Beware of four misunderstandings in senior high school mathematics learning.
Myth 1: If you understand the knowledge in class, you will master it.
In the process of mathematics learning, this phenomenon often occurs. Students understand it in class, but they are at a loss when they solve problems after class, especially when they encounter new problems. This shows that it is one thing to understand in class, and it is another to apply knowledge to solve problems. Boria put it well: "What the teacher said in class is of course important, but the students' ideas are a thousand times more important."
The problems listed by the teacher are examples and means of thinking training. As a student, we should not only learn the knowledge in the problem, but also learn to understand the thinking and skills of solving the problem and the mathematical thinking method contained in it.
Countermeasure 1: Do the example again by yourself. Countermeasure 2: Ask yourself: Why do you think so?
Countermeasure 3: Can the conditions and conclusions be changed?
Countermeasure 4: Are there any other conclusions?
Countermeasure 5: What problem-solving rules can I get?
Myth 2: You can always meet questions when you do more questions.
People who have this idea will always be disappointed. For each comprehensive test paper, the author should always avoid testing old questions and old questions, and try to design the questions from a new angle and level. But the knowledge points and mathematical thinking methods are unchanged. So if you do more questions, you won't happen to touch them at zero distance, but you will fall into an endless sea of questions. The way to solve the problem is to classify the problem from the perspective of knowledge points and thinking methods, sum up the experience of solving the problem, and at the same time confirm whether you really master it and confirm the key points of review.
Countermeasure 1: Let yourself spend some time sorting out the recently solved problems and ideas.
Countermeasure 2: Is this question similar to the last one?
Countermeasure 3: am I familiar with the knowledge points of this problem?
Countermeasure 4: What problems are similar in recent graphs? Can you classify it?
Countermeasure 5: The idea of solving this problem is also used in the previous topic. Let me find them!
Myth 3: The basic problem of studying difficult problems is very simple.
A student once said to me, "I like to do difficult problems." Studying math problems can make me feel happy in my mind. Simple topics are meaningless. " It should be said that this classmate has realized the happiness of mathematics learning, and he has begun to have his own understanding of mathematics. But strangely, his mathematics scores always fail to reach satisfactory high scores, and he always regrets his carelessness or some places have not paid attention to it after the exam. In fact, this also reflects the impetuous situation in our mathematics study to some extent. Teachers love to talk about difficult problems and comprehensive problems, and students want to do comprehensive problems and difficult problems. If you ignore the foundation, you will lose the direction of mathematics learning.
Countermeasure 1: Tell yourself that mathematical thinking is not equal to complex thinking, and the beauty of mathematics is often reflected in some small topics.
Countermeasure 2: "Simple but not simple" to experience the fun of mathematical thinking in ordinary problems.
Countermeasure 3: "A drop of morning dew can also reflect the brilliance of the sun." Let me find the shadow of comprehensive questions from the basic questions.
Countermeasure 4: Is this question really simple?
Countermeasure 5: I am an excellent student, and I can show my Excellence in the ordinary.
Myth 4: Thought is a bit unattainable.
When it comes to mathematical thinking methods, some students feel unfathomable and unattainable. In fact, every mathematical problem contains mathematical thinking methods. For example, the transformation idea is applied when the fractional equation is transformed into the integral equation, and the equation idea is embodied when the column equation is used to solve the application problem. The image and analytical formula in the plane rectangular coordinate system embody the idea of combining numbers and shapes, and the folding and rotation of graphics embody the idea of motion transformation. Mathematical thinking method is a very important policy to guide solving problems, which is conducive to cultivating students' extensive, profound, flexible and organized thinking. In the process of learning mathematics in the third grade, I might as well move and change the graphics, and link the conditions and conclusions with other aspects for mathematical thinking. The last question of the senior high school entrance examination is often to examine students' abilities of guessing and exploring, function and movement, transformation and classification while connecting several knowledge points in series, which puts forward higher requirements for the ability level.
Countermeasure 1: Mathematical thinking method is not mysterious, it is contained in the topic.
Countermeasure 2: Understand some mathematical ideas and find some typical problems.
Countermeasure 3: After solving the problem, ask yourself "What mathematical thinking method did I use"?
Countermeasure 4: Before solving the problem, ask yourself from what angle to think. (Equation Angle ... >>
Question 2: How do you get the corrected version of high school mathematics if you are too careless? Every time you make a mistake, do it again in the corrected book. Write down the reason of the mistake with a red pen next to it. Read it often. When you meet it again, you will remember the last mistake. Don't make any more mistakes. That's what I did before, and it worked well. You can try.
Question 3: What do you think of the carelessness in math study in senior three? I think I have the ability to answer. The problem of carelessness mainly lies in accumulation. To put it bluntly, do more. If you do something wrong, just look at what is wrong. There is a lot of teaching in high school, and slowly some error-prone problems will impress you. With a little attention, you can become cautious. That's what I used to do. If there is always one more missing item in the calculation, that is.
Question 4: How to make some low-level mistakes in the math exam? General carelessness often happens to students with good foundation. In fact, low-level mistakes did not happen suddenly during the exam. Think about it. When you do your homework, do you always feel that all the ideas are right? If there are many careless places in your exercise book, you should start from usual. Homework is not only to exercise your thinking, but also to practice writing, such as writing. First of all, carefully examine the questions when you do them, and remember to draw the important conditions appropriately. This is aimed at your careful examination of the questions in the exam. When you are doing your homework, you will start with a careful and slow check and go through a careful and quick check. When you take an exam, you will naturally examine the questions carefully and quickly, and drawing conditions will help you to examine the questions more accurately. Secondly, be careful when you work. On the one hand, exercise your computing ability, on the other hand, know where the teacher will open the pit and miss the negative sign. If you can't do addition and subtraction well, if you like, you have time to do 2-digit and 3-digit addition and subtraction oral arithmetic problems. Write slowly, do slowly, and sometimes you will read the wrong numbers if you write badly. Then, don't expect to check. After calculating one side wrong, it is likely to be wrong again, because you have the influence of this question in your mind, which will affect your examination this time. Of course, it doesn't mean not to check. If you go back to check a problem without doing it, the wrong solution and calculation in your mind will only lead to your invalid check. If you want to check all of them, you should check the uncertain questions with strange answers again. Of course, it is best to do it right once. It may be too late for the senior high school entrance examination, so you will have little time to check the college entrance examination in the future. Finally, the mentality and order of doing the questions. There must be something wrong with a piece of paper, but you can't if you are confused. It's hard for you to adjust yourself. You can try your usual homework as an exam and get used to that kind of tension. Mentality is a little hard to say. In order to do the questions, it is necessary to make them easy first and then difficult. When you see something difficult, think about it a little. Do that one, if not, skip it immediately. In the math exam, the problem of printing is the exam topic, and this paper itself is also the topic. Tell yourself that getting the most points in the specified time is the goal, not answering the most difficult questions. In addition, talk about my own views. I was also careless in junior high school. After the exam, I looked at the careless question and said, "Oh, carelessness, the correct thinking is right." In high school, teachers approved papers quickly and the answers were all wrong. This paper is a great failure. No one will forgive your carelessness. No matter the teacher or yourself, don't have the mentality of "Oh, careless again, it doesn't matter". Even if the addition and subtraction are wrong, we should correct them well, punish them slightly and remember them for a long time.
Question 5: What should I do if I am always careless in high school mathematics? The most annoying thing is that my parents' carelessness affects my academic performance, because I am not infallible. And the same problem has just been corrected today, and the same mistake will be made tomorrow. Under the chagrin, parents' accusations will follow: why are you so careless, why are you so ignorant of being strong, and so on.
In fact, parents' accusations are unreasonable in most cases. There are many reasons for carelessness, but basically it has nothing to do with children's "hard work" and "lack of progress". Among many reasons, the lagging development of learning ability is the fundamental reason.
(A) poor development of attention ability
Distraction is the direct and common cause of sloppy study.
For example, some children do their homework while watching TV, which leads to sloppy learning; Some children always think about computer games or fun toys, and poor attention direction leads to sloppy learning; Other children have poor attention stability when learning difficulty increases, which leads to sloppy learning. ......
(B) poor development of perception
For careless children, the imbalance of visual perception development is the deepest reason. Why do some children write 69 as 96? Why do some children calculate correctly and copy the wrong answers? Why do some children often miss words when reading? The main reason should be the following lack of development of visual perception ability: poor visual perception tracking ability (missing words); Poor visual resolution (Zhang Guan Dai Li); Poor visual perception memory ability (I read it correctly, but didn't remember it, so I wrote it wrong); Poor visual perception integration ability (eyes, brain and hands can't coordinate and dominate, eyes don't reach the brain, eyes and brains don't reach the hand); Wait a minute.
(C) the development of thinking comprehension ability is not enough
On the surface, some children's mistakes are sloppy examination. The deep-seated reason may be the development of thinking ability, such as insufficient development of depth, dialectics and creativity (reverse thinking). So they didn't really understand the meaning of the topic at that time and made mistakes. When they look back, they want to find that they can do it, so they or their parents think it is sloppy.
It should be said that occasional carelessness may be related to other reasons, such as fatigue, depression, inaccurate knowledge and so on. However, if you are often careless, then the above-mentioned poor learning ability is definitely the main reason.
If the ability development is not good, the child is willing but unable. It's not a problem that he doesn't want to pay attention. Therefore, what parents should do is to fundamentally solve the problem of improving children's learning ability. Otherwise, it's useless for you to make up more lessons and criticize more.
After 20 days of training, the learning ability training of interesting learning can quickly improve children's various abilities and effectively solve the problems of children's lack of interest in learning, inattention, poor memory, playfulness, carelessness and low learning efficiency. Solving the problem of the origin of learning and establishing good study habits can greatly improve academic performance even if you don't make up the culture class.
Question 6: What should I do if I am always careless in math and physics in senior two? I used to be like this, but now I can't. Relax, don't be nervous. Just watch it twice. You don't have to sketch word for word, just mark the key points.
It's just that you feel focused. You just focus on playing games.
Usually be careful not to stay up late or something, and you need to pay attention to your diet, otherwise your body will also affect your attention.
Question 7: What should I do if I am always careless in math exams? Carelessness is not the cause, but the appearance. There must be more fundamental reasons behind it, such as inattention, irritability and negative emotions.
In high school, I always blamed my mistakes on carelessness. As a result, there has been no obvious progress for a whole year, and there is always a hurdle that I can't cross. Later, I carefully checked my carelessness and found that the root cause was operability, such as how to use standard steps, but I jumped at will instead of step by step, or the calculations in the draft were too sloppy and did not identify mistakes. ...
Later, after research, I found that most carelessness has fundamental and technical problems, and these problems are concentrated on self-righteousness. In many places, I think I am very skilled and free. Are you really familiar with it? Is there a way for you to answer your name casually when you wake up at midnight?
In short, when people reflect on themselves, they will attribute some factors to very abstract and empty reasons, such as carelessness and absence. In fact, these are just appearances rather than real reasons.
So instead of worrying about carelessness and asking for solutions everywhere, it is better to re-examine those careless places and find out the real reasons, and the solutions will be solved!
Question 8: How can we not lose points in the high school math exam because of carelessness? First of all, we should keep a normal mind and firmly believe that the exam is only to improve ourselves, so that we can better understand ourselves and know how to avoid mistakes.
Don't be too confused in the draft, so that you can check the mistakes better and faster in the rest of the time after you finish the problem.
Moreover, many exams do not lose points because of carelessness. The reason why we are careless is that we usually do less problems and have less training. This will make us waste a lot of time in the process of doing the problem, so we will panic and affect the efficiency of doing the problem later.
So I think the most important thing is to do more questions and pay more attention to accumulation.
Many things can't be rushed for success, which is a kind of accumulation, not to say that you can change them at once if you want to.
Also, when giving yourself some encouragement, you can't have negative encouragement. I can't be careless (This is wrong)
I'll be careful. I will be very serious. Something like this.
Question 9: The carelessness and slowness in high school math problems is not because you check the calculations. Add and subtract in ten minutes, plus "checking". How long can you spend?
This is a question of proficiency. Your real problem is that you don't have a clear grasp of knowledge points and a mathematical idea. High school mathematics is nothing more than derivative inequality, probability sequence, conic space geometric trigonometric function. Do more derivatives, and remember the derivative formula. The derivative is not fancy, and the comparison formula can be directly calculated. The idea of scale in inequality is the key and a difficult point in senior high school. We mainly use general proving problems such as square difference formula, complete square formula and mean inequality to observe the types of things to be proved and analyze how they are simplified. If not, ask the teacher more. Generally speaking, scaling is the last big problem to use, otherwise it is certainly not difficult. There are classical probability permutations and combinations, and it is not a big problem to find a suitable sample space. The high school of sequence is mainly dislocation subtraction, which is mostly used to find recursive formulas. In high school, I calculated the conic curve as super painful, but in college, I thought it was super simple. Put all the known conditions together and bring them into the calculation against the basic quantitative relations of hyperbola, ellipse and parabola, and the result comes out. Don't be afraid of trouble. This kind of problem can eventually merge similar items. More than four basic items indicate that you have done something wrong. Most people are too lazy to calculate this kind of problem, but it is this kind of problem that you'd better get points. Generally speaking, there are two kinds of space geometry, and tetrahedron is more difficult. It is necessary to comprehensively use the vertical relationship between line and surface to establish the coordinate system of cube and calculate the position relationship with vector. The trigonometric function part mainly uses the inductive formulas of double angle and half angle. General formulas are easy to use, but usually unnecessary. Generally, product, difference and difference product are not needed. You can try some disgusting questions without asking.
The biggest feature of high school mathematics is that there are many knowledge points and many things to recite. Each test site contains more than a dozen formulas, which are very consistent. Some problems arise when formulas are written in a natural way and depend on common types. You must solve this problem by yourself. At first glance, the question seems to have nothing to do with what you want. Take two steps and find a guide. Maybe it will be clear after the deduction. Checking calculation is necessary. If there is still an hour left after all the questions are tested, you can check one question after another, or you can count them together after you finish. You are not in the mood to look at the blank calculations at the back.
When you count the questions, you will find that it is nothing more than those things being tossed over and over again. If the basic formula is clear, the problem will be solved faster and faster.
That's it.
Listening to classes is king.