What do you think when you learn to solve problems in mathematics?

Many students have no idea when they see the topic. Today we will introduce it to you. What did Xueba think when he saw the topic? Why do they have ideas when they see the topic? In fact, the first thing that comes to mind is: Have I seen this question?

Then there is whether you have seen similar topics. Then relate the test questions to the one you have seen.

If they are all negative, then go to what Paulia or others said, the process, what transformation conditions and so on.

I used to think of "mathematical thinking" or something. Of course, this thing is really useful, but later I found out that it was because I read it quickly and solved 80% of the exam questions with it.

A person who is not good at math has read it, but he doesn't remember it. Too many people are like this.

The other is that there is no "out of mode".

So "Zhang San in a black suit" and "Zhang San in a yellow vest" are two people in their eyes, but they are one person in the eyes of people who are good at math.

The above is the math before the college entrance examination.

After college, especially those who study mathematics, it is not clear.

I had another whim.

This "seeing" is done in an instant, and most of the topics can be done in an instant, so I generally didn't notice it until someone asked me, "I did what you said, and what conditions changed?" Why can't I do it? " Or why I still can't figure out how to do it? )"

Then I analyzed the process of thinking and found that:

(1) For most problems, there may be a ratio of 4% or 50%. I made a rough estimate. In fact, because I did too many similar problems, I immediately solved them directly.

For example, the first multiple-choice question in the college entrance examination, the set question, should we talk about "mathematical thinking"?

So I have done and read similar topics, which is the foundation.

Solving problems cannot be "water without a source, wood without a root".

So the first moment you see a topic, it must be "have you seen this topic" or "have you seen a similar topic", but this idea is too fast, so it is ignored.

(2) 30% of the questions are probably "can be transformed and quickly return to similar topics".

I remembered a joke. A mathematician lost his job and became a fireman. After a period of training, the general manager then tested him: "If a house is on fire, what steps should be taken to put out the fire?" The mathematician answered fluently.

The manager was very satisfied, so he made a joke and asked the mathematician, "What if you see a house that is not on fire?"

The mathematician said, "Then I'll light it and it will become a known problem."

Although it is a joke, I think the way of thinking when solving problems is actually like this.

Although there are some differences on the surface, these problems can be easily controlled through the "model".

It's just a detour

People who learn well think like this: take a step forward and "bang" on topics they are familiar with.

People with poor learning are like this: change your step and don't know; I don't know how to take another step; Take another step ...

In actual combat, if this is the case, then it has often started to go in the wrong direction and even started to go back.

(3) In the end, about 20% of the topics may really examine mathematical thinking. But I think the real proportion in the college entrance examination paper is less than 20%.

For example, the topic of analytic geometry, as long as it is not the finale, I think it is a test of computing ability and proficiency, and has nothing to do with mathematical thinking.

The last question of multiple-choice questions and fill-in-the-blank questions, as well as the last question, only have a certain probability of reaching the so-called "mathematical thinking", 50%? The proportion is uncertain.

For example, the question 16 of 20 15 new college entrance examination standard 2 can be calculated as simple as 1 or 2 minutes. Just write the answer correctly in the simplest and rudest way.

Then in the end, I estimate that the topic that really needs to be considered is about 10%. At this time, all kinds of thinking may be used, and the transformation and graphic combination are at sixes and sevens.

Finally, there is this question: how to define a person who is good at mathematics?

Mathematicians won the college entrance examination? Full marks in mathematics? Mathematical genius (Gauss)?

In the context, I think I am qualified to answer this question. Of course, if you want to limit the above categories of people, I won't say much.

Then, my major is not mathematics, so although I feel it should be similar, I dare not talk nonsense. I can only say that it is at least before the college entrance examination.

Finally, I looked at Paulia's thinking process again. In fact, he said the same thing to me.

He put "examination" in front, and then "see if you have read (similar topics)".

If we say "the difference between people who are good at mathematics and ordinary people in mathematics", I think it is the difference between "leaving the model".

People who are good at mathematics should have strong direct and abstract thinking ability.