Let's talk about how it is usually done!
Read more textbooks according to your specific situation. Books are the most important thing. Generally speaking, as long as you explain the knowledge in the book clearly, no matter how the questioner tests you, you can cope. Why? You know, the exam is always like this, and its prototype is always the knowledge in books. No matter how difficult the topic is, we can break it down into several small questions, which are basically from books.
Let you read a book, not word by word, but carefully read the important things in it, such as formulas, which will certainly pass (of course, more than one factor). Like when I was in high school, I always focused on textbooks, so I got the first place in hundreds of exams in high school, more than 90% of the time. Now, I am a tutor, and my students can do anything.
Usually, you should do the questions in moderation, not too much, and certainly not too little. If you do less, you may not be familiar with doing the questions during the exam!
Let's talk about the exam. First of all, it is a matter of time. For most people, it is normal not to have enough time to do math, so there are many times when you don't always think about how to finish the paper. My math teacher said before that it is wise to give up some topics and try to ensure the correctness of the finished topics, but this does not mean that you deliberately give up some topics to check, depending on the specific situation. For example, when you feel that you really can't work out a single topic, and there are many uncertain topics (not difficult) before, then you can go to the front to check. Don't take chances, always thinking, "Maybe what I did before may be right." The previous one was more than five points. It's a pity to lose! Or you think you did well in the front, and there are still a certain number of questions (which you think you can do) that you haven't done, so do the latter, after all, there are so many points left behind!
In addition, when making a fuss, try to pay attention to skills. Don't always be honest. 120 minutes. How could you do that? You should try some simple methods, which I think are very clear in many books. As long as you seriously understand and appreciate beauty, it is no problem to master those methods!
To talk about some other problems is to try not to think about other things when doing the problem. How many points do I have to get in this exam? If I don't do well in the exam, there will be any bad results. Anyway, in a word, concentrate when you do it! Pay close attention!
One more thing I want to say, don't care too much about your usual grades. If you care too much, you may spend most of your energy. If you have such energy, you might as well spend it on your study, so the effect may be better.
Believe in yourself, there is no need to worry, as long as you don't lose heart, you should be fine.
I always think that there is no fixed method for learning, it depends on the specific situation, so I can't think of any good methods for others. It is very likely that you have a good method, but you didn't show it!
Senior one is a critical period for mathematics learning. Many excellent students in elementary school and junior high school entered the high school stage, and the first one was planted in mathematics. For many successful students in junior high school, their math scores are not ideal after entering senior high school, and their math learning is frustrated. I think the main reason for this result is that these students don't understand the characteristics of high school mathematics, and they can't learn regularly, which leads to a decline in their grades.
First, the changes in the characteristics of high school mathematics and junior high school mathematics.
1, the mathematical language has a sudden change in abstraction.
Many students reflect that the concepts of set and mapping are difficult to understand, and they feel far away from life and seem to be "mysterious". Indeed, there are significant differences in mathematics language between junior high school and senior high school. Junior high school mathematics is mainly expressed in vivid and popular language. Mathematics in senior one involves abstract set language, logical operation language, functional language, space solid geometry and so on.
2. Transition of thinking mode to rational level.
Another reason why senior one students have obstacles in mathematics learning is that the thinking method of mathematics in senior high school is very different from that in junior high school. In junior high school, many teachers have established a unified thinking mode for students to solve various problems, such as how to solve the fractional equation in several steps, what to look at first and then what to look at with factorization. Even for plane geometry problems with flexible thinking, they have determined their own thinking routines for equal line segments, equal angles,,, and. Therefore, junior high school students are used to the stereotype that machinery is easy to operate, while senior high school mathematics has undergone great changes in its thinking form. As mentioned in the last section, the abstraction of mathematical language puts forward high requirements for thinking ability. Of course, the cultivation of ability is gradual, not overnight. This sudden change in ability requirements has made many freshmen feel uncomfortable, leading to a decline in their grades. Freshmen in senior high school must be able to transition from empirical abstract thinking to theoretical abstract thinking, and finally need to initially form dialectical thinking.
3. The total amount of knowledge content has increased dramatically.
Another obvious difference between high school mathematics and junior high school mathematics is the sharp increase in knowledge content. Compared with junior high school mathematics, the amount of knowledge and information received per unit time has increased a lot, and the class hours for assisting exercises and digestion have decreased accordingly. This requires, first, to review after class and remember a lot of knowledge; Second, we should understand and master the internal relationship between old and new knowledge, so that the new knowledge can be assimilated into the original knowledge structure smoothly; Thirdly, because knowledge teaching is mostly carried out in a piecemeal way, when the amount of knowledge information is too large, its memory effect will not be very good. Therefore, we should learn to sort out the knowledge structure, form a plate structure, and implement "full container", such as tabulation, so that the knowledge structure can be seen at a glance; Classification, from one case to one class, from one class to many classes, from many classes to unity; Make several kinds of problems isomorphic to the same knowledge method; Fourth, it is necessary to summarize and classify more and establish a knowledge structure network of disciplines.
Second, the learning state is poor.
1, learning habits are backward because of dependence.
The dependence of junior high school students on learning is obvious. First, in order to improve scores, teachers list various types of questions in junior high school mathematics teaching, and students rely on teachers to provide them with "model essays" to apply; Second, parents are eager for their children to succeed, and counseling is also common after returning to China. After entering senior high school, teachers' teaching methods have changed, the applied "model" is gone, and parents' counseling ability can't keep up, from "participating in learning" to "urging learning". After entering high school, many students, like junior high school, are very dependent, follow the inertia of teachers and have no initiative in learning. It is manifested in the uncertain plan, waiting for class, not previewing before class, not knowing the teacher's class content, being busy taking notes in class and not hearing the "doorway".
2. lax thinking. Some students transplanted their ideas from junior high school to senior high school. They think that they didn't study hard in the first and second days of junior high school, but only worked hard for a month or two before the junior high school exam, and some may be key classes in key middle schools. Therefore, they think there is no need to study hard in high school. As long as you work hard for a month or two before the senior three exam, you can be admitted to an ideal university. Students who have this idea are all wet. Because in Guangzhou, it can be said that high school education has been popularized, and there is no obvious selectivity in the topics of the senior high school entrance examination, so it is easy for students to get high marks. But the college entrance examination is different. At present, it is impossible to popularize higher education in our country. Higher education can still be said to be elite education, and only some students with good grades can be selected to go to college. Therefore, the topics of the college entrance examination are highly selective. If you are lucky enough to want to go to college in senior three, you will regret it in the end. Students may wish to check the current senior three. How many students are anxious to find a tutor because they don't study hard in Grade One and Grade Two? Now they are approaching the college entrance examination and find that they have missed a lot of knowledge.
You can't learn law. Teachers usually explain the ins and outs of knowledge in class, analyze the connotation of concepts, analyze key and difficult points, and highlight thinking methods. However, some students didn't concentrate in class, didn't hear the main points clearly or didn't listen to them all, and took a big notebook, which caused many problems. After class, we can't consolidate, summarize and find the connection between knowledge in time. We just do our homework in a hurry, confuse the problems, have a little knowledge of concepts, laws, formulas and theorems, mechanically imitate and memorize. Some students work overtime at night, are listless during the day, or don't attend classes at all.
4, do not pay attention to the foundation. Some students who "feel good about themselves" often despise the study and training of basic knowledge, basic skills and basic methods, and often only know how to do it, but they are very interested in difficult problems to show their "level", set too high a goal, emphasize "quantity" over "quality" and fall into the sea of questions. In regular homework or exams, either calculus is wrong or "stuck" in the middle.
5. Do not have the conditions for further study. Compared with junior high school mathematics, senior high school mathematics is a leap in depth, breadth and ability requirements. This requires you to master basic knowledge and skills to prepare for further study. High school mathematics is difficult in many places, with new methods and high analytical ability. For example, the solution of quadratic function value, the discussion of real root distribution and parametric variables, the deformation and flexible application of triangular formula, the formation of spatial concept, the application of permutation and combination and practical application problems. Some contents are still out of touch with junior high school textbooks. If we don't take remedial measures, we can't keep up with the requirements of senior three.
Third, scientific study.
It is not enough for senior high school students to study, but also to "learn", pay attention to scientific learning methods, improve learning efficiency, change passive learning into active learning, and improve academic performance.
1, cultivate good study habits. Repeated use of methods will become people's habit. What is a good study habit? Good study habits include making plans, self-study before class, paying attention to class, reviewing in time, working independently, solving problems, systematically summarizing and studying after class.
(1) Making a plan makes the learning purpose clear, the time arrangement reasonable, unhurried and steady, which is the internal motivation to promote our active learning and overcome difficulties. But the plan must be practical, with both long-term plans and short-term arrangements. In the process of implementation, we must be strict with ourselves and temper our learning will.
(2) Self-study before class is the basis of good new lessons and good learning results. Self-study before class can not only cultivate self-study ability, but also improve interest in learning new lessons and master the initiative in learning. Don't go through the motions in self-study, pay attention to quality, try to understand the teaching materials before class, pay attention to the teacher's ideas in class, grasp the key points, break through the difficulties and solve the problems in class as much as possible.
(3) Classroom is the key link to understand and master basic knowledge, skills and methods. "Learning is not enough." Students who have taught themselves before class can concentrate more on the class. They know what should be detailed and what can pass by, so they can write down what they should remember instead of copying it all down and recording it. To learn mathematics, we must first cultivate interest and listen carefully in class, but we don't know how to ask questions at once. Don't wait until class is over. You should understand this formula ... don't memorize it, practice more, so that you can successfully take the exam and not waste time.
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 II
To learn mathematics well, senior high school students must solve two problems: one is to understand the problem; The second is the method.
Some students think that learning to teach well is to cope with the senior high school entrance examination, because mathematics accounts for a large proportion; Some students think that learning mathematics well is to lay a good foundation for further study of related majors. These understandings are reasonable, but not comprehensive enough. In fact, the more important purpose of learning and teaching is to accept the influence of mathematical thought and spirit and improve their own thinking quality and scientific literacy. If so, they will benefit for life. A leader once told me that the work report drafted by his liberal arts secretary was not satisfactory, because it was flashy and lacked logic, so he had to write it himself. It can be seen that even if you are engaged in secretarial work in the future, you must have strong scientific thinking ability, and learning mathematics is the best thinking gymnastics. Some senior one students feel that they have just graduated from junior high school, and there are still three years before their next graduation. They can breathe a sigh of relief first, and it is not too late to wait until they are in senior two and senior three. They even regard it as a "successful" experience to "relax first and then tighten" in primary and junior high schools. As we all know, first of all, at present, the teaching arrangement of senior high school mathematics is to finish three years' courses in two years, and the senior three is engaged in general review, so the teaching progress is very tight; Second, the most important and difficult content of high school mathematics (such as function and algebra) is in Grade One. Once these contents are not learned well, it will be difficult for the whole high school mathematics to learn well. Therefore, we must pay close attention to it at the beginning, even if we are slightly relaxed subconsciously, it will weaken our learning perseverance and affect the learning effect.
As for the emphasis on learning methods, each student can choose a suitable learning method according to his own foundation, study habits and intellectual characteristics. Here, I mainly put forward some points according to the characteristics of the textbook for your reference.
L, pay attention to the understanding of mathematical concepts. The biggest difference between high school mathematics and junior high school mathematics is that there are many concepts and abstractions, and the "taste" of learning is very different from the past. The method of solving problems usually comes from the concept itself. When learning a concept, it is not enough to know its literal meaning, but also to understand its hidden deep meaning and master various equivalent expressions. For example, why the images of functions y=f(x) and y=f- 1(x) are symmetrical about the straight line y = x, but the images of y=f(x) and x=f- 1(y) are the same; Another example is why when f (x-l) = f (1-x), the image of function y=f(x) is symmetrical about y axis, while the images of y = f (x-l) and y = f (1-x) are symmetrical about the straight line x = 1.
2' Learning solid geometry requires good spatial imagination, and there are two ways to cultivate spatial imagination: one is to draw pictures frequently; Second, the self-made model is helpful for imagination. For example, the model with four right-angled triangular pyramids is much more seen and thought than the exercises. But in the end, it is necessary to reach the realm that can be imagined without relying on the model.
3. When learning analytic geometry, don't treat it as algebra, just don't draw it. The correct way is to calculate while drawing, and try to calculate in drawing.
On the basis of personal study, it is also a good learning method to invite several students of the same level to discuss together, which can often solve problems more thoroughly and benefit everyone.
Answer one, get one free:
How to be the first in learning?
Learning first, every student can do it. There are two main reasons for not getting the first place in the exam: one is that the lifestyle and learning methods are incorrect, and the other is that there is no strong perseverance. Perseverance is the first important thing here, and learning methods are the second important. In real life, more than 70% of students in China are the first, but they are not the most persistent, or their learning methods and lifestyles are not the best. They may be number one today, but they won't be tomorrow. In other words, if you study and exercise according to the first method, you will generally surpass the existing first method.
Is it necessary to work hard for the brilliant first place? It is difficult because "cultivating strong perseverance" is the most difficult job in the world. Only with strong perseverance can we become the first. Of course, the correct lifestyle and learning methods are also particularly important. What is strong perseverance here? As long as you can follow the following requirements and keep records every day for one semester, one year and three years, then your perseverance is enough to meet the first requirement. I'm afraid there will be a gap between you in this exercise. Wind and rain, mood, illness, housework and so on are not reasons for you to stop exercising. You should remember that studying hard is the most important thing in your student life, and nothing is more important than it. In addition to strong perseverance, correct learning methods and lifestyles are also important.
Everyone can get the first place in the exam. The students who got the first place in the exam before are not necessarily smarter than you, and there are not necessarily more brain cells than you. Didn't Edison say that "genius is 99% perspiration and 1% inspiration"? ! So you have to go through the psychological barrier first, that is to say, you have to firmly believe that you will succeed, and you will definitely surpass the existing first, including yourself who is now the first.
Second, you should exercise every day. Without good health, you can't do anything well, even if you do it occasionally, it won't last long. Exercise for about 30 minutes every day and insist on it every day. There are various forms of exercise, such as running, playing table tennis, playing basketball, push-ups, standing long jump and so on. Some students have great face. They can't run when they see others. They are afraid to run by themselves. If others see it, it will be embarrassing. That is wrong. What is really embarrassing is that they have worked hard for several years and failed to get into college, but they have to be laid off after several years of college. If you can't support yourself in the future, it will be really embarrassing.
Third, we should have a correct attitude towards learning. Before each class, you must preview what the teacher wants to say, mark what you don't understand and can't, and listen carefully when the teacher speaks. If the teacher doesn't know after speaking, be sure to ask the teacher again until you understand. When a question can't be answered after two or three times, ordinary students are embarrassed to ask. Don't do this. Teachers like the character of "Don't give up if you don't know". Listen carefully, think carefully and take notes in class. When taking notes, you must be clear, because the value of notes is more than that of textbooks, and future review mainly depends on it.
The first thing after class is not to do homework, but to learn the knowledge points in notes and textbooks first. The contents of notes must be memorized. This will greatly improve the speed of your homework, which is often said, "sharpen your knife and don't miss the woodcutter." When you do your homework, you should think independently. If you really can't solve the problem, discuss it with your classmates and teachers. When you ask your classmates, don't ask what the result of this problem is, but ask "how to do this problem?" "What is the title of this road?"
Fourth, correctly face mistakes and failures. When you don't learn some knowledge in class, when you make mistakes in practice or do poorly in exams, you should neither complain nor be discouraged. You have to face up to the reality that you don't want. It doesn't matter if you haven't studied it. Write this knowledge in your memo, then ask your classmates and teachers, and then write the correct explanation or result on other pages. The same is true of wrong questions. Aren't there many wrong questions when you fail the exam? The correct way is to copy the original question into the memo, learn the correct method, and write the practice and results on other pages. If you can pay attention to the matters needing attention in doing this kind of problems, your learning efficiency will be improved by 30%-60%. The reason why the answers or explanations are written on other pages is to think about the understanding and explanation of the knowledge points next time you look at the knowledge points or wrong questions, and then practice the exercises and answers of the questions. Mistakes and failures are not terrible. As long as you can face them squarely, everything will be the driving force for your success.
Fifth, bookkeeping. You must keep an account book for your study. Write it down when you do well, and write it down when you do wrong (note: only the title of today's mistake is "memo" ×× page× title). When did you learn English after class and keep good records? When did you learn physics? Write it down. Record every minute of exercise and study in life in your own account book, and record the correct number, wrong number and wrong number (page number on the memo) in the account book one by one. Write down all the knowledge you learn every day in your account book, so that you can check whether you really have mastered these knowledge points tomorrow and the day after tomorrow. You must learn and master what you have spent several days in books.
The ledger records every detail of your study and exercise. In this way, it is recorded that in school life, there are about 32 pages of paper every day, and there may be two pages of 32 papers when you are not in school. Don't stop on weekdays and holidays. Accumulate your account day after day, which is the first way you take.
Although in today's quality education, the school is not ranked second, but learning achievement is the goal of our efforts, the necessary condition for us to enter a higher-level school, and the capital for us to do everything well after entering the society. Students, strive for the first place. If you follow the above requirements year after year, you are the first.
If everyone does this, even if you can't win the first place, you must be an excellent student in China, because most students in China don't have such perseverance, such a good learning method and lifestyle. Students, strive for a better tomorrow.
Physics is similar to mathematics! With the method, you can learn everything well! Abstract: We found many cases of students improving their mathematics learning from the internet, books and surveys. In order to improve middle school students' mathematics study, we hope it will help you in your future mathematics study.
We found many cases in which students improved their mathematics learning through the Internet, books and surveys. In order to improve middle school students' mathematics study, we hope it will help you in your future mathematics study.
Case 1: Ren Jing never passed the math exam before the third grade, so her father asked the teacher to help her. In fact, she didn't do anything, but went to the teacher's house once a week to give a lecture and asked her to tell the teacher what she had learned in class until the teacher was satisfied. After half a year, his math scores improved rapidly. When she graduated from senior three, she took two mock exams, one with 148 and the other with 149. Later, he was admitted to Peking University. Less than a year after I entered Peking University, I was admitted to an American university and went to study in the United States. Last year, she sent an email to her teacher, saying that her American classmates said he was a math genius, but the American classmates didn't know how bad her math was until the third grade!
Case 2: A teacher with poor math performance in Grade One of Senior High School has to test his students every week, and publicly tells his students that the questions are all examples he talked about in class. The students began to be in an uproar, but 90% of them were confident to get full marks. Only the worst students in the class dare not say so. Soon, the preliminary test results came out, with a pass rate of 48% and a perfect score of less than 8%. The second time, things got better. In the first year of junior high school, the average score of this class is different from that of the special class in the same grade 12.5 points. Grade two is only 1.5 points worse than the average grade 10 points. After graduating from the third grade, this class is almost the same as the special math class. Therefore, learning examples and learning examples well are shortcuts to learning mathematics.
Case 3: Ma Yiyang saw the following classification of students' learning characteristics in the study newspaper: the first one, excellent, solid foundation, good learning, high intelligence, stable and excellent grades; The second type, loose, has strong learning ability, but can't take the initiative, learning is not practical, the foundation is not solid, and the academic performance is unstable; Third, be serious and diligent in learning. Inferior type. Not interested in learning, not working hard, poor foundation, dead methods, weak ability, poor academic performance, in a state of "learning derailment" and "vicious circle". For different types of students, the guidance methods and emphasis should be different. The first focuses on helping gifted students and consciously using learning methods; For the second, it mainly solves the problem of learning attitude; For the third main solution; Ma Yiyang thinks that he belongs to the third kind, so he asks his teacher for math learning methods. The teacher carefully pointed out the specific operation methods of class, preview, review and homework. He persisted in applying it for three months and got 92 points in a unit test.
Case 4. Ma Yaping is a middle school student. In order to improve her math performance, she studies strictly according to the contents of the reflection card told by the math teacher every day. This reflection card is divided into cognitive field and emotional field according to the evaluation index. Time-based classes: cognitive fields include: 1. Subject (geometry or algebra); 2. The content of the lecture; 3. Grasp the situation in class; 4. What is not mastered and the reasons; 5. do your homework; 6. The time of day to study math. Emotional fields include: 1. Attend lectures; 2. Mathematics learning experience; 3. Say a few words to the teacher; 4. Say a few words to yourself. After 9 weeks of experiments, Ma Yaping's math scores in unit tests and mid-term exams have been greatly improved.
Case 5. A math teacher in Beijing mainly teaches his students the following five feasible and effective learning methods suitable for middle schools: 1, cultivating methods and habits, and thoroughly mastering basic knowledge; 2. Cultivate the method of thoroughly understanding typical cases; 3. Cultivate the good habit of classroom memory; 4. Cultivate confidence in the accuracy of operation; 5. Cultivate the methods and habits of research and analysis. Sha Wenhua thinks that among the five methods, "calculation accuracy" is most suitable for him. In normal times, he is easy to make careless mistakes, either copying the numbers wrong or taking the plus sign as the minus sign, as in the midterm physics exam. So he asked the teacher to tell him all kinds of measures to solve the problem of "calculation accuracy". He followed the method step by step, which not only did not make careless mistakes, but also shortened the time to do the questions and greatly improved the exam results. In addition, good books for senior high school students' mathematics guidance are: 5-year college entrance examination, 3-year simulation (with simulation examples), whole-course optimization paper (which belongs to mathematics promotion paper), middle school miracle class (a very good explanation book covering all the key points, difficulties, examples, expansion, knowledge points and simulation questions), and basic standards (suggestions and).