How can I learn math well?
★ How can I learn math well?
The answer to this question seems simple: just remember theorems and formulas, think hard and ask questions, and do more questions.
Actually, it's not. For example, some students can recite the bold words in the book word by word, but they can't use them. Some students do not attach importance to the process of knowledge and methods, and memorize conclusions mechanically; Some students are too arrogant to think and speak, but when it comes to writing and calculation, they are full of loopholes and mistakes. Some students are too lazy to do the problem, thinking that it is too difficult, too boring and too heavy a burden; Some students did a lot of exercises and read a lot of counseling books, but their grades just couldn't get up. Some students failed to review, learned a paragraph and lost a paragraph.
There are two reasons: First, the problem of learning attitude: some students are ambiguous in learning, unable to tell whether they are enterprising or retreating, insisting or giving up, maintaining or improving, their determination to study hard is often shaken, their learning energy is also very limited, their thinking is usually passive, shallow and extensive, and their academic performance is always stagnant. On the contrary, some students have clear learning goals and strong learning motivation. They have indomitable will, the spirit of hard study and the consciousness of independent study. They always try their best to solve the difficulties encountered in their studies and take the initiative to consult their classmates and teachers. They have good self-awareness and the ability to create learning conditions. Second, the problem of learning methods: some students don't ponder the learning methods at all, passively follow the teacher, take notes in class, do homework after class, cope mechanically, and have average grades; Some students try this method today, and try that method tomorrow. They are "in a hurry to see a doctor", and they never seriously understand the essence of learning methods, nor will they integrate various learning methods into their daily learning links to develop good study habits. More students have a one-sided or even wrong understanding of learning methods, such as what is "knowing"? Is it "understandable" or "able to write" or "able to speak" This kind of evaluative experience is very different for different students, which affects their learning behavior and its effect.
Thus, the correct learning attitude and scientific learning methods are the two cornerstones of learning mathematics well. The formation of these two cornerstones can not be separated from the usual mathematics learning practice. Let's talk about how to learn mathematics well on some specific problems in mathematics learning practice.
First, mathematical operations.
Operation is the basic skill to learn mathematics well. Junior high school is the golden age to cultivate mathematical operation ability. The main contents of junior high school algebra are related to operations, such as rational number operation, algebraic operation, factorization, fractional operation, radical operation, solving equations and so on. The poor operation ability of junior high school will directly affect the learning of senior high school mathematics: judging from the current mathematical evaluation, accurate operation is still a very important aspect, and repeated mistakes in operation will undermine students' confidence in learning mathematics. From the perspective of personality quality, students with poor computing ability are often careless, unsophisticated and low-minded, which hinders the further development of mathematical thinking. From the self-analysis of students' test papers, there are not a few questions that will be wrong, and most of them are operational errors, and they are extremely simple small operations, such as 71-kloc-0/9 = 68, (3+3)2=8 1 and so on. Although mistakes are small, they must not be taken lightly, let alone left unchecked. It is one of the effective means to improve students' computing ability to help students carefully analyze the specific reasons for errors in operation. In the face of complex operations, we often pay attention to the following two points:
① Emotional stability, clear arithmetic, reasonable process, even speed and accurate results;
Have confidence and try to do it right once; Slow down and think carefully before writing; Less mental arithmetic, less skipping rope, and clear draft paper.
Second, the basic knowledge of mathematics
Understanding and memorizing the basic knowledge of mathematics is the premise of learning mathematics well.
★ What is understanding?
According to constructivism, understanding is to explain the meaning of things in your own words. The same mathematical concept exists in different forms in the minds of different students. Therefore, understanding is an individual's active reprocessing process of external or internal information and a creative "labor".
The standards of understanding are "accuracy", "simplicity" and "comprehensiveness". "Accuracy" means grasping the essence of things; "Jane" means simple and concise; "All-round" means "seeing both trees and forests", with no emphasis or omission. The understanding of the basic knowledge of mathematics can be divided into two levels: first, the formation process and expression of knowledge; The second is the extension of knowledge and its implied mathematical thinking method and mathematical thinking method.
★ What is memory?
Generally speaking, memory is an individual's memory, maintenance and reproduction of his experience, and it is the input, coding, storage and extraction of information. It is an effective memory method to try to recall with the help of keywords or hints. For example, when you see the word "parabola", you will think: What is the definition of parabola? What is the standard equation? How many properties does a parabola have? What are the typical mathematical problems about parabola? You might as well write down your thoughts first, and then consult and compare them, so that you will be more impressed. In addition, in mathematics learning, memory and reasoning should be closely combined. For example, in the chapter of trigonometric function, all formulas are based on the definition and addition theorem of trigonometric function. If we can master the method of deducing the formula while reciting it, we can effectively prevent forgetting.
In a word, sorting out the basic knowledge of mathematics in stages and memorizing it on the basis of understanding will greatly promote the learning of mathematics.
Third, solve mathematical problems.
There is no shortcut to learning mathematics, and ensuring the quantity and quality of doing problems is the only way to learn mathematics well.
1, how to ensure the quantity?
(1) Select a tutorial or workbook that is synchronized with the textbook.
(2) After completing all the exercises in a section, correct the answers. Never do a pair of answers, because it will cause thinking interruption and dependence on answers; Easy first, then difficult. When you encounter a problem that you can't do, you must jump over it first, go through all the problems at a steady speed, and solve the problems that you can do first; Don't be impatient and discouraged when there are too many questions you can't answer. In fact, the questions you think are difficult are the same for others, but it takes some time and patience; There are two ways to deal with examples: "do it first, then look at it" and "look at it first, then take the exam".
(3) Choose questions with thinking value, communicate with classmates and teachers, and record your own experience in the self-study book.
(4) guarantee the practice time of about 1 hour every day.
2. How to ensure the quality?
(1) There are not many topics, but they are good. Learn to dissect sparrows. Fully understand the meaning of the question, pay attention to the translation of the whole question, and deepen the understanding of a certain condition in the question; See what basic mathematical knowledge it is related to, and whether there are some new functions or uses? Reproduce the process of thinking activities, analyze the source of ideas and the causes of mistakes, and ask to describe your own problems and feelings in colloquial language, and write whatever comes to mind in order to dig out general mathematical thinking methods and mathematical thinking methods; One question has multiple solutions, one question is changeable and pluralistic.
② Execution: Not only the thinking process but also the solving process should be executed.
(3) Review: "Reviewing the past and learning the new", redoing some classic questions several times and reflecting on the wrong questions as a mirror is also an efficient and targeted learning method.
Fourth, mathematical thinking.
The integration of mathematical thinking and philosophical thinking is a high-level requirement for learning mathematics well. For example, mathematical thinking methods do not exist alone, but all have their opposites, which can be transformed and supplemented each other in the process of solving problems, such as intuition and logic, divergence and orientation, macro and micro, forward and reverse. If we can consciously turn to the opposite method when one method fails, there may be a feeling that "there is no way to doubt the mountains and rivers, and there is another village." For example, in some series problems, in addition to deductive reasoning, inductive reasoning can also be used to find the sum formula of general formula and the first n terms. It should be said that understanding the philosophical thinking in mathematical thinking and carrying out mathematical thinking under the guidance of philosophical thinking are important methods to improve students' mathematical literacy and cultivate their mathematical ability.
In short, as long as we attach importance to the cultivation of computing ability, grasp the basic knowledge of mathematics in a down-to-earth manner, learn to do problems intelligently, and reflect on our own mathematical thinking activities from a philosophical point of view, we will certainly enter the free kingdom of mathematics learning as soon as possible.
Responder: Ping Pong Jumping Bean-Devil 16 Level 7- 14 20:03
Other answers *** 1 1
I personally don't think so. Although I like math since I was a child, I remember a classmate in primary school. When she first transferred to our class, her math score was 50 points. After a semester, she actually scored more than 90 points in the touch-up exam, ranking first in the class, so as long as she works hard.
Respondents: nana 165- magic apprentice level 7- 14 14:54.
I like math very much, too. I think the most important thing to learn mathematics is that you are interested in mathematics at first, and then you have been studying happily, so that you can learn mathematics well! Diligence alone is not enough. Diligence is not everything, but no diligence is absolutely impossible! Cultivate your interest in mathematics and have confidence in yourself, and you will learn well!
Respondent: evolcheng- second assistant 7- 14 15:0 1
No matter what you learn, you have to work hard. There are no rules for success.
"success = x+y+z" x = diligence, y= few excuses, z= confidence,
I hope you can overcome this hurdle in your life.
Responder: Edison 000 1- magic apprentice level 7- 14 15:04
Talent is an advantage. Without talent, you may not lose!
Interviewee: Kimi _ hui- Scholar Level 2 7-1415:11.
Yes! ! You can't do it without a little talent
Respondent: Hai-Assistant Level 2 7- 14 15: 14.
You learn quickly if you have talent. If not, you will be more diligent than others.
Interviewee: Dark Wind 26- probationary period level 7- 14 15:48.
Need.
Because when you really study advanced mathematics, you will find that talent is very important.
Although it can't be said that hard work alone is not enough, few people really study hard.
Respondent: Tan Kuang-probationary period level 7- 14 15:58.
Anything can be achieved as long as you work hard.
Responder: oO Feng Shan Xin oO- Magic Apprentice Level 1 7- 15 10:26
With talent, it may be easier to understand and master.
But people who are not smart can practice it a few times.
Respondent: I love Yuan Yuan very much-probation period level 1 7- 16 00:58.
It depends on talent!
Respondents: Baobao and Lele-the probation period is 7- 19 15:38.
Of course not!
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 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, fight for a better tomorrow!
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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.