Seeking the learning method of senior high school mathematics

On the Learning Methods of Mathematics in Senior High School

After entering high school, many students often can't adapt to mathematics learning, which in turn affects their enthusiasm for learning and even their grades plummet. There are many reasons for this. But it is mainly caused by students' ignorance of the characteristics of high school mathematics teaching content and their own learning methods. According to the characteristics of high school mathematics teaching content, this paper talks about learning methods of high school mathematics for students' reference.

First, changes in the characteristics of high school mathematics and junior high school mathematics

1, mathematical language is abrupt in abstraction.

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 very abstract set language, logical operation language, function language, image language and so on.

2. Transition of thinking method 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 many steps to solve the fractional equation, what to look at first and then what to look at in factorization, and so on. Therefore, junior high school students are used to this mechanical and easy-to-operate stereotype, while senior high school mathematics has undergone great changes in the form of thinking, and the abstraction of mathematical language puts forward high requirements for thinking ability. This sudden change in ability requirements has made many freshmen feel uncomfortable, leading to a decline in their grades.

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.

4. Knowledge is very independent.

The systematicness of junior high school knowledge is more rigorous, which brings great convenience to our study. Because it is easy to remember and suitable for the extraction and use of knowledge. However, high school mathematics is different. It consists of several relatively independent pieces of knowledge (such as a set, propositions, inequalities, properties of functions, exponential and logarithmic functions, exponential and logarithmic equations, trigonometric ratios, trigonometric functions, series, etc.). ). Often, as soon as a knowledge point is learned, new knowledge appears immediately. Therefore, paying attention to their internal small systems and their connections has become the focus of learning.

Second, how to learn high school mathematics well

1, form a good habit of learning mathematics.

Establishing a good habit of learning mathematics will make you feel orderly and relaxed in your study. The good habits of high school mathematics should be: asking more questions, thinking hard, doing easily, summarizing again and paying attention to application. In the process of learning mathematics, students should translate the knowledge taught by teachers into their own unique language and keep it in their minds forever. Good habits of learning mathematics include self-study before class, paying attention to class, reviewing in time, working independently, solving problems, systematically summarizing and studying after class.

2, timely understand and master the commonly used mathematical ideas and methods.

To learn high school mathematics well, we need to master it from the height of mathematical thinking methods. Mathematics thoughts that should be mastered in middle school mathematics learning include: set and correspondence thoughts, classified discussion thoughts, combination of numbers and shapes, movement thoughts, transformation thoughts and transformation thoughts. With mathematical ideas, we should master specific methods, such as method of substitution, undetermined coefficient method, mathematical induction, analysis, synthesis and induction. In terms of specific methods, commonly used are: observation and experiment, association and analogy, comparison and classification, analysis and synthesis, induction and deduction, general and special, finite and infinite, abstraction and generalization.

When solving mathematical problems, we should also pay attention to solving the problem of thinking strategy, and often think about what angle to choose and what principles to follow. The commonly used mathematical thinking strategies in senior high school mathematics include: controlling complexity with simplicity, combining numbers with shapes, advancing forward and backward with each other, turning life into familiarity, turning difficulties into difficulties, turning retreat into progress, turning static into dynamic, and separating and combining.

3. Gradually form a "self-centered" learning model.

Mathematics is not taught by teachers, but acquired through active thinking activities under the guidance of teachers. To learn mathematics, we must actively participate in the learning process, develop a scientific attitude of seeking truth from facts, and have the innovative spirit of independent thinking and bold exploration; Correctly treat difficulties and setbacks in learning, persevere in failure, be neither arrogant nor impetuous in victory, and develop good psychological qualities of initiative, perseverance and resistance to setbacks; In the process of learning, we should follow the cognitive law, be good at using our brains, actively find problems, pay attention to the internal relationship between old and new knowledge, not be satisfied with the ready-made ideas and conclusions, and often think about the problem from many aspects and angles and explore the essence of the problem. When learning mathematics, we must pay attention to "living". You can't just read books without doing problems, and you can't just bury your head in doing problems without summing up the accumulation. We should be able to learn from textbooks and find the best learning method according to our own characteristics.

4. Take some concrete measures according to your own learning situation.

Take math notes, especially about different aspects of concept understanding and mathematical laws. The teacher is in class.

Expand extracurricular knowledge. Write down the most valuable thinking methods or examples in this chapter, as well as your unsolved problems, so as to make up for them in the future.

Establish a mathematical error correction book. Write down the knowledge or reasoning that is easy to make mistakes at ordinary times to prevent it from happening again.

Submit. Strive to find wrong mistakes, analyze them, correct them and prevent them. Understanding: being able to deeply understand the right things from the opposite side; Guo Shuo can get to the root of the error, so as to prescribe the right medicine; Answer questions completely and reason strictly.

Recite some mathematical rules and small conclusions to automate your usual operation skills.

Or semi-automated proficiency.

Knowledge structure is often combed into plate structure, and "full container" is implemented, such as tabular,

Make the knowledge structure clear at a glance; Often classify exercises, from a case to a class, from a class to multiple classes, from multiple classes to unity; Several kinds of problems boil down to the same knowledge method.

Read math extracurricular books and newspapers, participate in math extracurricular activities and lectures, and take more math classes.

Foreign topics, increase self-study and expand knowledge.

Review in time, strengthen the understanding and memory of the basic concept knowledge system, and repeat it appropriately.

Solid, eliminate forgetting before school.

Learn to summarize and classify from multiple angles and levels. Such as: ① Classification from mathematical thought ② Solution.

Classification of questions and methods (3) Classification from knowledge application and other aspects. Make the knowledge learned systematic, organized, thematic and networked.

Often do some "reflection" after doing the problem, think about the basic knowledge used in this problem, mathematics.

What is the way of thinking, why do you think so, whether there are other ideas and solutions, and whether the analytical methods and solutions of this problem are used to solve other problems.

Whether it's homework or exams, we should put accuracy first, general methods first, and

Instead of blindly pursuing speed or skill, learning math well is the important issue. How to learn math well

First of all, you should be interested in learning mathematics. More than 2,000 years ago, Confucius said, "Knowing is not as good as being kind, and being kind is not as good as being happy." The "good" and "happy" here are willing to learn, love learning and have interest in learning. Einstein, a world-famous great scientist and founder of the theory of relativity, also said: "In school and life, the most important motivation for work is the fun at work." The fun of learning lies in the initiative and enthusiasm of learning. We often see some students burying themselves in reading and thinking for a long time in order to find a mathematical concept. In order to solve a math problem, forget all about eating and sleeping. First of all, because they are interested in mathematics study and research, it is hard to imagine that they are not interested in mathematics. People who have a headache when they see math problems can learn math well. To cultivate their interest in learning mathematics, we must first understand the importance of learning mathematics. Mathematics, known as the queen of science, is an essential tool for learning and applying scientific knowledge. It can be said that without mathematics, it is impossible to learn other subjects well; Secondly, we should have the spirit of learning and the tenacity to learn well. In the process of in-depth study, we can appreciate the mystery of mathematics and the joy of learning mathematics to succeed. If you persist for a long time, you will naturally have a strong interest in mathematics and arouse your high consciousness and enthusiasm in learning mathematics well.

With the interest and enthusiasm in learning mathematics, we should learn mathematics well, pay attention to learning methods and develop good study habits.

Knowledge is the foundation of ability, so we should learn basic knowledge well. The learning of basic mathematics knowledge includes three aspects: concept learning, theorem and formula learning and problem-solving learning. To learn a mathematical concept, we should be good at grasping its essential attribute, which is different from other concepts; To learn theorem formulas, we should firmly grasp the internal relationship of theorem directions, grasp the applicable scope and types of theorem formulas, and skillfully use these theorem formulas. Solving mathematical problems is actually solving contradictions on the basis of mastering concepts and theorems and formulas, and completing the transformation from "unknown" to "known". We should focus on learning various transformation methods and cultivate transformation ability. In short, in the study of basic mathematics knowledge, we should pay attention to grasping the overall essence of knowledge, understanding its laws and essence, forming a closely related overall understanding system, and promoting the mutual migration and transformation among various forms. At the same time, we should also pay attention to people's ways, means and strategies to solve problems in the process of knowledge formation, and take mathematical ideas and methods as guidance everywhere, which is what we want to learn most when learning knowledge.

Mathematical thinking method is a bridge to transform knowledge and skills into abilities, and it is a powerful pillar in mathematical structure. In middle school mathematics textbooks, there are ideas such as function, equation, combination of numbers and shapes, logical division, equivalent transformation, analogy induction and so on. This paper introduces the matching method, elimination method, method of substitution, undetermined coefficient method, reduction to absurdity, mathematical induction and so on. While learning math well, we should also learn from others.

In mathematics learning, we should pay special attention to the cultivation of the ability to solve practical problems by using mathematical knowledge. The socialization trend of mathematics makes the slogan of "popular mathematics" sweep the world. Some people think that future jobs are for those who are ready to study mathematics. "Preparing for mathematics" here not only refers to understanding mathematical theory, but also refers to learning mathematical ideas and using mathematical knowledge flexibly to solve practical problems. To cultivate mathematics application ability, we must first form the habit of mathematizing practical problems; Secondly, we should master the general method of mathematizing practical problems, that is, the method of establishing mathematical models. At the same time, we should strengthen the connection between mathematics and other disciplines. In addition to the connection with traditional disciplines such as physics and chemistry, we can also properly understand the application of mathematics in economy, management and industry.

If we study mathematics knowledge and skills in a down-to-earth manner, firmly grasp mathematical ideas and methods, and flexibly apply them to solving practical problems, then we are on the road to success in mathematics learning. Everyone can learn math well.

It is an indisputable fact that mathematics is boring, abstruse and abstract for many people, but it does not mean that it is difficult to learn. A famous mathematical figure once said, "Mastering mathematics means being good at solving problems, but it does not depend entirely on the number of problems solved, but also on the analysis, exploration and thorough research before solving problems." In other words, solving mathematical problems is not to regard yourself as a problem-solving machine or a problem-solving slave, but to strive to be the master of problem-solving. It is to absorb the methods and ideas of solving problems and exercise your own thinking. This is the so-called "math problem should examine the ability of candidates." So how to "analyze and explore", "think deeply and study hard" before and after solving the problem? In fact, everything in the world is interlinked. I wonder if students like Chinese? If you want to write an excellent composition, you must be careful, creative and have a writing outline. This kind of creativity must come from your own life, your own personal experience, feelings and ideas, and you can never write a good article by making it up. Then to solve a math problem, we should also examine the problem and find out what the problem is known. What are you waiting for? This is called "targeted". "De" means opening the channel between "known" and "to be sought", that is, "creativity", that is, using one's existing mathematical knowledge and problem-solving methods to communicate this connection, or breaking the problem into parts, or turning it into a familiar problem. This "creativity" is a long-term accumulation of mathematical thinking, a summary of one's own experience in solving problems, and a feeling after solving problems. So the summary after solving the problem is the most important. I remember that since primary school, the Chinese teacher always asked us to tell the central idea of an article after reading it. what is the purpose? When we finish a math problem, we should also think about and summarize its central idea: what knowledge points are involved in the problem; What problem-solving methods or ideas are used in solving problems, so as to "communicate" with the proposer and reach the realm of "understanding". Of course, the summary after solving problems should also be considered: whether there are other solutions to the problem; Whether it can be popularized to solve similar problems. Only by "drawing inferences from others" can we really "touch the analogy". In short, any study should not be greedy for perfection, but should strive for perfection.

2. Pay attention to improving study habits

1. Three bad habits in the process of mastering knowledge

Ignoring understanding, rote memorization: thinking that everything will be fine as long as you remember formulas and theorems, while ignoring the understanding of the process of knowledge deduction, it is not only difficult to extract applied knowledge, but also lose the absorption of ideas and methods involved in the process of knowledge deduction. For example, this is the fundamental reason why the trigonometric formula "often remembers and often forgets, but can't remember repeatedly", and then there is no sense of solving problems with trigonometric transformation.

Emphasis on conclusion over process: the characteristic of mathematical proposition is the causal relationship between conditions and conclusions. Ignoring the mastery of conditions will often lead to wrong results, even correct results and wrong processes. If you can't see when and how to discuss it in your study. One of the reasons is that the preconditions of mathematical knowledge are vague (such as monotonicity of logarithmic function, properties of inequality, summation formula of proportional series, maximum theorem, etc.). )

Ignore reviewing in time and strengthen understanding: Everyone knows the simple truth of "reviewing the past and learning the new", but few people persistently apply it in the learning process. Because under the careful guidance of the teacher, the content of each class seems to be "understood", so I can't bear to spend eight to ten minutes reviewing the old knowledge of the day. I don't know that "understanding" in class is the result of the joint efforts of teachers and students. If you want to "know" yourself, you must have a process of "internalization", which must extend from classroom to extracurricular. Remember, there must be a process of "understanding" from "understanding" to "meeting", and no one can forbid it.

2. Four kinds of bad mentality in the process of solving problems

Lack of accumulation of typical topics and methods that have been learned: some students have done a lot of exercises, but the effect is little and the effect is not good. The reason is that they are forced to do the problem passively in order to complete the task, lacking the necessary summary and accumulation. On the basis of accumulation, we can strengthen the "theme" and "sense of theme", gradually form a "module", and constantly draw intellectual nutrition from it, thus realizing the mathematical thinking method hidden in the model. This is the process from quantitative accumulation to qualitative change, and only "accumulation-digestion-absorption" can "sublimate".

When solving new problems, there is a lack of exploration spirit: "learning mathematics without doing problems is equivalent to entering Baoshan and returning to empty space" (Chinese). In the society we are facing, new problems appear constantly and everywhere, especially in the information age. Learning mathematics requires constant exploration in problem-solving practice. Fear of difficulties and excessive dependence on teachers will form the habit of not learning actively over time. We adopt the method of "thinking before speaking, doing before commenting" in classroom teaching, precisely to stimulate learners' enthusiasm for active exploration. It is hoped that students will enhance their self-confidence, be brave in guessing, actively cooperate with teachers, and make mathematics classroom teaching a communication process of learners' thinking activities.

Ignore the standardization of problem-solving process and only pursue the answer: the process of mathematical problem-solving is a process of transformation, and of course it is inseparable from standardized and rigorous reasoning and judgment. In solving problems, jumping too much, scribbling letters and drawing by hand, it is difficult to produce correct answers with such an attitude towards slightly difficult problems. We say that the standardization of problem-solving process is not only the standardization of writing, but also the standardization of "thinking method". Students should learn to constantly standardize their own thinking process and strive to solve problems perfectly.

Do not pay attention to arithmetic, ignore the choice and implementation of operation methods: mathematical operation is carried out according to rules, and the general rules and methods must of course be firmly grasped. However, the relativity of stillness and the absoluteness of motion determine that the general methods to solve mathematical problems cannot be fixed. Therefore, when using generality, generality and general principles to solve problems, we should not ignore arithmetic, but pay more attention to guessing and inference, and choose reasonable and simple operation methods. The method of solving problems without thinking must be improved. Replacing "doing" with "seeing" or "thinking" is the root cause of poor computing ability and complicated calculation.

3. Review and consolidate three misunderstandings.

It is believed that doing more problems can replace reviewing comprehension: it is necessary to learn mathematics well and do a lot of supporting exercises. But just practicing without thinking, thinking and summing up may not have a good result. Students who only bury themselves in solving problems and don't think upward, although they have done a lot of problems, it is difficult to keep the knowledge they have learned at random. Only by rolling summary can knowledge be "preserved" forever and a leap in knowledge level can be achieved. The exercises in our usual review, midterm and monthly exams are precisely to guide students to review and understand in a multi-level, all-round and multi-angle way, so that knowledge can be networked. Therefore, in the review process, good thinking and diligent summary are necessary, and also an effective way to accumulate knowledge and methods.

Do not pay attention to the connection between knowledge and the systematization of knowledge: the proposition of mathematics in college entrance examination often examines students' comprehensive application ability at the intersection of knowledge. If we only rely on a single knowledge to master it, we will not fully understand the relationship between knowledge and knowledge system, which will inevitably lead to superficial understanding and poor comprehensive ability, and of course it is difficult to achieve good results. The "before and after" and "summary of problem-solving rules" in our usual teaching are aimed at strengthening the connection between knowledge, hoping to attract students' enough attention.

Not good at correcting mistakes that have been made: the process of correcting mistakes is the process of learning and progress, and human society is also developing in the process of fighting against mistakes. Therefore, being good at correcting mistakes and summing up experiences and lessons in time is also an important part of learning. Some students often stop at "√" and "×" in the homework corrected by the teacher, or even turn a blind eye; Just ask the test scores, and don't care or seldom care why they are "wrong". Note: Memories, whether sweet or bitter, are always beneficial and beautiful, and always encourage yourself to face the future with more confidence! The process of correcting mistakes is the process of learning and progress.

In short, do a good job of psychological preparation before class; In class, the brain, ears, hands and mouth operate in coordination to improve the absorption efficiency for 45 minutes; Review and summarize after class, think fully and internalize. I believe that through students' active study, they will definitely become masters of mathematics.

How to learn math well 1

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 "Today's wrong title is memo ×× page × title"). )

I hope I can help you.