pjbooks Chapter 12: Going with the Flow
Chapter 12: Going with the Flow
The second class the following morning was math class.
Holding the graded exam papers, Cao Wen walked into the classroom and stood on the podium.
The previously noisy discussion in Class 09 instantly quieted down.
After scanning the classroom with his eyes, Cao Wen slammed a thick stack of test papers onto the desk.
"In yesterday's mock monthly exam, the class average score was 86.4, which is 1.2 points lower than last month's diagnostic test!"
Cao Wen's gaze swept from the podium across the silent classroom.
"Can anyone tell me what's going on?"
"Are you getting worse the more you study? All that knowledge has been wasted?"
The classroom was deathly silent, the atmosphere so quiet it was almost oppressive.
On the podium, Cao Wen continued to "exert his knowledge": "How have I been teaching you? Hmm? When you encounter a problem you don't know how to solve, no matter what, don't leave it blank!"
"Even breaking down the equations in the problem and listing the relevant theorems might earn you points!"
"And you?"
"Out of 46 students in the class, 23 only wrote a solution for the last few challenging questions!"
"Some people didn't even write down the solution!"
"What's wrong with you guys? Don't you even want to go to college?!"
At this point, Cao Wen slammed his hand on the table, glanced around the classroom, and then looked towards Han Chuan in the middle and back rows.
"Two students surprised me in this monthly exam."
"Han Chuan, Li Hao!"
Upon hearing their names called, the two people who were sitting in their seats, eyes downcast and seemingly oblivious to their surroundings, instinctively stood up.
Han Chuan didn't feel much, after all, he was quite aware of his current level and knew that he had definitely improved.
However, Li Hao, standing to the side, seemed a little nervous, his hands unconsciously gripping the hem of his clothes, his eyes darting around, probably because he hadn't expected Cao Wen to call him out, especially in such a setting.
Cao Wen continued, "In this monthly exam, both Han Chuan and Li Hao have made significant progress."
"Li Hao improved by nearly 15 points compared to the last monthly exam, while Han Chuan improved by 30 points, achieving a score of 94."
These words immediately caused a stir in the classroom, with all the students turning their attention to that person.
Holy crap, that's awesome!
94 points! How is that possible?
"His score has improved by almost 30 points in just one month. Did he cheat?"
"Don't talk nonsense. Teacher Cao is so strict, how could cheating not be discovered? Besides, Li Hao has improved by more than ten points. It's impossible for both of them to cheat, right?"
Although most high school students don't really care about other students' grades.
When top students do well on exams, most people will only sigh briefly and then forget about it.
But this time is different.
While the average score was dropping, one of my classmates jumped by nearly thirty points, which cannot be explained by luck.
Without stopping the sudden noise in the classroom, Cao Wen continued, "Although this result is still a long way from excellent, I believe that with his hard work, it's only a matter of time before he achieves good results."
"What makes me even more pleased is that everyone can come up and take a look at Han Chuan's exam paper!"
Even for problems he didn't know how to solve, he filled them with his own solutions!
"If I were a teacher grading the college entrance exam, seeing a paper like this, even if the answers were wrong, it would be difficult for me not to give some points for the steps!"
"Sometimes, it's just a matter of two points; the university you get into can be worlds apart!"
After a pause, Cao Wen's gaze swept across the classroom before he continued, "Those whose names are called, come up to get your test papers. While you're at it, take a look at Han Chuan's paper and study it carefully!"
"Zhou Ji, 87 points."
"Wang Heli, 79 points."
"Hu Penghai, 89 points."
"....."
One by one, students were called up to the stage to collect their exam papers, and then they "worshiped" Han Chuan's exam paper.
Sitting in the middle or back row by the window, watching his classmates, who were originally better than him, scrutinize his exam paper, Han Chuan felt so embarrassed he could dig out a three-bedroom apartment.
But why does this feeling feel so good?
"Han Chuan, come up here and get your exam paper."
Finally, it was his turn to take the last exam paper. Han Chuan stood up from his seat and could feel many eyes on him as he walked down the aisle.
Some were surprised, some were envious, and some were puzzled.
To most of the students in the class, it was truly baffling that this "academic underachiever," whose grades were usually far inferior to theirs, had suddenly shown such talent and was being praised by Teacher Cao.
"Good, your grades have improved, but you still need to work harder, especially on the last big question. I've made some annotations for you, so take a look when you get back."
On the podium, Cao Wen finally smiled.
Reaching out to take the test paper, Han Chuan smiled and nodded, "It's all thanks to your excellent teaching, Teacher Cao."
Cao Wen glanced at him and said, "I didn't teach you to use numerical trial and error to solve problems. That's not compliant. Go down."
.....
After the hair test was completed, Cao Wen tapped the blackboard twice on the podium.
"Quiet down, today we'll go over the test!"
The classroom quieted down again, and Cao Wen drew a rough graph of a function on the blackboard, marking several key points.
"This time we'll start with the last big question!"
"We just learned about differentiation at the beginning of the month, and this time more than half of the students left it blank, some didn't even write a solution!"
"Only a small number of students solved some of the problems by using the concept of derivatives."
He paused for a moment, glanced around the classroom, and then wrote two names on the blackboard.
"Two students' solutions are worth learning from: Chen Li and Han Chuan!"
"Chen Li used the definition of the derivative to deduce that the limit of the increment ratio is used to judge monotonicity, which shows that he has a deep understanding of the concept of limit."
"This shows that he has studied hard. He understands what a derivative is and has been able to apply it."
"And Han Chuan..."
He paused for a moment, then repeated Han Chuan's solution steps onto the blackboard.
"Han Chuan used a different method."
"He didn't use derivatives or limits. He directly selected five points within the interval, manually calculated the function values, and determined the monotonic intervals by comparing their magnitudes."
"Although it may seem silly, its core logic is rigorous—it doesn't rely on advanced tools, but only uses the most basic knowledge to approach the correct answer."
As he spoke, Cao Wen turned around and tapped the first value of the function problem on the blackboard with a piece of chalk.
x=0、x=0.5、x=1、x=1.5、x=2....五个点，五次代入计算，从0到1函数值一直往下降，从1到2一直往上升。
In the classroom, upon seeing the equation on the blackboard, one student couldn't help but exclaim, "This works?"
Cao Wen caught the surprised sound, but instead of criticizing, he went along with the conversation.
"Perhaps you think that using five points to perform addition, subtraction, multiplication, and division is too stupid, too low-level, and not like 'mathematics' at all."
"But do you know what this method is called by people who actually do engineering? It's called numerical discrete sampling."
"In aeronautical engineering, when the aerodynamic functions of an aircraft are so complex that it is impossible to calculate the derivative by hand, engineers will use point approximation to study its changing trends."
"This is not a stupid approach; it's a different way of thinking."
Cao Wen put down the test paper, his voice deepening: "This semester you will learn more differentiation formulas and more seemingly 'advanced' problem-solving tools."
"But what I want to say today is that a tool is always just a tool."
"Derivatives, limits, inequalities—if you don't understand the logic behind these things, memorizing any number of formulas will be futile."
"And today Han Chuan used five points of addition, subtraction, multiplication, and division to prove the same thing—in which intervals does a function rise and in which intervals does it fall."
"He didn't have a grasp of derivatives, but he learned to use what he already had to solve problems."
"And this is precisely the core competency of mathematics."
At this point, Cao Wen's voice softened, and he looked at Han Chuan before continuing.
"Of course, I do not advocate this way of solving problems."
"It's not recommended, at least not during your high school years, because this method is based to some extent on 'guessing' or 'exceptions'."
"It cannot be guaranteed to hold true in all situations, especially in proof questions or open-ended questions, where logical deduction and complete calculations are the key to scoring. If you use this method in the college entrance examination, you are likely to lose points or even get no points because of non-standard steps."
"I'm putting Han Chuan's solution process and the standard answer side by side on the blackboard today, not because I expect you all to learn this 'point selection method' to solve problems."
"You should focus on learning differentiation, and use the tools specified in the exam guidelines."
"The reason I cited this special case is so that you will learn from Han Chuan!"
"When you encounter a problem you don't know how to solve, don't shut your mind. Don't just leave it blank because you think you haven't learned it or haven't mastered it!"
"If the knowledge and mathematical tools you've learned aren't enough to solve a problem, then try to use what you've learned to approximate it."
"Your current method might not get you a perfect score, but just taking that first step has already put you ahead of those who stay put and wait for the standard answer!"
"Leaving it blank guarantees no points, but as long as you write something, you have a chance to get points for each step, and a chance to get closer to the correct answer!"
The chalk marked the last period on the blackboard. Cao Wen clapped his hands, returned to the podium, picked up his enamel mug, and took a sip of water.
"Alright, let's continue with the questions!"
......
During a break in the math teacher's explanation, Li Hao, sitting next to Han Chuan, quietly peeked over from behind his propped-up books, craned his neck to look at the test paper on the table, and spoke with a hint of sourness.
"Wow, Brother Chuan is awesome! This is the first time I've ever heard Lao Cao praise someone like that in class!"
It has to be said that Cao Wen's praise of Han Chuan and his hope that everyone would learn from Han Chuan were indeed out of envy for him.
This student, who used to be a poor student like him and was criticized, has now transformed into someone everyone should learn from.
Of course, he would only do that to a good friend.
I'm afraid my brother is suffering, but I'm also afraid he's driving a Land Rover.
When his brother was a poor student, he encouraged him to study hard, but if his brother suddenly went from being a poor student to a top student, he would be the one feeling jealous.
Li Hao was like that. Seeing how quickly Han Chuan was progressing, he was unwilling to stay in the same place. He also wanted to study hard and get praise from his teachers and recognition from his classmates.
Hearing this, Han Chuan turned to look at Li Hao and said with a smile, "Why do I feel like there's something behind your words? Are you jealous?"
Li Hao curled his lip, deliberately feigning disdain, and said, "We agreed to be slackers together, what happened to you? How could you betray our revolutionary friendship?"
Han Chuan: "I didn't have a choice back then, but now... I just want to be a top student!"
Li Hao rolled his eyes, then asked curiously.
"By the way, that five-point sampling calculation method that Teacher Cao praised you for, did you really come up with it yourself?"
"Strictly speaking, no," Han Chuan shook his head and said, "This is something my teacher taught me."
"Which teacher? Didn't Teacher Cao just say he didn't teach that?"
Upon hearing this question, Han Chuan paused for a moment, his fingers tracing the cover of the math textbook by Ge Junshu under his desk.
"Just treat them as someone you met outside."
Upon hearing this, Li Hao let out a long "Oh," and said, "So your parents hired a tutor for you. No wonder your grades have been soaring lately!"
Han Chuan smiled and said, "I guess so."
Ge Jun's presence was indeed like that of a private tutor to him, and it could be said that he was far more than a typical private tutor.
After all, this is a top-tier expert who can compile textbooks and set questions for the college entrance examination.
It would be a good thing to make Li Hao "misunderstand" that he has a tutor, so that Li Hao would probably not force him to compare his learning progress.
He had noticed Li Hao's efforts in his studies during this time; after all, young people are always competitive.
Han Chuan knew his current state; without a doubt, with his "cheat code" activated, he would far surpass his former self.
If he falls too far behind in his studies, it will definitely dampen Li Hao's motivation to learn, making him feel inferior and even causing him to give up on his studies.
This is something Han Chuan doesn't want to see.
It would be better to find an excuse like tutoring; at least that would give me a reason.
He paused for a moment, then continued, "Actually, you can improve quickly too. Compared to the last monthly exam, didn't you improve by more than ten points?"
"You've only been studying for a little over a week. If this continues, what score do you think you'll get on the final exam?"
As soon as he finished speaking, Li Hao's eyes lit up.
If he can get over 100 points on his final math exam, his allowance will double.
Then Lao Zhou will be able to pick and choose any of the new DVDs he gets.
Thinking of this, Li Hao's eyes lit up as he said, "Brother Chuan, you have to help me!"
Han Chuan was taken aback for a moment, then asked, "Help you with what?"
Li Hao looked at me earnestly with eager eyes and said quickly, "Teach me math, and if you get over 100 on the final exam, I'll cover your breakfast next semester!"
His tone was serious, and his eyes were full of expectation.
He knew that Han Chuan's math grades were very good, and he had a tutor, so he must have a lot of good study methods. As long as Han Chuan was willing to teach him, he would definitely improve quickly and get a score of over 100.
Although Han Chuan himself doesn't even have a perfect score of 100, he inexplicably has this confidence in his heart!
.....