I am reborn and just want to concentrate on my studies

As soon as Tang Guangrong entered the office, Yi Yang knocked on the door.

Just after putting down the lesson plan, Tang Guangrong looked back and saw a student in his class. He showed a slightly surprised expression and asked, "Is something wrong?"

Yi Yang hesitated for a moment, because the teacher did not say "please come in", so he stood at the door and said, "There is a little problem..."

Teacher Tang said: "Come in and talk."

Only then did Yi Yang walk into the office.

Tang Guangrong unscrewed the lid of the tea cup, blew lightly, took a sip, and asked, "What's the problem?"

Yi Yang stood up, organized his language a little, and said, "Teacher Tang, my score dropped a bit in this math test. I heard you talk about scientific thinking in class today, and I felt that I I don’t have that kind of scientific thinking yet, so I came here to ask you to help me analyze it.”

Tang Guangrong did not interrupt Yi Yang and listened carefully to what he said. Then he thought about it and nodded: "I probably understand what you mean."

He glanced at Yi Yang again and thought for a moment, "Your name is Yi Yang, right..."

Although it has been a long time since school started, Tang Guangrong, a subject teacher, still cannot remember the names of the students in the class. The main reason is that Yi Yang always keeps a low profile, and Tang Guangrong does not have the habit of asking questions in class.

Of course, this is treated equally. Tang Guangrong has never been in the habit of memorizing students' names.

Yi Yang nodded.

Tang Guangrong smiled and said, "You have two questions. Let's talk about them one by one."

"The first thing is the decline in grades this time."

"In fact, you don't need to worry too much about this matter. In fact, the difficulty of the test questions this time is on the high side. You may not find it difficult, but there are a few places where your thinking needs to be turned, and the settings are relatively obscure. This set of questions is what I If you can score more than 110 points on this set of test papers, I think it is reasonable to set the college entrance examination difficulty level to about 130 points."

Yi Yang was slightly startled, is it difficult?

"The second question is about scientific thinking."

"Well..." Tang Guangrong looked at his watch. He had just finished class and still had time, so he thought about it and said, "There is no standard definition of the so-called scientific thinking. The following concepts are all mine. You can use some personal insights in your study practice. If it suits you, use it. If it doesn’t suit you, you can also explore a learning method that suits you.”

Yi Yang nodded quickly.

"I use two words to summarize this scientific way of thinking: management."

Yi Yang frowned slightly.

"What is management? To put it simply, it is the ability to manage knowledge systems."

As he spoke, Tang Guangrong opened the mathematics book and said, "Here, let me give you an example so that you can understand this concept more intuitively."

Turned to the "Concept of Sets" page.

Only one page contains the definitions of sets and elements, the certainty of set elements, the uniqueness of set elements, the equality of sets... eight or nine concepts.

Tang Guangrong said: "This page very typically reflects the characteristics of high school science. It is driven by a conceptual knowledge system, with a high density of concepts, a large amount of knowledge, a strong correlation of knowledge, and layer-by-layer dependence, with a high degree of abstraction. "

"If you don't understand, memorize it first, answer the questions after you can do it, and learn this knowledge through repeated contact and proficient problem solving, it probably means that you have not yet formed a management mindset."

Yi Yang was silent for a moment and couldn't help but say: "I actually have a knowledge system in my mind..."

Tang Guangrong laughed loudly, waved his hand and said, "I'm not targeting you, but what I want to say is that the so-called knowledge system established by most students, such as the mind maps you often use, is actually a What is a system that is forcibly pieced together? Let me give you an example. The knowledge system that many students have established is no different from the table of contents at the front of our math book. When I think back, oh, we have learned this knowledge. But that is a classified system, a patchwork system. If setting up the system was so simple, everyone would just have to memorize the table of contents..."

Yi Yang was stunned. When he thought about it carefully, all his summarizations and summaries of knowledge since junior high school were indeed more like a more detailed catalog...

Anyway, this knowledge system is very useful when studying history.

Tang Guangrong took another sip of tea and continued: "But the system knowledge forcibly pieced together allows you to have a memory of what you have learned. In the final analysis, it is still liberal arts thinking. The nature of science and liberal arts is different. Use this kind of thinking There is no way to truly understand the subject through this method.”

Yi Yang couldn't help but ask: "Then Teacher Tang...how can we master the real system?"

Tang Guangrong smiled slightly. He saw the light of an extreme thirst for knowledge in Yi Yang's eyes. This strong and fiery emotion made him very happy.

Because this is a key high school, the vast majority of students are not lacking in self-consciousness and hard work, but they lack a kind of humility.

Why do you say that? It can be concluded that since he entered the key high school to teach, at least half of the students he has taught prefer self-study. The teacher talks above and they do their own things below.

There is a joke that says:

In ordinary high school, you think the teacher is stupid, and the teacher thinks so of you.

In key high schools, if you think the teachers are awesome, the teachers will think so of you.

Tang Guangrong doesn't know if his students think they are awesome, but he does know that most of the students who can enter key high schools have IQs at least above the average, and their self-learning ability and understanding are not to mention. Some students even Putting the teacher to shame...

Over time, he didn't care what the students below were doing during class. They walked at their own pace, which didn't matter. They had to follow the teacher's pace, which was naturally better.

Wang Yangming said that knowledge and action are integrated. Most students in key high schools have their own set of learning methods and ways of thinking. If you instill some of your own things into them, they may not be happy to accept it.

Therefore, he would not take the initiative to tell students about some things about learning experience.

There was something special about Yi Yang in front of him, he was very humble.

Tang Guangrong smiled and said: "How to master the real system... two words, reasoning!"

"reasoning?"

"Yes, reasoning. This learning method is applicable to all science subjects. This is an ability that must be acquired through continuous training. It is the ability to deduce the core knowledge system of the subject with bare hands."

"Only a system that you have derived by yourself has a clear context and strong organization. You can still effectively control hundreds or even thousands of subject knowledge points."

"Let's take the first section of the collection as an example. How can we form a real knowledge system? Come on, follow my train of thought and I'll take you through it."

"There are many knowledge points in this section, including the representation and description of sets, belonging and not belonging... there are ten of them. If you are asked to name these knowledge points, you can only memorize them by rote because you do not understand these knowledge points. interrelationships and overall structure.”

"First of all, we start learning from the definition. The definition of sets and elements is the starting point of the set knowledge system."

"With a definition, there will be properties. We study the basic properties of sets, which are certainty and uniqueness."

"Next, we start to study relationships. We already have the definitions of two basic concepts, sets and elements, so we are studying the basic relationship between the two. What is it? It means belonging and not belonging."

"Next, in order to facilitate research, we need a more concise and efficient expression, so the next thing we will learn is the representation of sets..."

"Okay, this is the knowledge context of this section. How can we deduce the core knowledge system of this section from scratch through such refining and combing? No need to memorize it by rote?"

"You can understand now. If the knowledge system is compared to a tree, the patchwork knowledge system is that you have a picture of a tree in your mind, how many branches are there on the trunk, and how many branches are there on the branches? You remember it."

"As for the logical system, you should learn and understand the knowledge and have the backbone of the knowledge. Then every branch and branch of it can be deduced in a very short time when needed. There is no need to memorize. This is a kind of ability. Once you master this ability, knowledge will not be easily forgotten and can be used throughout your life."

“To learn mathematics, you don’t need to memorize, just understand.”

At this time, the bell rang.

Yi Yang silently remembered and digested Tang Guangrong's words, and said seriously: "Thank you, Teacher Tang!"

Tang Guangrong waved his hand: "Thank you, the teacher should do it. You can practice it yourself after you come down. It may not be useful to every student... Well, let's go to class."

…

It will take some time to digest and integrate what Teacher Tang said, but it has already opened up a new way of learning for Yi Yang.

He has always known the importance of a knowledge system, but as Teacher Tang said, the knowledge system constructed before was more inclined to a system based on liberal arts thinking.

Compared with science, some knowledge in liberal arts can actually be connected using this kind of logic, but more still requires memorizing some things, especially if there are not many conceptual things involved, so the "patchwork knowledge system" sometimes even It is necessary.

But science is different. Think about Luo Bing at this time. He has such an ability. He does not spend that much time on memory. For example, if he masters a concept, he can then follow its properties, expressions, and corresponding formulas. , through the little impressions learned in class, you can recall it in a few seconds when doing the questions...

Now I understand that it is not a memory, but actually a derivation.

It’s just that this ability is simple to say, but to be able to really apply it in exam situations, on the one hand, you must have a thorough understanding, and on the other hand... it still requires a lot of practice!

This kind of exercise is not a mindless exercise.

Instead, we understand and build a conceptual knowledge system in a targeted manner.

Science is a discipline based on a conceptual knowledge system!

Once you understand this clearly, the next learning direction will be clear.

At this moment, Yi Yang felt a sudden enlightenment.

The correct way to start studying science is to have a thorough understanding.

Exam-oriented education is the pursuit of skilled application.

Of course, you can't aim too high. From a performance perspective, skilled application is also effective in the short term. This is probably why some people can keep up with the pace when they first enter high school.

It’s just that as the knowledge system becomes more and more complex, there are more and more knowledge points, and the relationship between concepts becomes closer, the more difficult this approach becomes to work.

This is also why some students’ grades plummet in the later stages of high school.

It is because I have too much knowledge in late high school and have not established a good knowledge system, which makes me confused.

Next, we need to build a new knowledge system in this way.

But it can also be foreseen that this will be a longer and more difficult process... Some simple concepts can be easily understood, but some slightly more complex concepts and properties, formulas, and variations of formulas derived through complex concepts , maybe the derivation process is enough to burn the brain, and what he wants to achieve is to be able to quickly deduce when doing the questions in the continuous understanding process, which is even more difficult.

If you can't master it once, just try it a few more times, and the questions will serve as a touchstone to test how firmly you master the knowledge.

Building your own knowledge system bit by bit in this way will be of endless benefit.

This class was a Chinese class, but Yi Yang couldn't help but open the math book at this time.

At this time, the head teacher Shen Xiaoding was talking about Cao Cao's short song line very passionately.

While Wang Sangning was reading Liquor and Song, The Geometry of Life, she was inspired and wrote down in her notebook...

I read poems to my father,

Recite Cao Cao's song of wine and wine,

Thinking about Cao Cao’s life,

Father said,

Cao Cao is a powerful man,

but,

You are underage,

No alcohol allowed.

After finishing writing, she couldn't help but smile, and then she felt ashamed for not doing her job properly, and secretly glanced at Teacher Shen...

But then, she saw Yi Yang holding a math book and writing and drawing on a scratch pad.

For a moment, Wang Sangning had a complicated expression.

Yi Yang tried to use this method to derive the knowledge system related to equations and inequalities.

Naturally, all this knowledge is mastered. After all, this part of the knowledge is very difficult in the high school mathematics knowledge system, so this process does not take long.

Based on the basic concepts of inequalities, we gradually derive its properties, basic inequalities... various advanced concepts, and compare them one by one with the knowledge points in the book.

In this process, every step is interlocked and is a complete logical chain. Then when a certain knowledge point is half understood, it can be clearly reflected in the constructed knowledge system, oh here Haven't completely mastered it yet.

In this way, whether you ask the teacher or your classmates, slowly understand, and you will be able to master all the knowledge thoroughly without leaving any blind spots.

This method is more taxing and time-consuming than simply memorizing formulas, but Yi Yang believes that spending more time on this is much better than meaninglessly answering questions.

Of course, this does not mean that answering questions is useless, but it is only meaningful to answer questions on the basis of understanding the basic knowledge.

When Yi Yang was immersed in the pleasure of building a knowledge system and couldn't extricate himself, Teacher Shen suddenly said: "Let me ask a classmate to share his experience of reading this poem... Well, Yi Yang!"

Everyone looked over.

Yi Yang was startled and stood up subconsciously.

Oops...what poem? How many pages? Which sentence?

Although he was panicking inside, Yi Yang's expression was very calm and he said: "When I read this poem, my heart was extremely excited..."

Then I caught a glimpse of Wang Sangning's notebook.

"However, I'm underage, so it's best not to drink..."