All-round mathematician
Chapter 17 Mathematical Thinking
Chapter 17 Mathematical Thinking
On the afternoon of the 1th, Yang Fan took a nap for an hour to let his brain refresh for a while.Set the alarm clock to 10 o'clock, get up, and run to school in [-] minutes.
There were three students in the classroom. Lin Yuwei saw Yang Fan appearing from a distance, a look of surprise flashed across her face, and she pretended to be calm and did not speak.
Yang Fan pretended to say hello to the other two, returned to his seat, and said, "Take out the paper."
Lin Yuwei obediently handed it over. Yang Fan saw that there were already many messy handwriting on the last two questions. She must have tried many times, and finally came to ask for help when she had no choice.
"Lin Yuwei, please tell me first, I think you have written about your own thinking, but it may not be on point."
Lin Yuwei approached, wrote and drew on the paper, and whispered some thoughts.
This intimate act fell into the eyes of the remaining one man and one woman.They looked at each other and gave each other a grimace.
"Hey, I'm telling you two, don't make random guesses." No need to look behind, Yang Fan and the others are joking, "If there is really an inside story, will it be in the classroom?"
The two passers-by were stunned for a moment, that's right, where they can't go, but they have to choose a classroom, it seems that they have made a mistake.
Lin Yuwei's heart is warm, he is really a careful boy.
"Lin Yuwei, this question is difficult, but it is not impossible to do it at all. Let me tell you, you must first put yourself in the perspective of the questioner. Are they deliberately making things difficult for you and leaving you clueless?
Obviously not, they are trying to dig a trap to divert your thinking.Some questions are easy because of the lack of variables, and some are difficult, just digging holes for you to enter. "
These words fell into the ears of the three of them, their eyes suddenly brightened, and there was a sense of far-sightedness in an instant, pushing away the clouds and mist.
"Yang Fan, I don't know how, add me."
"Yang Fan, you speak well, can I listen too?"
"Okay, you guys come here too. Recently, I have some experience in mathematics. It's no problem for everyone to communicate with each other."
The four sat around a table, with Yang Fan as the center, sitting in a pile.Yang Fan is not just addressing that issue, it is better to teach a man to fish than to give him a fish.
After talking like this for nearly an hour, Yang Fan spoke frankly, and the listeners were even more delighted.
"Let me tell you, here... ouch." Yang Fan bumped his head against Lin Yuwei, touched his forehead, and saw that there were seven or eight people surrounded.
"Hey, Yang Fan, why don't you talk about it, talk about it quickly."
"I just heard something, hurry up."
"Yes, yes."
"No, everyone is crowded together, and there is no place to put their heads." Seven or eight heads were piled together, and they would bump into each other with a slight movement.
"No, you have to tell me, what does it matter if everyone squeezes together?"
"You can't just talk to Lin Yuwei, I'm going to gossip if you act like this."
Lin Yuwei's face turned red, why did she get involved.
The students were eager to study, and Yang Fan felt a flame in his heart, and said: "Okay, you all sit in your seats, and I will write on the blackboard. Today, I will talk to you."
Yang Fan confidently walked to the podium, wrote down the questions, waited for them to sit down one by one, nodded and said: "As I said just now, math questions will never deviate from the outline. Difficult questions and simple questions are similar to a certain level.
When you entered Wuzhou Middle School, you were all top students in junior high school.No one has a low IQ.We must first have a pair of eyes to see through the fog. This question gives four conditions.Let's simply calculate what results can be obtained after each condition is given..."
Yang Fan talks eloquently, flamboyantly and calmly.For a mathematical problem, under his hands, from difficult to easy, he will analyze the answer in three or five sentences.
"This condition is actually misleading by the person who made the question. He doesn't directly tell you what you can get, but lets you guess. After matching the answer, we will know his sinister intentions, and let your thinking go to the abyss..."
It was already two or three o'clock in the afternoon, which happened to be the peak time for day students to enter the school.When the students entered the class, they found Yang Fan explaining on the podium, and consciously entered through the back door.
Listening, I was instantly attracted by his thoughts, and joined the team who listened carefully.
In science, the most difficult question is usually the last question.For the students who came to school, someone made it, but it took a lot of time.
But now, listening to Yang Fan's explanation, I realized that there is a world of difference between myself and him.The kind of bloody tearing apart the subject's purpose is more incisive and shocking.
"Okay, now we know the answer. Let me ask, when you want to test your classmates with a question, what will you do when you are also the tester. These four conditions are all necessary.
If you want to make it the most difficult, it is the current format, and if you want to make it a little easier, it is some steps in our problem-solving process.Now, who doubts it? "
Twenty or so students closed their eyes and meditated at the same time, and suddenly found that the last question seemed to be easier than the previous ones. Why?
It is clear.I understand.
Lin Yuwei was the first to applaud. She was excited that her understanding of mathematics had greatly increased, and she was excited to find the right person.
The other students applauded, and some people yelled even louder: "Yang Fan, bull B."
"Don't be funny, the class next door heard it." Yang Fan waved his hand.
Suddenly someone in the corridor applauded.
Next door is the fourth class of the same grade, and someone has already found out about the third class.Yang Fan didn't pay attention on the podium, and the audience didn't pay attention, but the enthusiasm of a group of students for knowledge must not be underestimated.
"Yang Fan, it's still early. Both of our classes are working on this paper, and now we just got the answer right." The class leader Zeng Sisi thought about it. Once she spoke, who would dare to object.
"Everyone in the corridor, we are not all here yet, come in and listen together, stand with a notebook, people will say that our class is stingy."
Zeng Sisi directed the last few people to vacate their seats and invited them to sit in the back row.
A few people from the next class entered shyly, and some even returned to their own class immediately, picked up the papers and ran over.
Yang Fan was a little bit stuck, how could it be like this.Not my intention.
"Yang Fan, hurry up."
"First question, I choose B, how about you?"
"Don't talk to anyone, listen to Teacher Yang." Zeng Sisi yelled, laughing too.
"Okay. Then let's start with the first question. It's C."
The class is very active, so there is no need to pay attention to discipline at this time. Once you find yourself wrong, you will scream. If you are right, you will be complacent, and at the same time ridicule other students' low-level mistakes.
For each question, Yang Fan would ask the wrong students to raise their hands, and skip it when there were few people, and analyze them one by one when there were too many people.
"There is a trap here, so half of the students made a mistake. This mistake is very low-level. Two points are lost. Let's see..."
"There is a difference of thought here. Left and right look right, but they are all wrong. Be careful..."
One lecture lasted another hour, and when I looked up, the seats in the class were full, and the class next door took up a small half.
The teachers in both classes repeated that they were both opponents and comrades-in-arms.
There are many people in my own class.Song Minghui was restless and didn't speak.
Ye Haoran would nod in agreement from time to time, obviously following Yang Fan's train of thought.
Qi Yueshu was always hesitating between bowing his head and raising his head, shy after his eyes collided.
Xiao Hongye also arrived, dragging his chin with both hands, staring at the podium without moving, and not long after, the saliva dripped onto the textbook.Let all the single-born dogs in the class next door who watched the goddess collapse their beliefs.
At this moment, Yuan Wenbo arrived in a hurry. He hadn't figured out the situation yet, and shouted: "Everyone is here, brothers, the sophomores are robbing our court, come and help us. We are being beaten by them."
The cry was very loud, Yuan Wenbo expressed his sympathy, and spoke very sadly.
Zeng Sisi glanced at him reproachfully, there are too many muscular men, it's really hard to figure it out, she won't do a few more questions in this time.
Just as he was about to be driven away, a group of male classmates refused.
"What, you are so arrogant."
"A sophomore in high school, don't you know how to respect your seniors?"
"Kill them, let's go."
Teaching one person is not the same as teaching a class. Yang Fan also felt that he was working too hard, so he should run away early and go to the stadium to relax.
"Okay, it's over. Yuan Wenbo, let's go."
"Hey, Teacher Xiao Yang, tell me more."
"You male classmates are all idiots. You have high hormones all day long."
"Yang Fan, you..."
Seeing someone calling him, Yang Fan didn't dare to linger, nodded to Lin Yuwei, and shouted: "I am a sports boy, born to play basketball, let's go."
A group of male students followed immediately, but the female students were silent, so go and have a look.
(End of this chapter)
On the afternoon of the 1th, Yang Fan took a nap for an hour to let his brain refresh for a while.Set the alarm clock to 10 o'clock, get up, and run to school in [-] minutes.
There were three students in the classroom. Lin Yuwei saw Yang Fan appearing from a distance, a look of surprise flashed across her face, and she pretended to be calm and did not speak.
Yang Fan pretended to say hello to the other two, returned to his seat, and said, "Take out the paper."
Lin Yuwei obediently handed it over. Yang Fan saw that there were already many messy handwriting on the last two questions. She must have tried many times, and finally came to ask for help when she had no choice.
"Lin Yuwei, please tell me first, I think you have written about your own thinking, but it may not be on point."
Lin Yuwei approached, wrote and drew on the paper, and whispered some thoughts.
This intimate act fell into the eyes of the remaining one man and one woman.They looked at each other and gave each other a grimace.
"Hey, I'm telling you two, don't make random guesses." No need to look behind, Yang Fan and the others are joking, "If there is really an inside story, will it be in the classroom?"
The two passers-by were stunned for a moment, that's right, where they can't go, but they have to choose a classroom, it seems that they have made a mistake.
Lin Yuwei's heart is warm, he is really a careful boy.
"Lin Yuwei, this question is difficult, but it is not impossible to do it at all. Let me tell you, you must first put yourself in the perspective of the questioner. Are they deliberately making things difficult for you and leaving you clueless?
Obviously not, they are trying to dig a trap to divert your thinking.Some questions are easy because of the lack of variables, and some are difficult, just digging holes for you to enter. "
These words fell into the ears of the three of them, their eyes suddenly brightened, and there was a sense of far-sightedness in an instant, pushing away the clouds and mist.
"Yang Fan, I don't know how, add me."
"Yang Fan, you speak well, can I listen too?"
"Okay, you guys come here too. Recently, I have some experience in mathematics. It's no problem for everyone to communicate with each other."
The four sat around a table, with Yang Fan as the center, sitting in a pile.Yang Fan is not just addressing that issue, it is better to teach a man to fish than to give him a fish.
After talking like this for nearly an hour, Yang Fan spoke frankly, and the listeners were even more delighted.
"Let me tell you, here... ouch." Yang Fan bumped his head against Lin Yuwei, touched his forehead, and saw that there were seven or eight people surrounded.
"Hey, Yang Fan, why don't you talk about it, talk about it quickly."
"I just heard something, hurry up."
"Yes, yes."
"No, everyone is crowded together, and there is no place to put their heads." Seven or eight heads were piled together, and they would bump into each other with a slight movement.
"No, you have to tell me, what does it matter if everyone squeezes together?"
"You can't just talk to Lin Yuwei, I'm going to gossip if you act like this."
Lin Yuwei's face turned red, why did she get involved.
The students were eager to study, and Yang Fan felt a flame in his heart, and said: "Okay, you all sit in your seats, and I will write on the blackboard. Today, I will talk to you."
Yang Fan confidently walked to the podium, wrote down the questions, waited for them to sit down one by one, nodded and said: "As I said just now, math questions will never deviate from the outline. Difficult questions and simple questions are similar to a certain level.
When you entered Wuzhou Middle School, you were all top students in junior high school.No one has a low IQ.We must first have a pair of eyes to see through the fog. This question gives four conditions.Let's simply calculate what results can be obtained after each condition is given..."
Yang Fan talks eloquently, flamboyantly and calmly.For a mathematical problem, under his hands, from difficult to easy, he will analyze the answer in three or five sentences.
"This condition is actually misleading by the person who made the question. He doesn't directly tell you what you can get, but lets you guess. After matching the answer, we will know his sinister intentions, and let your thinking go to the abyss..."
It was already two or three o'clock in the afternoon, which happened to be the peak time for day students to enter the school.When the students entered the class, they found Yang Fan explaining on the podium, and consciously entered through the back door.
Listening, I was instantly attracted by his thoughts, and joined the team who listened carefully.
In science, the most difficult question is usually the last question.For the students who came to school, someone made it, but it took a lot of time.
But now, listening to Yang Fan's explanation, I realized that there is a world of difference between myself and him.The kind of bloody tearing apart the subject's purpose is more incisive and shocking.
"Okay, now we know the answer. Let me ask, when you want to test your classmates with a question, what will you do when you are also the tester. These four conditions are all necessary.
If you want to make it the most difficult, it is the current format, and if you want to make it a little easier, it is some steps in our problem-solving process.Now, who doubts it? "
Twenty or so students closed their eyes and meditated at the same time, and suddenly found that the last question seemed to be easier than the previous ones. Why?
It is clear.I understand.
Lin Yuwei was the first to applaud. She was excited that her understanding of mathematics had greatly increased, and she was excited to find the right person.
The other students applauded, and some people yelled even louder: "Yang Fan, bull B."
"Don't be funny, the class next door heard it." Yang Fan waved his hand.
Suddenly someone in the corridor applauded.
Next door is the fourth class of the same grade, and someone has already found out about the third class.Yang Fan didn't pay attention on the podium, and the audience didn't pay attention, but the enthusiasm of a group of students for knowledge must not be underestimated.
"Yang Fan, it's still early. Both of our classes are working on this paper, and now we just got the answer right." The class leader Zeng Sisi thought about it. Once she spoke, who would dare to object.
"Everyone in the corridor, we are not all here yet, come in and listen together, stand with a notebook, people will say that our class is stingy."
Zeng Sisi directed the last few people to vacate their seats and invited them to sit in the back row.
A few people from the next class entered shyly, and some even returned to their own class immediately, picked up the papers and ran over.
Yang Fan was a little bit stuck, how could it be like this.Not my intention.
"Yang Fan, hurry up."
"First question, I choose B, how about you?"
"Don't talk to anyone, listen to Teacher Yang." Zeng Sisi yelled, laughing too.
"Okay. Then let's start with the first question. It's C."
The class is very active, so there is no need to pay attention to discipline at this time. Once you find yourself wrong, you will scream. If you are right, you will be complacent, and at the same time ridicule other students' low-level mistakes.
For each question, Yang Fan would ask the wrong students to raise their hands, and skip it when there were few people, and analyze them one by one when there were too many people.
"There is a trap here, so half of the students made a mistake. This mistake is very low-level. Two points are lost. Let's see..."
"There is a difference of thought here. Left and right look right, but they are all wrong. Be careful..."
One lecture lasted another hour, and when I looked up, the seats in the class were full, and the class next door took up a small half.
The teachers in both classes repeated that they were both opponents and comrades-in-arms.
There are many people in my own class.Song Minghui was restless and didn't speak.
Ye Haoran would nod in agreement from time to time, obviously following Yang Fan's train of thought.
Qi Yueshu was always hesitating between bowing his head and raising his head, shy after his eyes collided.
Xiao Hongye also arrived, dragging his chin with both hands, staring at the podium without moving, and not long after, the saliva dripped onto the textbook.Let all the single-born dogs in the class next door who watched the goddess collapse their beliefs.
At this moment, Yuan Wenbo arrived in a hurry. He hadn't figured out the situation yet, and shouted: "Everyone is here, brothers, the sophomores are robbing our court, come and help us. We are being beaten by them."
The cry was very loud, Yuan Wenbo expressed his sympathy, and spoke very sadly.
Zeng Sisi glanced at him reproachfully, there are too many muscular men, it's really hard to figure it out, she won't do a few more questions in this time.
Just as he was about to be driven away, a group of male classmates refused.
"What, you are so arrogant."
"A sophomore in high school, don't you know how to respect your seniors?"
"Kill them, let's go."
Teaching one person is not the same as teaching a class. Yang Fan also felt that he was working too hard, so he should run away early and go to the stadium to relax.
"Okay, it's over. Yuan Wenbo, let's go."
"Hey, Teacher Xiao Yang, tell me more."
"You male classmates are all idiots. You have high hormones all day long."
"Yang Fan, you..."
Seeing someone calling him, Yang Fan didn't dare to linger, nodded to Lin Yuwei, and shouted: "I am a sports boy, born to play basketball, let's go."
A group of male students followed immediately, but the female students were silent, so go and have a look.
(End of this chapter)
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