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 finishing 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!

How to learn English well?

How to learn English well seems an old topic. In the three years of college life, I am most proud of my English grades. Of course, my English is not outstanding, but the progress I have made is very gratifying. When I was in high school, my English score was average, and my college entrance examination score was only 98. As soon as I entered the university, I was confused by English learning. If you can't learn English well again, it will add obstacles to your future road. Therefore, there is still a long way to go in Xiu Yuan. I will learn English from beginning to end. Finally, it was worth the money, and I finally achieved excellent results. After passing CET-4, I also got the oral exam qualification, and the oral exam was also c+. Last year, I passed Band 6 again. What makes me most gratified is that when I was a sophomore, I won the third prize of national english contest for college students. All my achievements also prove a truth: no pains, no gains.

Based on three years' experience in learning English, I have summarized the following points. For your reference.

First of all, to learn English well, the most important thing is to be interested. As the saying goes, interest is the best teacher. It is a young teacher who teaches us English. His lectures are very interesting. He always lets us give lectures and perform sketches by ourselves. Vivid English teaching made me interested in English.

It's not enough to be interested. We need to know how to study.

Say the words by heart first! Memorizing words is undoubtedly a very painful thing for many students. When I recite words, I don't recite them one by one in the word book, which makes people feel very annoyed and easy to forget. I take a few pictures of my back every page, which is very casual. Usually, you can make some small cards and write them in places that are difficult to remember. You can come out and look at them as soon as you have time. You can also put some cards on the bedside and look at them before going to bed every day. Before going to bed, have a guessing contest with your classmates in the dormitory, and the effect will be better. Every time I guess the words I learned that day, I can remember them well. Of course, the most important thing in memorizing words is to keep reviewing.

Many students have a headache in reading comprehension. First, time is tight, and second, it is difficult to understand. If time is tight, I'll teach you a trick. That is to say, treat every exercise as an exam, limit your time and guess if you can finish it. Over time, there will be an invisible alarm clock in your heart, so that you always have a sense of urgency when doing the problem. Practice for a long time and you will get used to it.

For understanding, I think we should expand the scope of reading. We can read English newspapers or magazines. I watched English Salon in both Chinese and English when I was a freshman. With the increase of my vocabulary, I began to read English newspapers. I often read Shanghai Star. This newspaper covers a wide range and is easy to understand. When reading newspapers, I don't like to look up word by word. I guess when I meet new words and copy them when I meet good words. Three years later, I have several such small excerpts. In short, reading English newspapers can not only gain more knowledge, but also cultivate a sense of language and practice reading speed.

Listening is also a headache for everyone. I don't think it is enough to use listening tapes to improve listening. We can use other methods! For example, we can listen to English news. I often listen to live it up at eleven o'clock in Shanghai at 990. This talk show is quite good. Of course, another way is to go to the English corner. I started to participate in the English corner last year, where a large group of English lovers got together to chat and give speeches in English. Sometimes I have the opportunity to get in close contact with foreigners. Speak more and listen more, and your listening and speaking ability will be improved unconsciously. Go to the English corner to speak, listen and feel, and you will find it not difficult to speak English!

When learning English, you should also learn to be a conscientious person. Every time you see an English signboard on the street or an English abbreviation on the Internet, have you ever thought about its full name? BBS, everyone has used it, but do you know its full name bulletin board system? I often see RMB in newspapers. What is this abbreviation? Of course, it's short for RMB in Chinese. And GDP, MBA, MPA and so on. Over time, you will find that English has not only appeared in the classroom, but has been integrated into the whole society. Look at your clothes, maybe there is a word on them that you don't know! Hurry up and learn!

Everyone has his own learning method, maybe the method you seek is more effective! Isn't it good to communicate with classmates often? A philosopher once said that two people each have an apple, and you will only have one after the exchange, but only by exchanging ideas will you have one more idea in your mind. What did you say?/Sorry?

How to learn Chinese well?

Chinese is a broad and profound subject, and it is very important to have interest in learning and good study habits. Some people find it difficult to learn Chinese. I think it's mainly because they don't have the right method and a golden key to open the door to Chinese.

To learn Chinese well, we should pay attention to cultivating learning interest, forming good study habits, accumulating learning methods and enhancing learning ability. I hope that after reading this "bad article", you can pave the way for your Chinese, contribute to your Chinese building, and pave the way to heaven for your study.

Being interested in Chinese learning will lay the most solid foundation for your Chinese learning. No matter what you do, interest is the most important thing. Two thousand years ago in Wen Sheng, Confucius once said, "Knowing is not as good as being kind, and being kind is not as good as being happy". This sentence just shows that "good" and "happy" can be said to be spiritual pillars for a person to pursue something, friends. If you are not interested in Chinese for the time being, it doesn't matter, you can start with "0". To cultivate interest, you can recite and copy some wonderful fragments, philosophical sayings and extracurricular knowledge. In this way, slowly accumulate, one day, you will suddenly find that it is so easy to be a knowledgeable scholar. You can also take part in some activities about Chinese, such as lectures, compositions and so on. Einstein said: "In school and life, the most important motivation for work is the pleasure in work, the pleasure in obtaining the result of work, and the understanding of the social value of this result." Like I said just now, you can take part in social activities, and then someone will ask. If you win, it will definitely boost our morale and make us more interested. Instead, it will dampen our enthusiasm and dislike Chinese. Isn't that counterproductive? I can definitely answer "No". See how you realize the value of the result. As the saying goes, we will learn Chinese well with confidence. If we fail, we can reflect on what we did badly. "Frustration is a great wealth for the strong and an abyss for the weak." You can think about it. It is precisely because of the discovery of defects that we will make up for them and do better. If learning interest is the foundation, good study habits are excellent architects.

The quality of your study habits is directly related to the quality of your study. Ye Shengtao believes: "From primary school teachers to university professors, their task is to help students develop good habits and help students develop good habits in politics, culture and science." From this sentence, we can at least see the importance of good habits. In fact, good habits are mainly cultivated by themselves. There is a saying in the countryside that "habit becomes nature". If you stick to a good study habit, it will become "nature" over time. How to develop good study habits can be understood from study practice and articles. The Book of Rites says, "Be knowledgeable, interrogate, think carefully, distinguish clearly and stick to it." This is a good study habit, and we can gradually integrate it into our study. "Learning without thinking is useless, thinking without learning is dangerous", which sounds the alarm of combining "learning" with "thinking" for us. "Learn from time to time" and "Review the past and learn the new" Many famous people have summarized their own learning, so we might as well try (but not blindly). In fact, it is more important that we sum up from our study. For example, in a quiet place, we might as well sit down and think quietly about essays and famous sayings, which will not only make us feel happier, but also deepen our impression. If a good study habit is an original architect, then a good study method is exquisite and practical building materials.

Speaking of learning methods, there are actually many intersections with learning habits, such as copying wonderful fragments, reciting ancient poems, and writing down wonderful moments at any time. The important thing in Chinese learning is accumulation and application, and the above methods are all important means of accumulation. Our knowledge of using Chinese can be said to be all-encompassing, which can be used in social, writing, oral and other aspects ... they are all closely related to us. Some people learn Chinese very well, but when they use it, they put jiaozi in a teapot-they can't pour it out. In fact, the purpose of learning is to use, which is the key. Since the methods vary from person to person, I won't discuss them much! I believe my dear friend, you will have a trick up your sleeve. Good study habits, strong interest and correct methods are useless if you don't have the ability to learn Chinese.

Learning ability is gradually cultivated and accumulated. Some people say that Lu Xun's article is difficult to understand, in fact, because we have not found a breakthrough. When we understand a sentence, we must contact the background and context of the times, so that you can easily solve the problem. To learn to re-recognize the consolidation of basic ability, we must first remember the intentions of some words, rhetoric and symbols. With such a solid foundation, we can improve. The cultivation of the learning ability of "haste makes waste" is not a day's work, and you need to persevere.

All the above are my humble opinions, mostly superficial words. In fact, everyone has their own classics and a set of undiscovered (and of course some have been discovered) learning cheats.

My friend, when you read this article, I hope you can also benefit from it when you hide your thoughts. For those with poor Chinese proficiency, change the status quo and add icing on the cake to the good Chinese proficiency.

I said a lot of nonsense, I hope it will be useful to you!