Talking about how to learn mathematics

The first is active learning and fostering interest. Learning mathematics should not only be satisfied with passively accepting knowledge, but learning on its own initiative. Interest can generate motivation, help you overcome difficulties, and step by step. The second is to pay attention to the depth of learning, not blindly pursue progress. When learning new content, you should analyze it in detail. The more difficult it is to understand, the more you should try to understand. In order to ensure the quality of learning, it is no problem to read slowly. Third, we must pay attention to basic knowledge and basic concepts, and proceed step by step. The foundation is solid, and it is easier to learn in the depths. The fourth is to pay attention to the coherence of knowledge before and after. The contents of each branch of mathematics are not isolated. Pay attention to finding out their inner connections and combining them to deepen understanding and memory and make them a complete system. Specifically, every link in mathematics learning plays an important role and cannot be ignored. First, preview. Use the free time such as holidays, read the book once, do some marks in places that you don't understand, pay special attention to the class; you can also do related exercises with moderate difficulty to test the learning effect. Second, class. In the 45 minutes of class, I should concentrate on listening to the teacher's lectures, and at the same time, I should actively think and cooperate with the teacher. When the teacher talks about the concept of the theorem, he listens to it while he is listening, and deepens his understanding during the teacher's explanation and example process. This way, the memory of the church not only saves a lot of spare time, but also concentrates on class. Third, notes. Notebooks are necessary in math class, but they can't be delayed in class because of copying questions, which affects the class. Therefore, when copying the questions, try to be as concise and succinct as possible. You should use the knowledge you have learned to solve the problem. When the teacher comments, you can't just copy the answers. You must record the points on the basis of understanding and sort out after class. The content that can't be remembered can be compared with the classmates. Exchange, seek supplements. Fourth, homework. You should insist on completing your homework independently, seeing it as an understanding of what you are saying in the classroom, and reviewing feedback on the information. For the wrong question, you should analyze the reason and carefully correct it. You may wish to prepare a wrong book and record the error analysis and correct solution. This will become an important learning material just like a notebook. Fifth, review. Each person can select one or two reference books based on the actual situation under the guidance of the teacher. When you refer to the reference book, you should first familiarize yourself with the text, and you should not look at it when you look at it. Can not look at the practice, but should pay attention to practice, hands-on solution, can not easily let go of the problem. However, for some simple methods, the calculation of cumbersome problems can be bypassed, and the method can be mastered. From the reference book, you can learn a lot of typical problem-solving ideas and thinking methods, but you can't take the nose of the reference book. When reviewing, you should stick to the textbook and supplement the reference book. Many students want to learn mathematics well, but they find it difficult to learn. I don't know how to learn well. Is there a good way to learn mathematics? Is it really only a "smart person" to learn mathematics? Here I will talk about some of my experiences for your reference and hope to help you. I think that to learn mathematics, you can simply say - "understand and practice." Remember to memorize the mathematics knowledge, rigidly rigid. To fully understand its meaning, it is best to use your own language to correctly represent it. Specifically, the understanding of the concept requires four sessions: the correct narrative of the language, the judgment, the example, and the application. The understanding of rules, formulas, theorems and properties requires accurate understanding of conditions and conclusions, mastering the ideas and methods of reasoning, understanding the process of reasoning, and applying the conclusions obtained flexibly. The understanding of the example should be able to clear the meaning of the question, first try to solve the problem, and then compare with the answer in the book, through reflection, summed up the rules and methods to answer such questions. Focus on the discovery of problem-solving ideas and the summary of problem-solving methods. Learning mathematics is to cultivate our ability of computing, thinking, logical reasoning, analysis and problem solving. However, "ability" is a skill that cannot be formed without necessary training. A mathematician in the United States said Over: The only way to learn math is to "do math." The so-called practice is to complete considerable practice. We know that China's famous mathematician Chen Jingrun has made a breakthrough achievement in Goethebach's conjecture and shocked the world. However, there are several sacks in the draft paper he used! It can be seen how important the practice is. Everyone must work hard to complete the exercises on the textbook independently. Students who have spare time should also read some extracurricular readings, such as "School of Middle School Mathematics" and "Mathematic Weekly", which can broaden our horizons and improve our mathematics. In addition, students with opportunities and conditions should actively participate in various math competitions to train and train themselves. When doing exercises, it is best to do more than one solution, change the problem, sum up experience, master skills, skills, do the opposite, touch the analogy, find the "general law", this general method is useful for life. . In the process of learning, we must overcome the following problems. Now some students will not read the book and use the book as a workbook. The teacher will do the homework and the homework will be done. In fact, reading books is very important, you must read it. The reading study should be "three readings". That is, first reading, perusing, and intensive reading. "First reading" is a normal preparation. Read the full text before class, understand the content, and make a mark on the place where you don't know, so that you can pay special attention when the teacher attends class. "Care reading" is to read the textbooks in detail after class or after class. If you don't know clearly, you should read them repeatedly and understand all the knowledge points. As the saying goes, the book is read a hundred times, and its intention is self-evident. This is the truth. At the same time, it is necessary to compare the explanations with the teacher and understand the memory. "Intensive reading" is based on perusal, in-depth exploration of individual content, bold ideas, broadening ideas, creative reading, and doubts in the book. Many mathematicians are making a blockbuster and moving towards success. For example, Mr. Hua Luogeng, a famous mathematician in China, is negating the root formula of higher-order equations and starting to master mathematics. We know that the method of using parallel lines of equal line segments has only been the only method introduced in the book for more than two thousand years. However, a middle school student and his teacher in the United States discovered a new method in the past two years, so they are in the United States and The world is famous. Descartes, the father of Analytic Geometry, said, "We must dare to doubt everything." Finally, we must overcome the psychological obstacles, do not think that we are not born smart, not the mathematics of the "material." Mathematical level, the formation of mathematical ability is mainly the result of the efforts of the day after tomorrow. For a person who is not outstanding in intelligence, Non-intellectual factors are more important than intellectual factors. It is necessary to have good study habits, strong perseverance, perseverance in pursuing spirit, rigorous scientific attitude, strong will to return to the country, and the lofty quality of glory for the country. Well, the days when our country’s mathematics is ahead of the world are realized in your hands as soon as possible! Learning English is to remember words. Here is the method of remembering words: experts teach you how to actively and effectively remember words. In theory, everyone can be up to one month. Is the number of English words memorized 3000?6000?8000? Or 10000? To answer this question, we must first understand the essential relationship between this question and what factors, and make the problem clear, we can carry out science. Estimated. 1. What is the relationship between the number of word memories? The amount of word memory is mainly related to one person. The five factors of memory, perseverance, forgetting law, difficulty of memory objects, and degree of memory are related. These are briefly described below to give you a contour. Memory is a measure of a person's short-term memory ability. Usually in 10 minutes. A value is measured in units of 4 hours, usually measured in one hour. The memory process is mostly a boring job, especially the massive memory of English vocabulary. At this time, perseverance plays a role. From a psychological point of view, any memory that has not been in a state of solid memory, if not able to review it in a timely manner, will be completely forgotten. Different people have different laws of forgetting The difficulty of memorizing objects is not to see whether your memory has been memorized in isolation, but to see if it can establish a logical relationship with the knowledge already in your brain. The degree of memory can be simply divided into rough memory. And exact memory, the time they take is very different, For example, in the memory of English words, if you only need to know, then the time required is far less than the time to reach the proficient spelling state. 2. The difference between the hourly volume, the diary amount, the monthly volume and the annual volume Volume and diary are measures of the amount of memory in a short period of time. The monthly and annual records are measures of the amount of memory over a long period of time. Any ordinary person with a certain memory can remember one in 30 seconds. English words, can you conclude that he can remember 120 English words in an hour? If you calculate this, can you conclude that he remembers an hour a day, and can remember 3600 English words in a month? Can you remember 43200 English words? You don't have to say that you understand that such a decision is definitely wrong. According to the famous "Ebbinghaus Forgetting Principle", any new words that have been memorized must be done at the appropriate time. Review, otherwise there will be a possibility of being completely forgotten. Some people may ask, I will review each word once a day, isn't it not forgotten? The answer tells you that this is very unscientific. First, it is a waste of time. Even if you review a word in 3 seconds, you will review 1200 words in an hour and learn 1200 words in one month. Second, the effect is not obvious. Because of the large amount of memory each time, psychology has the sayings of "pre-suppression" and "post-suppression", resulting in insignificant effects. It is very easy to answer how many English words a person can remember in an hour, because it is only determined by one's memory. If you want to answer how many English words a person can remember in a month, it is not an easy task. If you have participated in the English Level 4, GRE and other exams and have experienced the English word memory, you will have such feelings. It feels quite good in the first few days. After ten days and eight days, you will start to feel confused. State, which words have been remembered, which words still need to be reviewed, when do you need to review? This is the so-called "double forgetting" phenomenon proposed in "The Manchu Memory". What is the "double forgetting" phenomenon? One is to forget the English words that have been memorized, and the second is to forget when to review the English words that are about to be forgotten. Now we know that there is a qualitative difference between the amount of time, the amount of diary, and the amount of annual notes. It is a question of how to prevent forgetting. For the amount of time and the amount of the diary, there is basically no need to consider the problem of preventing forgetting. For the monthly volume and the annual volume, how to prevent forgetting is a very critical issue. 3. Memory is not the only measure of how many English words are remembered every month. It is undeniable that memory plays a big role in the process of memory, but it is not the only basis for measurement. So, what is the basis? The answer is “review the plan in a timely manner”. Memory is used to overcome the "double forgetting" phenomenon, and the "timely review plan" is used to overcome the "double forgetting" phenomenon. Why does the “just review plan” play a key role? According to the famous "Ebbinghaus Forgetting" principle and the latest memory theory "Manchu Memory Theory", memorizing any English word, if it does not reach a firm state, then there will be forgotten. It is not a matter of two hours a day to remember an English word firmly, not a two-hour hour, but a long-term process of continuous review to achieve a firm state, and each review should be arranged with a very scientific basis. It is unscientific to review in advance or postpone review. Memory is only reflected in short-term memory and a small amount of memory. If you want to carry out massive memory and long-term memory, you must have a scientific "timely review plan". You should understand here that how many English words you can remember in a month depends on whether you have a "just-in-time review plan" for your own science. Everyone’s “just-in-time review plan” is different, which is related to the individual’s law of forgetting. At the same time, you must have the perseverance to implement the “timely review plan”. If your "timely review plan" is unreasonable or not formulated at all, then it is very possible to repeat the story of "monkey picking peaches", write down the words that follow, and end up giving the words that have been memorized before. forgotten. In the end, the words that can really be backed up are only a few. 4. Answer: In theory, people can remember up to 6,500 English words per month, assuming you have a set of “timely review plans” that suits you. According to the theory and experimental data of "Ebbinghaus's Forgotten Law", "Manchu Memory Theory" and "Ebbinghaus-Manai Town Differential Memory Algorithm Model", for the memory of English words, it is assumed that one hour is remembered every day. Every word reaches the state of memorization. In other words, when you see an English word, you can immediately think of his Chinese meaning. Then, each word needs to be reviewed for 5-12 times. Each time you want to review it, it takes about 5-50 seconds each time, which means that the total time to remember a word is 25--600 seconds. Calculated this way, remembering one hour a day, one month is 180--4320 English words. Is it a memory of 2 hours a day, so that you can double it in one month? In other words, can you memorize 360--8640 English words? The answer is no, it will be less than this number. So how long is the best memory in a day? According to my experience, the time of day's memory is 1. 5--3. 0 hours is best, and about 220--9600 English words can be firmly remembered in one month. Every day from 1.5 to 3. 0 hours, you can firmly remember 6500 words per month. This is the best state for ordinary people, and very few people can exceed this number. For ordinary people in the normal state, the general range is 2800--5600 words. 5. How to remember to remember 6500 English words every month? The key is to develop a “just-in-time review plan” that suits you. Only the memory of each word is the easiest, the number of review is the least, and the time spent on each review is the least. It is possible to remember 6500 English words per month. The “timely review plan” is not static, and different people have different “timely review plans”. When the same person is at different times, or when he remembers different things, the "review plan at the right time" is also different, which is mainly determined by his own law of forgetting. The "Ebbinghaus Forgetting Principle" provides a scientific theoretical basis for finding out the law of forgetting. Is it very difficult to formulate the "timely review plan"? The answer is yes and it is very difficult. First you must understand your own law of forgetting. Some time ago, I saw an article "The most scientific way to recite words". In the middle, I mentioned that "I must recite a lot of time every time. Because I am not smarter than others, I have to recite the words, others forget one-fifth, and they never It will be less forgotten than others. However, if someone else recites ten words a day, he can recite one hundred, forget one-fifth, and have eighty left, ten times the most intelligent state. One hundred a day. It's the minimum. It's more than a word. A word can't be remembered, depending on how often it meets on different occasions, not the length of time it looks at it. Generally want to remember a word, every week and it See three to four times on 'different occasions'." This is a back-to-word approach that does not understand the law of forgetting the memory but follows the law of forgetting in the subconscious. The better way is: first step, prepare the work: prepare a number of small notes, the number is determined by the number of words you want to remember, used to write the English words you want to remember, in principle, only one note per note Words; 30 small cartons are prepared, the first box stores the words learned and reviewed today, the second box stores the words reviewed tomorrow, and so on, and the 30th box stores the words reviewed on the 30th day. The second step is to add a new word: put 220 new words into the box 1 every day, put the words of the box 2 into the box 1, put the words of the box 3 in the box 2, and so on. The third step, learning and review: start learning the words in box 1, and decide which box in the 2--30 is just the words you just learned based on your own forgotten parameter values. Adjust your forgetting parameter values ​​according to your review results. The best way is to apply "Ebbinghaus--Manai Town Differential Memory Algorithm Model". This mode is the easiest to remember, the least number of reviews, and the least time spent reviewing each time. The model can automatically adapt to your forgetting rules, dynamically maintain a set of forgetting parameters for each memory item of each person, and maintain it dynamically during the process of memory, reminding you to review when you need the most review, until The memory is familiar. Using this model for memory is easier, faster, and more secure than the traditional method. You don't have to worry about when to learn new words, when to review the words that should be reviewed, all work is done automatically by the system, is the traditional mode. incomparable. When you find a set of "timely review plans" that are perfect for you, remembering 6500 English words per month is no longer a dream.

First day: Wu Qiaoyu