and expression of knowledge; The second is the extension of knowledge and its implied mathematical thinking method and mathematical thinking method.

★ What is memory?

Generally speaking, memory is an individual's memory, maintenance and reproduction of his experience, and it is the input, coding, storage and extraction of information. It is an effective memory method to try to recall with the help of keywords or hints. For example, when you see the word "parabola", you will think: What is the definition of parabola? What is the standard equation? How many properties does a parabola have? What are the typical mathematical problems about parabola? You might as well write down your thoughts first, and then consult and compare them, so that you will be more impressed. In addition, in mathematics learning, memory and reasoning should be closely combined. For example, in the chapter of trigonometric function, all formulas are based on the definition and addition theorem of trigonometric function. If we can master the method of deducing the formula while reciting it, we can effectively prevent forgetting.

In a word, sorting out the basic knowledge of mathematics in stages and memorizing it on the basis of understanding will greatly promote the learning of mathematics.

Third, solve mathematical problems.

There is no shortcut to learning mathematics, and ensuring the quantity and quality of doing problems is the only way to learn mathematics well.

1, how to ensure the quantity?

(1) Select a tutorial or workbook that is synchronized with the textbook.

(2) After completing all the exercises in a section, correct the answers. Never do a pair of answers, because it will cause thinking interruption and dependence on answers; Easy first, then difficult. When you encounter a problem that you can't do, you must jump over it first, go through all the problems at a steady speed, and solve the problems that you can do first; Don't be impatient and discouraged when there are too many questions you can't answer. In fact, the questions you think are difficult are the same for others, but it takes some time and patience; There are two ways to deal with examples: "do it first, then look at it" and "look at it first, then take the exam".

(3) Choose questions with thinking value, communicate with classmates and teachers, and record your own experience in the self-study book.

(4) guarantee the practice time of about 1 hour every day.

2. How to ensure the quality?

(1) There are not many topics, but they are good. Learn to dissect sparrows. Fully understand the meaning of the question, pay attention to the translation of the whole question, and deepen the understanding of a certain condition in the question; See what basic mathematical knowledge it is related to, and whether there are some new functions or uses? Reproduce the process of thinking activities, analyze the source of ideas and the causes of mistakes, and ask to describe your own problems and feelings in colloquial language, and write whatever comes to mind in order to dig out general mathematical thinking methods and mathematical thinking methods; One question has multiple solutions, one question is changeable and pluralistic.

② Execution: Not only the thinking process but also the solving process should be executed.

(3) Review: "Reviewing the past and learning the new", redoing some classic questions several times and reflecting on the wrong questions as a mirror is also an efficient and targeted learning method.

Fourth, mathematical thinking.

The integration of mathematical thinking and philosophical thinking is a high-level requirement for learning mathematics well. For example, mathematical thinking methods do not exist alone, but all have their opposites, which can be transformed and supplemented each other in the process of solving problems, such as intuition and logic, divergence and orientation, macro and micro, forward and reverse. If we can consciously turn to the opposite method when one method fails, there may be a feeling that "there is no way to doubt the mountains and rivers, and there is another village." For example, in some series problems, in addition to deductive reasoning, inductive reasoning can also be used to find the sum formula of general formula and the first n terms. It should be said that understanding the philosophical thinking in mathematical thinking and carrying out mathematical thinking under the guidance of philosophical thinking are important methods to improve students' mathematical literacy and cultivate their mathematical ability.

In short, as long as we attach importance to the cultivation of computing ability, grasp the basic knowledge of mathematics in a down-to-earth manner, learn to do problems intelligently, and reflect on our own mathematical thinking activities from a philosophical point of view, we will certainly enter the free kingdom of mathematics learning as soon as possible.

Many people can't get their actual level and ideal scores in the exam. The reason is that their psychological quality is not too hard and they are too nervous during the exam. There is also that they pay too much attention to the exam scores, which leads to the failure of the exam. You should learn to put yourself in the other's shoes, and you should learn to adjust your mentality. It is often said that getting three points in the exam is level and seven points is psychology. It is for this reason that excessive pursuit is often lost. Don't take the score too seriously, that is, treat the exam as a general homework, sort out your own ideas, take every question seriously, and you will definitely get good results in the exam; You should learn to surpass yourself, that is, don't always think about scores and rankings; As long as my score in this exam is better than that in the last exam, even if it is only one point higher, then I have surpassed myself; In other words, don't compare your grades with others, compare with yourself, so that your mind will be much calmer, your pressure will be less, and you will feel relaxed when you study and take exams; If you try to adjust yourself in this way, you will find that your grades will improve a lot inadvertently;

This is my experience. My mother taught me the truth, which made me pass through the middle school stage smoothly, and also made my grades enter the top 10 from more than 30 students in Grade One to Grade Three. I didn't feel any pressure, so I learned easily. You might as well try. I hope my experience can reduce your stress and improve your grades, so I will be pleased.

I wish you progress in your study!