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 your life in your account book, and record the correct number, wrong number and wrong number (page number on the memo) in your 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!
Every obstacle to be overcome is inseparable from willpower; In the face of every difficult decision we make, we rely on our inner strength. In fact, willpower is not an innate or unchangeable characteristic, but a skill that can be cultivated and developed.
In the dictionary, "willpower" is interpreted as "the power to control people's impulses and actions", and the most key words are "control" and "strength". "Power" exists objectively, and the problem is how to "control" it.
The following will help to strengthen your willpower. Just try it.
First of all, be proactive.
Don't confuse willpower with self-denial. When it is applied to positive goals, it will become a great force.
A businessman on the east coast of the United States knows that he has drunk too much, but he is engaged in a very annoying job. Drinking a few glasses of wine before eating seems to relax people's nervous mood. But wine and tiring work make him sleepy, so he often falls asleep as soon as he drinks it. One day, the manager realized that he was drinking to drown his sorrows and waste his time. So he decided to give up drinking and spend more time with his children. It was not easy at first, and I often thought of the mellow wine, but he warned himself that what he was doing now was not worth the loss. It turned out that the more he cared about his family and children, the more motivated he was to work.
Positive willpower can help you overcome inertia and focus on the future. When encountering resistance, imagine your happiness after overcoming it; If you actively participate in the concrete practice of achieving the goal, you can stick to it.
Second, make up your mind
James Pross, a professor of psychology at the University of Rhode Island in the United States, divided the realization of a transformation into four steps:
Resist-unwilling to change;
Consideration-weigh the gains and losses of transformation;
Action-cultivate willpower to achieve change;
Persistence-constantly changing with willpower.
Some people are "chronic decision makers". They know that they should reduce their drinking, but they are indecisive when making a decision, and as a result, they can't put it into action.
In order to make up your mind, you can set a deadline for your goal. Maggie Collins, a teacher in California, USA, is very concerned about how to lose weight. Later, she was elected as the president of a civic organization and decided to lose 6 kilograms. To this end, she bought clothes two sizes smaller than herself and will wear them every year in three months. Thanks to perseverance, Collins finally got what he wanted.
Third, the goal is clear
Professor Pross studied a group of experimental subjects who planned to change their behavior from New Year's Day, and found that the most successful people were those with the most specific goals. One of the men is determined to treat his wife kindly and equally every day. Later, he did it. The other party just said in a general way that he wanted to be nice to his family, and it was the same in a few days, and he quarreled.
Don't say such empty words: "I'm going to do more physical exercise" or "I'm going to read more". Instead, it should be specific and clear-"I plan to walk for 45 minutes every morning" or "I plan to read for an hour every Monday, Wednesday and Friday".
Fourth, weigh the pros and cons.
If you are half-hearted about physical exercise because you can't see the actual benefits, you can't make you wear running shoes willingly just by wishing.
Professor Pross suggested that those who went to consult him could draw four squares on a piece of paper and fill in the short-term and long-term gains and losses respectively. If you are going to quit smoking, you can fill in the short-term loss in the top two boxes: "I felt very sad at first", and the short-term gain: "I can save a sum of money"; Fill in the bottom two boxes with long-term gains: "My body will become healthier" and long-term losses: "I will promote a method to relieve boredom". Through such careful comparison, it is easier to gather the willpower to quit smoking.
Five, change yourself
However, just knowing the harvest is not enough. The most fundamental motivation comes from wanting to change your image and control your life. Truth can be convincing sometimes, but only when emotional factors are aroused can we really respond.
Tom smokes three boxes of cigarettes every day. Although he coughed badly, he didn't listen to the doctor's advice. It's about going your own way and smoking correctly. "One day, I suddenly realized how stupid I was." He recalled, "Isn't this suicide? In order to survive, we have to quit smoking. " Because quitting smoking can make him feel better, Tom has the perseverance to get rid of bad habits.
Sixth, pay attention to the spirit.
Toulouse,/kloc-a famous French general in the 0/7th century, is famous for being the first soldier. He always stands at the front of the team in every war. When asked about it, he bluntly said, "I acted like a brave man, but I was scared from beginning to end." I didn't give in to my timidity, but said to my body,' Old chap, although you are shaking, you must go forward bravely!' "As a result, resolutely charge before.
A large number of facts have proved that acting as if you have a strong will helps you become a strong-willed person.
Seven, temper the will
As early as 19 15, psychologist Boyd Barrett once put forward a set of methods to exercise his will. This includes getting up from the chair and sitting down for 30 times, emptying a box of matches and then putting them back in the box one by one. He believes that these exercises can strengthen willpower so as to face more severe and difficult challenges in the future. Barrett's specific suggestions seem a bit outdated, but his ideas are enlightening. For example, you can arrange what you want to do on Sunday morning in advance and make up your mind not to eat lunch unless you do it well.
Bill bradley from New Jersey is the star of new york professional basketball team. In addition to normal training, he comes to the court early every morning to practice shooting and aiming at foul balls alone. He finally became the person who scored the most shots in the team.
Eight, stick to the end
As the saying goes, "Where there is a will, there is a way", which means to fight against difficulties and overcome them. After studying people who quit smoking and started smoking again, Pross found that many people did not seriously consider how to deal with the temptation of cigarettes. So despite the courage to quit smoking, you still can't stick to it. When someone handed a cigarette, they took it and smoked it.
If you are determined to give up drinking, don't touch the cup on any occasion. If you insist on jogging, you can exercise indoors as usual even if it rains heavily in the morning.
Nine, seeking truth from facts
If you are required to lose 25 kilograms in three months, or you must do physical exercise for three hours every day, then no matter how strong your will is, it will not help such an unattainable goal. Moreover, the consequences of failure will eventually make you want to try again.
In many cases, it is a good idea to break down a single big goal or multiple small goals. Bob, who is going to quit smoking, put up a sign in his room-"Don't drink every day". Because the overall goal of abstinence is broken down into concrete actions day by day, I can make my determination clear again the next day. By the end of the week, when Bob looked back on his series of "victories" in the past seven days, he was full of confidence and finally said goodbye to the wine.
Ten, step by step training
Strong will is not suddenly produced overnight, it is gradually formed in the process of accumulation. There will inevitably be setbacks and failures in the middle, so we must find out the reasons that make us lose our fighting spirit, so as to solve them in a targeted way.
When Mary gave up smoking for the first time, she made great determination, but it ended in failure. When analyzing the reasons, I realized that I needed to do something, not take cigarettes. Later, when she wanted to smoke, she bought knitting wool. A few months later, Mary gave up smoking completely and knitted a sweater vest for her husband, killing two birds with one stone.
XI。 Win a victory
Practice has proved that every success will further enhance willpower. If you overcome a bad habit with tenacious will, you can gain the confidence to duel with another challenge and win.
Every success can increase your self-confidence and provide you with a solid "foothold" in the difficult cliff climbing journey. Perhaps the new task we face is more arduous, but since we have succeeded in the past, we will certainly win this time and in the future.
Will is not born, only exercise can make it. Young friends can consciously cultivate and exercise their good will quality from the following aspects.
1. Establishing a correct outlook on life can stimulate people's strong will to face all kinds of difficulties in life and consciously and firmly achieve their goals in life. Although some egoists can also exert strong willpower, they can't reach the perfect height after all. Only by establishing a beneficial and effective outlook on life and putting it into concrete actions can we maintain strong and lasting willpower.
2. Exercise their will quality with the help of collective strength. Teenagers often live in groups (such as schools and classes). Living in a group, we must abide by the discipline and rules and regulations of the group, which in itself is the process of will action. The supervision of collective public opinion, the praise or criticism of your behavior in the collective, the tasks entrusted to you by the collective or the responsibilities you undertake in the collective may all become great motivation to motivate you to realize your will and action. Therefore, you should set clear requirements for yourself in the group, learn from the behaviors of outstanding members in the group, strive to make your performance conform to the group orientation, and overcome all kinds of difficulties that may be encountered in the process.
3. Exercise your will through some specific methods.
(1) Try to do meaningful work that you are not interested in but must do. Not everything in life is so charming. Some things need to be refreshed before they can be done well, such as paying attention to lectures in class and insisting on running. Doing so is a good opportunity to test and exercise your will. You should set a goal and force yourself to do it. Of course, you can start with small things, such as getting up on time and keeping a diary. The process of completing these little things is also a process of improving your willpower.
(2) Exercise the quality of will through physical activities or participating in labor within one's power. Every sport can exercise the corresponding will quality, such as running, cycling, swimming and so on. You can exercise tenacity, dive, run obstacles and climb mountains. You can exercise courage and determination, ball games can exercise initiative and independence, gymnastics, skills, track and field, perseverance and self-control and so on. Labor can also exercise various will qualities. Therefore, as long as you often participate in sports and labor, you can naturally exercise your perseverance and perseverance, which will help to improve the overall quality of your will.
Whether you are a student or a teacher, whether you are a white-collar worker or an ordinary employee, I believe that people have strong will and extraordinary willpower, and can be competent for many jobs and even develop unlimited potential. The development of unlimited potential ultimately depends on willpower.
People who have no willpower are anticlimactic in everything they do. Cantonese means "refresh a fresh pit in three days", but many things in this world can't be completed in three to five days. If you learn any skills, it is unlikely that you can learn a high level in three to five days. Without willpower, it is almost impossible to make yourself a learned and successful person. Success requires persistence and never give up, until the belief in success requires a strong will.
How can I exercise a person's willpower? My personal experience is to practice push-ups every day. I remember when I started practicing in 2003, because I haven't practiced since I came out of school. When I do 25 push-ups at a time, I can't hold up to 30. Then I insisted on doing push-ups every day. At first, it was two days plus one. I can do 50 push-ups at a time in less than a month. In order to exercise my willpower, I insist on doing push-ups every night before taking a shower and going to bed, and exercise by the way. A year later, I competed with other colleagues and supported more than 80. Colleagues say that my skills are not up to standard, and I can only support 50 according to the most standard. Later, I practiced every day, and now I can support 80 in a very standard posture. My goal is to support 65,438+000 soldiers this year. It seems that China's special forces are also a force supporting 100 people. I want to keep up with them. Practicing push-ups makes my body stronger and stronger, and my figure is also very standard. There is no excess fat, only strong muscles, and more importantly, a strong will.
When training students in the super whole brain learning method, I deeply know that a student can't apply the learned method to his own study for a long time without strong willpower, so I also call on students to exercise in my course. Boys practice push-ups and girls practice sit-ups every day. As long as we persist, as long as we love this exercise with confidence, as long as we make a little progress every day, we will soon kill two birds with one stone.
Another way to exercise willpower is to practice long-distance running. Long-distance running is an exercise. It can exercise our endurance and will. If you are a sports enthusiast, you might as well run long distances every morning.
Another trick to exercise your will is to keep a diary every day. As students, what should we write? What you have to write every day is:
1. Review your thoughts and behaviors during the day, ask yourself what you are happy about during the day, and ask yourself if there are any problems in your study during the day and how to improve it.
2. Make new goals and plans through review, whether it is a life plan or a study plan. Simply writing it down will help you realize it tomorrow.
3. Write about the experience that you deeply felt. People can express anything that happened that day.
4. Write down positive words that can motivate you to make progress. For example, what are the benefits of this matter? We should be good at turning disadvantages into advantages and write down every day: "I am the best, I will succeed!" " There must be a successful way, not impossible, but I haven't found a way yet! I must stick to it and I won't stop until I succeed! "
As long as you actively think and act every day, constantly break through yourself and change yourself, I believe you will become a very outstanding and successful person! Success is not far away, let's do it!