Liu Zhiyuan concentrated his attention, wrote and drew on the manuscript paper, and immediately came up with two different ideas for solving the problem.
While he was thinking, he looked around the classroom. Everyone was busy with their homework, writing furiously, or thinking intently. The junior high school student in front of him was looking at them with curiosity.
Liu Zhiyuan didn't know how long the little girl in front of the podium took to solve the problem, but he decided not to wait any longer. In order to save time, he raised his hand in advance.
Teacher Xie blinked and asked, "What can I do for you, student?"
Liu Zhiyuan stood up and said, "I have found the answer."
Many people put down their pens, and the whole class turned their eyes to him.
"This student is very eager to learn. Can you tell me about the process?"
Liu Zhiyuan broke out in a cold sweat, but in fact he did not really complete the problem-solving process.
"How long did it take you, Mr. Lin, to come up with the answer?" he asked with forced composure.
"More than 3 points?"
Liu Zhiyuan's brain started to work frantically. He had to come up with an answer immediately. The easiest way was to use enumeration. He held his breath and concentrated for a moment. Then his eyes lit up and he said, "4."
There was a moment of silence in the class, followed by a small commotion among the junior high school students.
Liu Zhiyuan looked at Teacher Jie nervously, wanting to know whether he was right or wrong, but there was no expression on his face, and his heart sank.
"Come to the blackboard and write down the process." Xie Ran said.
Liu Zhiyuan walked stiffly to the blackboard. As he got closer, he could see the chalk marks that had just been erased from the blackboard. On them were the formulas that had just been written on the blackboard. They were very similar to his first idea, which was still to take the model.
Liu Zhiyuan felt relieved a little.
He couldn't help but look back at the little girl behind him.
It was just his subconscious action, but when he looked over, Lin Chaoxi took a half step back, his dark eyes flashed slightly, but he deliberately avoided his sight.
Liu Zhiyuan felt like he was being looked down upon, but in the current situation, he could only turn his head to look at the blackboard, pick up the chalk, and try the second method: set unknown variables, write equations, take the modulus, and solve...
On the blackboard, formulas were written line by line, and the solution process gradually became complete.
But the more Liu Zhiyuan wrote, the more he felt there was a problem. He turned his back to everyone, but the noise in the classroom became louder and louder.
His nose was sweating and even his hands were shaking. He knew that he had calculated wrongly.
After writing the last answer, he put down the chalk heavily.
"The process was quite good," praised Mr. Wan from their high school department.
"The ideas are very clear." Teacher Xie also said.
Liu Zhiyuan wiped the sweat off his nose with the back of his hand: "It's hard to say, I was wrong, the answer should be 2."
He was about to leave the stage when he was stopped.
"Student Liu, would you like to analyze why you made the mistake?"
Liu Zhiyuan was a little angry, as if this was a naked humiliation, but he still answered the question: "I calculated too quickly and did not deduct my brother's money."
"Why didn't you take away your brother's money?"
"Because... because..." Liu Zhiyuan found it difficult to answer why not, but he did miss something in the process of thinking.
"What did you learn from this mistake?"
"This is just an interesting math problem," "The focus of this interesting problem is modular operation..." When he said this, he suddenly felt that something was wrong. Why did a training team like theirs start with an interesting problem?
Sure enough, Teacher Xie asked, "What does Lin Chaoxi think?"
The little girl looked at me with a look that said, "Stop acting!" and said, "You've already said it before... The key point is mathematical thinking and mathematical language..."
"Oh, you discovered this." Teacher Xie joked.
At this point, Liu Zhiyuan suddenly felt that he might have been fooled.
Teacher Wan was also a little angry: "What does Teacher Jie mean?"
"The meaning is very simple. For everyone, this question is not difficult, but it is an easy-to-error question. Under pressure, you will abandon precise mathematical language and be forced to think about the problem in a more tricky way, such as starting with, "I'll try to give each sheep 5 yuan, will it work?" But in mathematics, imprecision can easily lead to mistakes."
“Are you saying that I answered 4 before because I didn’t have a formula?”
"It's not just the formula, but the way of thinking here." Jie Ran nodded and continued, "The next question is this: students from two schools solved this math problem on the blackboard. Please judge whether there is a problem with this statement?"
"There were questions, and we answered them for students from more than two schools!"
"There are others!"
It was the turn of the four students from Yongchuan Middle School sitting in the front row to make a noise.
The class became a little more lively, and the high school students sitting in the back also relaxed from their initial tense state.
"Everyone can think about this answer." Xie Ran looked at Liu Zhiyuan first, "Are you interested in answering first?"
Liu Zhiyuan answered seriously: "This sentence is ambiguous. Students from two schools can be understood as me and...her..." Liu Zhiyuan glanced at Lin Chaoxi and continued, "a. We are students from two different schools and solved the problem on the blackboard; b. We are students from the same school and we solved the problem on the blackboard."
"What about you?" Xie Ran did not comment and asked Lin Chaoxi again.
"If you ask me this question, I think in this context, this statement is not a big problem; but if it is not in this context, it is almost the same as Liu's answer."
“You see, this creates a problem.”
It was completely different from what Liu Zhiyuan had imagined, where the teacher would evaluate the answers. Xie Ran picked up the chalk and wrote the question he had just asked on the blackboard, and then said very seriously, "Because we have the context to support our oral conversations and thinking, we will omit some things for simplicity, but this sometimes affects our written language and thinking process and makes them less accurate."
When he heard the word "precise", Lin Chaoxi raised his eyes and looked at Jie Ran.
This content sounded so familiar to her that she felt that this training team's teaching outline might have been written by Lao Lin.
This is completely different from the situation in elementary school where students would take exams right away. This time, the joint training for junior and senior high school students was more intense and classes started right away.
"For example, the process of you solving the problem quickly just now, and for example, this sentence..." Xie Ran knocked on the blackboard and said, "You don't think there is anything wrong with this sentence when you hear it now. But if it is printed on paper and read by people who are not in the classroom, it will cause ambiguity. And mathematics... the precision of mathematical language is very important. It ensures that you have a reliable basic structure when performing mathematical calculations and related arguments; at the same time, it ensures that the relevant content will not cause ambiguity during dissemination."
When Jie Ran said this, Liu Zhiyuan noticed that Lin Chaoxi had walked back to his seat without him noticing, and most of the students in the classroom began to listen attentively.
The classroom was silent and he hurried back to his seat.
"Mathematicians have spent a long time, almost as long as human history, to establish a relatively accurate symbolic language system. What we are about to learn is..."
"Mathematical symbols?"
"formula?"
"How do you prove it?"
The students sitting in the front row rushed to answer.
"No, it's language."
——
In the cafeteria of Sanwei University, only a few windows are open during the winter vacation.
Lin Chaoxi lay on the dining table, eating her lunch box while observing the slogans in the cafeteria and writing them down with a pen. Near her, many students from their training team were doing similar things.
This is their homework for this "Chinese class": to find out the irregularities in daily language and rewrite it using more precise language.
Lin Chaoxi wrote down two short sentences in the notebook.
Suddenly someone came with a tray and sat down next to her.
"Braised beef?" Xie Ran asked as he looked at what was written in her notebook.
Lin Chaoxi quickly covered up the answer.
In the magical book she borrowed from the library, someone had specifically discussed "canteen ambiguity" in a corner. She just happened to see the name of this dish, so she subconsciously wrote it down, and tasted it, and she really thought it was... a little delicious...
Lin Zhaoxi: "Most recipes have ambiguous meanings. For example, "braised beef in brown sauce" can refer to both 'the act of braising beef in brown sauce' and 'a dish'."
"Don't you think you're being too picky?" Xie Ran glanced towards the corner of the cafeteria. Although Xie Ran had said so much, there were still people who didn't understand why math training had to include "Chinese" homework.
Lu Zhihao: "We have done all kinds of things, no matter how tedious they are."
Pei Zhi saw through it directly: "Fortunately, Master has always been like this."
Zhang Liang: “Haha.”
Lin Chaoxi poked the lion's head with chopsticks. Jie Ran turned to look at her and said sincerely, "I envy you for having such a father."
"Don't be jealous. You can't see when I'm tired."
Hearing this, Jie Ran couldn't help laughing, but didn't continue to ask his questions before class.
Lin Chaoxi looked at his knowing smile and knew that he also accepted the fact that Mr. Lin would rather write a teaching outline than come to Yongchuan University to teach, and decided not to ask any further questions.
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