Is it important to memorize, reason, or comprehend in mathematics?

All important. Is bounce, balance, or physical strength more important in basketball? All important. It is impossible to say that only one aspect needs to be focused on, and the others are not left to care.

So how to improve the targeting.

Take learning math seriously and invest more time and energy. Read more books and take more notes, draw inferences when doing questions, and connect them with the main knowledge of the textbook, so that you will naturally remember it when you think too much. Insist on doing the questions first, think clearly and then write out the process, don't allow yourself to talk nonsense, don't allow yourself to write answers that you can't understand, insist on rigorous answers, and logical thinking will naturally be cultivated.

If you don't finish your homework, you're not allowed to eat, and even if you can't do it yourself, you have to ask others questions online and understand the answers before you're allowed to eat - if you're really interested in learning math, then how can you be in the mood to eat when you don't understand the basic concepts? In the same way, if you are not allowed to eat until the textbook is prepared, you are not allowed to play games, you are not allowed to eat if you don't understand the wrong questions, you are forced to overcome procrastination, and you push yourself a little, so what comprehension ability and messy ability will be raised. People who are really good at mathematics, they can't say what abilities are needed to learn mathematics, they are all internalized.

Of course, the most important thing is to have the heart to learn mathematics, at least a little interest.

I used to neglect memory, but now I feel more and more that memory is very important, and if learning math is like adventure, memory is that you know what you have traveled, which means that you will have more experience; Reasoning ability is whether you can go along this road or not, and whether you have a prospect. (I won't use an analogy if my comprehension is too basic).

As for improvement, I think everyone's method is different, memory mostly uses comprehensible memory and mechanical memory, for example, a very complex formula, generally can only be slightly mechanical to remember it (maybe the derivation process is complicated, the conclusion is also complicated), but for the conclusion of the perfect theory or theorem, such as the Lagrangian median value theorem, the fundamental theorem of calculus, Fermat's theorem, you can respectively from the geometry, the relationship between derivatives and definite integrals, the order of the element in zp, comprehensible memory, It is worth noting that you can draw a network of theoretical systems to remember the whole theory, the simplest example, the fundamental theorem of calculus can be derived from the Lagrangian median value theorem, which itself involves the concepts of derivatives, definite integrals, limits, etc., which can roughly outline the entire theoretical system of calculus, in this way, remember that a system has rules to follow, that is, starting from the core point, diverging, you can also string the systems together, such as the group ring field in the extraction, their isomorphism, the regular subgroup of the group, the ideal of the ring, The formal extension of the domain, the homomorphism theorem, can be compared with each other to assist memory.

Once I have built a large network, I have grasped the backbone of a theory, so that I can fill in some details, so that I can remember a lot of things, which is my personal learning method.

All are important, but I personally think that comprehension is more important, and if you understand the knowledge points of mathematics, you will naturally remember it and be able to use it flexibly, and be able to reason on the basis of understanding, so comprehension is very important.

are all important. You don't have a memory, how do you memorize formulas, you don't have reasoning skills, how do you do problems, you can't understand it, how do you learn.

I think the ability to understand is the most important thing, and the ability to understand is needed in the process of looking at the analysis.

Mathematical Reasoning Ability:

The ability to correctly use the laws and forms of thinking to analyze, synthesize, reason, and prove the properties of mathematical objects or mathematical problems.

Importance: Mathematics attaches importance to the basic concepts and basic principles of mathematics, which has the characteristics of rigorous logic, and logical reasoning ability should be one of the basic mathematical abilities that students must have. Teaching of basic concepts and basic principles is the core content of mathematics teaching. In mathematics teaching, students can use it to reason and prove that they are taught some necessary logical knowledge in combination with specific mathematics content.

In general, men's gray matter is twice that of women, and women's white matter is 10 times that of men, and the general structure of women's cerebral hemispheres is closely connected, so the brain hemispheres of the brain are highly efficient, which shows strong memory, but the male cerebral hemispheres are almost independent, so the ability to analyze specific things is strong. However, this is a congenital condition, and all this can also be improved by acquired exercise, for example, if a woman likes to think, then the amount of gray matter will also increase, and the same is true for white matter. On the contrary, even in men, if they don't like to use their brains, the apoptosis of gray matter will gradually accelerate, and the white matter of women is also the same, so the focus is not on the congenital condition, but on whether the acquired exercise is sufficient.

At the same time, I have also done some research in this area, and found that memory actually belongs to the realm of the mind, which cannot be attributed to the ability to analyze, and the so-called memory can only stay in simple propositions on the senses, and the memory of complex propositions needs to divide it into multiple simple propositions in an orderly manner, and it is still recombined through logical ability to complete the output when indexing. Therefore, when the analysis of complex propositions is not rigorous enough, it is likely to produce a certain deviation in the output. Therefore, the embodiment of memory ability also needs a certain logical ability as support, so it seems that memory ability and logical ability are not only not contradictory, but also coordinate with each other and are inseparable!

I hope my answer is helpful to you.

Logic is not innate, but.

It's nurture, reasoning is based on facts, not imagination, and I think if you have a strong reasoning ability.

people, memory is not good, so the common sense and basis of reasoning come from?

However, this kind of thing will happen if you say too much and believe it, and it is difficult for this situation to exist in most cases until the child has formed "common sense".

Not really. I am a person who has good logical reasoning skills. Since childhood, he has been highly gifted in mathematics.

And even though I am good in the liberal arts department, my memory is not bad.

Personally, I don't think there is a necessary connection.

Don't take all the words of those experts because you haven't studied them, he's up to them.

It's hard to say, because there are no definite theories in the world.

In our daily life and study, we have to come into contact with a large number of things every day, some of which are easy to remember, and some of which are not easy to remember. It turns out that memory is closely related to attention. Although Li Hewu often met, he did not attract ideological attention, so he forgot about it.

On the other hand, in the process of repeated observation and study of a certain thing, it is easy to remember it if you pay close attention to it.

Professor Wu Wenjun, a famous mathematician in China, was so busy studying mathematics that he couldn't even remember his birthday. One day, a guest came to visit him, and when he met him, he said:

Listen to your wife, today is your 60th birthday, I would like to congratulate you! ”

Professor Wu listened and said casually

Oh, is it so pure? I forgot! ”

The guest was puzzled and thought, "I'm afraid this mathematician is old and confused, otherwise why would he even forget his birthday?" However, when they talked about Professor Wu's research on the problem of proving geometry with a machine, the guest pointed to a machine designed by the professor and asked

When was this machine installed? ”

December 6 last year. "The professor doesn't think twice.

What progress have you made in researching the problem of proving geometry with machines? The guest asked again.

Big progress can't be talked about. By January 11 this year, I had programmed more than 300 'commands' for the computer and completed the first step of preparation. The professor continued.

At this time, the guest asked in great surprise

Professor Wu, you can't even remember your own birthday, but you remember these days very clearly, what is the reason for this? ”

Professor Wu smiled heartily:

I never keep track of those meaningless numbers. In my opinion, what does it matter if the birthday, one day earlier, one day late? So, I don't remember my birthday, my lover's birthday, my children's birthday, but there are some numbers that I have to remember and are easy to remember.

For example, the end of the year, December, of course; And 6 is exactly half of 12. At the beginning of the year, it was naturally January, and on January 11, the Arabic numerals were 111, and the three 1s were rowed, which was easy to remember. ”

Einstein's ** number is 24361. When asked how he remembered this data, he said:

Two dozen, plus 19 squared. ”

Bocieu (1730-1814), the author of a well-known textbook on mathematics and fluid mechanics, was visited by a friend of his friends when he learned that he was critically ill.

The patient is dying! The doctor said.

He can't speak anymore! "The relatives called for friends to disturb for a long time, but there was no response.

Don't worry," said the guest, "I have a solution." ”

He walked over to the dying Boxiu bed and asked loudly

What is the square of 12? ”

144！The mathematician whispered, and after saying the number, he stopped breathing.

Memory is the ability to recognize, maintain, recognise and reproduce the content and experience reflected in objective things.

The word "comprehension" is derived from the Latin "comprehender e", which means "grasping the whole", which means the ability to know, cognize, and transform a certain thing or thing.

Everything needs to understand the divine power, so we need to enhance our understanding and make Kaixiang himself take a big step forward.

Mathematical Reasoning Ability:

Correctly use the laws and forms of thinking to analyze and synthesize the properties of mathematical objects or mathematical problems, and reason to prove the ability to fail to judge.

Importance: Mathematics attaches importance to basic concepts and basic principles, and mathematical mathematics has the characteristics of rigorous logic, and logical reasoning ability should be one of the basic mathematical abilities that students must have. Emphasis on the teaching of basic concepts and basic principlesThe basic concepts, basic principles and basic volt modification methods in mathematics knowledge are the core content in mathematics teaching. In mathematics teaching, students can use them to reason and justify.