Let's first look at why children learn math well. In fact, there are four main reasons:
1, in order to enter a higher school: you need to take a math test in the entrance examination, and your grades directly affect which school you can go to, which in turn will affect your future.
2, in order to follow the crowd (comparison): other children are studying hard, my child can learn not bad, even if it is not better than other children, it can not be worse than other children.
3. For career: Learning mathematics can better engage in research or work related to mathematics, or need to use mathematical knowledge. Even if you don't learn well, you can rule out some options.
4, for thinking: learning mathematics can exercise the development of thinking, so even if the results are not good, it is worth learning.
It stands to reason that mathematics learning can have significance and influence in any direction. Then let's first analyze the tangible and intangible effects of learning mathematics on our studies, comparison, career and thinking.
In fact, what parents value is not the further education itself, but the growth environment, teacher environment, platform resources and employment situation brought by the school to their children after further education. This is what we can see, and the achievement in mathematics is an important part that affects further studies. In the end, this starting point is reasonable, no matter what the math scores and the results of further studies.
We don't study mathematics for the sake of mathematics itself, but take mathematics as a pure tool for further study. Of course, this is not unique to mathematics, and other disciplines may also have this problem.
Mathematics, as a connotative subject, is not learned because of its connotation. This "impure purpose" is a big obstacle to children's growth and learning (in a broad sense). If you have this kind of mentality since childhood, it is very normal that you don't have such a thing as "learning for the sake of learning" when you grow up, which will have a certain impact on your own growth and progress in all aspects.
Therefore, in order to eliminate this hidden danger, it is necessary to learn more about and study the significance of mathematics learning itself. It is much better to help children apply mathematics learning to life or to help children have fun from mathematics learning itself than to study mathematics simply for further study.
In fact, this is a common problem. Even if parents don't compare their children with other children, teachers, classmates or others may compare them intentionally or unintentionally. And if comparison is the purpose of learning mathematics, the following possibilities are likely to appear.
1, compare.
Comparing with others is not a good thing. On the one hand, it is easy to have inner imbalance and poor happiness. On the other hand, happiness may be based on the pain of others, and interpersonal relationships are easy to be tense.
Step 2 be proud
There are always children who are like a duck to water when learning mathematics. They may be children who imitate patterns, or they may be children who think patterns, but in any case, they have enough proud capital and may develop into pride or conceit. There are three major problems with pride: first, it is easy to think of yourself, look down on others, and cause communication or communication obstacles; One is easy to be self-righteous, but you can't learn the real skills; One is that if one day you suddenly find that you are not so good, you may collapse and suffer far more harm than a child with simple inferiority complex.
Step 3 feel inferior
It is particularly easy to feel inferior in mathematics learning, and the probability of feeling inferior in mathematics learning is much higher than that in Chinese, English and other subjects. This is not only because math is more prone to the phenomenon of poor study, but also because we often combine math scores with intelligence. Inferiority also has three major problems: first, it is difficult to feel happy and satisfied; One is that this fear of doing things often leads to greater failure; One is that children may try their best to hide their inferiority complex, which not only distorts their psychology, but also makes it easier for others to discover our inferiority complex. Once exposed, the damage will be even greater.
As long as it involves the factors of comparison (whether adults or children compare), it will break the ideal state of children's "learning for themselves". "Comparing with others", "pride" and "inferiority" are no joke, and each influence is far-reaching.
If the child learns well, let him know that "there are people outside, there are days behind" and "there is no end to learning and no end to knowing". If the child doesn't learn well, let him know that "there is no fire mountain that can't be crossed, there are always more ways than problems" and "everything will be solved in the end." "Not learning math well" is really far less terrible than "inferiority complex", while "learning math well" but "being conceited" may not be worth the loss, so comparing with others is risky and should be cautious.
In fact, it has been emphasized many times in previous articles that there is not much correlation between math scores and math ability under the math learning mode of memory and imitation, so this often puzzles me.
The author himself graduated from the Department of Mathematics. Most of the specialized courses in the department of mathematics are far away from life, and the teachers' lectures are relatively rigid. Almost all the exams are the original forms of learning and doing, or relatively simple original questions. This phenomenon is not only a single phenomenon in my school, but also in universities all over the country.
Why not change it? Because these original questions have failed some hard-working college students, if you change them again, the result will be even worse. College mathematics is more about changing imitation mode into memory mode, because the content is too complicated, so we have to learn by memory. Many college students majoring in mathematics study very hard.
Other majors may choose a major that is not suitable for them because they don't understand it when they apply for the college entrance examination. Students who apply for mathematics majors generally get good grades in mathematics. How can this happen? Mathematics in American universities is much more difficult and deeper than ours, but they learn better than us. How did we become like this? I think my math scores misled me.
So, be careful with math. If it is suitable for learning mathematics, and we have not chosen a career related to mathematics, it is a pity at most; It will be very painful if you choose a career that requires mathematical ability because it is not suitable for mathematics.
We often hear such words as "learning mathematics can improve intelligence", "learning mathematics can develop thinking" and "learning mathematics can exercise logical thinking", but are these words really correct?
Under the current situation of "imitation mode", "learning mathematics can exercise thinking" is very difficult, and "learning mathematics can exercise imitation" is true. Thinking can't be taught, and neither can math class. Thinking needs to be slowly experienced and perceived by children themselves under the premise of thinking mode. If they have more experience and sentiment, they will have the opportunity to understand the content of thinking and exercise their thinking.
Learning mathematics has the function of developing and exercising thinking, but it is impossible to exercise thinking if you don't have your own thinking in the learning process.
The above four points are all about the significance and influence from the starting point of learning mathematics, but the influence of learning mathematics is not limited to this. 12 years in our primary and secondary schools is not only an effort of 12 years, but also a vital physical and mental growth of 12 years. The influence of mathematics learning on children may be far beyond our imagination.
There are always various difficulties and choices in family, career, communication and life, which need us to face and solve.
In fact, we have the ability to solve problems since childhood. In order to achieve our goal, we can't solve it by crying when we can't speak, but by using words when we can speak and by using our hands when we can do it. After school, complaining to the teacher is to solve the problem that others bully you, lying to parents is to solve the problem that you have done something wrong to cover up, imitating parents' handwriting is to solve the problem that your exam results are not ideal, coquetry is to solve the problem that you want toys, and giving away children's gifts is to solve the problem that you want to make friends, and so on. These are not necessarily taught by children, but are basically countermeasures that children come up with according to their own environment and conditions. And we can find that children may solve problems in different ways in different environments. For example, shopping with mom to buy toys is a way of coquetry and good words, while shopping with dad to buy toys is a way of negotiation. As long as children are given time, space and opportunities for action and practice, they can always find their problem-solving ability, which is great.
So what happens to this ability after school? What does it have to do with mathematics?
1, the ability disappears.
There are always some people in life who are particularly afraid of things and hope that every day is the same pattern. When something bothers them, they are all at a loss and nervous. When they encounter something, they want others to help them or leave it to their fate. So where is your ability to solve problems?
Think about math study. Do you always follow the teacher's instructions step by step? It never occurred to you that you could have any other ideas? Do you always want to see all the questions in the exam? When you meet something you have never seen or are not familiar with, your heart will be pounding? Is it especially dependent on teachers or books?
2. Capacity degradation.
Some people, when encountering problems or puzzles, will not be at a loss, nervous and anxious, nor will they wait for others' help, but will think about who has experienced it and how to do it. If not, just look at Baidu and see how others do it in the network. If you are not at ease, look for relevant articles in this field.
Therefore, it is not difficult for us to understand why there are more and more articles like XXX's methods, XXX's misunderstandings, XXX's precautions, XXX's steps and even a complete interpretation of XXX.
But the same problem is not necessarily the same situation, at least the parties are different and the environment is definitely different. For example, others are suitable for postgraduate entrance examination, but they may not be suitable for themselves. Others are suitable for civil servants. So always do what others say, and there will often be situations that cannot be solved or can't be solved well. Furthermore, these methods are not my own ideas, but my own experience and summary. In other words, the ability to solve problems has deteriorated. Why is this?
Let's think about math learning. Do you always remember questions and formulas? Do you always want to find the corresponding problem when you encounter problems, and then start trying the corresponding formulas and methods? If the previous experience has no effect, is there no way? Have you never thought of any innovative methods by yourself, and never solved a problem that you have never learned?
3. Capacity development.
Some people will find that nothing happens to them. They will think carefully about what is the root of the matter, what factors are related to it, which directions are promising to solve it, what conditions these solutions need, what problems and influences they may encounter when implementing, what is the probability of solving the problem by each method, and where are the key points. When they make a choice, they will also analyze the pros and cons, combine their own goals, and think about the possible results and their acceptance. They will also pay attention to how others choose, but they will never simply look at how to choose, but will analyze it in light of their own situation. This not only greatly improves the probability of solving things, but also exercises the ability to analyze and solve problems, which is a virtuous circle.
Where does their ability to solve problems come from?
Let's think about math learning. Have you ever tried to think about many problems by yourself? Does the teacher always think why when he speaks? Do you dare to try when you encounter problems you have never seen before? Can you occasionally find some rules or skills that the teacher has not talked about? Aren't you superstitious about everything the teacher says?
12 math really won't be learned in vain. Doing every math problem is like solving every problem. After studying and exercising for so long, how can it not affect the future? Moreover, the more questions you do, the harder you study, and the greater your influence on the future. Although many people finally get rid of mathematics after graduation, the influence of the learning process will be lifelong.
We believe that this influence of learning mathematics on problem-solving ability is the greatest influence of mathematics learning on the future and the most far-reaching influence brought by learning mathematics itself. Therefore, as far as the starting point of learning mathematics is concerned, "problem-solving ability" is much more reliable and far-reaching than "for further study", "for satisfying comparison", "for providing career choices" and "for developing thinking", so we are not afraid of any side effects from this starting point.
Because of this, it is more important and meaningful to learn mathematics by thinking.