As soon as Li Kewang was about to ask about the situation, Liu Fang smiled at the students: "Thank you for coming and cheering, whoever will come to my class in the future can do it, but let me state first, the content I said may be a little difficult, if anyone can't understand, then you can't blame me." Pen | fun | pavilion www. ｂｉｑｕｇｅ。 ｉｎｆｏ”

The students smiled when they heard this:

"Teacher Liu, you just follow the normal course, if we don't understand, of course we won't blame you."

"Yes, we all came to audit voluntarily, and if we don't understand, it can only mean that our level is not enough, and it has nothing to do with you!"

…………

The students showed great enthusiasm for Liu Fang, everyone knew what level Liu Fang was at, of course the content he talked about would not be easy, if it was easy, Deputy Director Li would not be able to invite him to class.

"Thank you for your understanding, let's start the class officially."

After Liu Fang finished speaking, he took out a third-order Rubik's cube from his pocket, which he specially borrowed from Sophie.

The Rubik's Cube is extremely rare in China, and only a few of the students in the classroom recognize it, and these people are secretly curious: Didn't you say that you were in a math class? What did Mr. Liu do with the Rubik's Cube?

Liu Fang lifted the Rubik's Cube and let the whole classroom see it: "This thing is called the Rubik's Cube, which belongs to the puzzle toy, let me show you how to play the Rubik's Cube first." ”

After Liu Fang finished speaking, he quickly turned the Rubik's Cube that had been disrupted by color, and after a while, the Rubik's Cube was restored.

"Playing the Rubik's Cube is mainly to adjust the color of each side of it to be consistent, what I am holding in my hand is a third-order Rubik's Cube, each side has three variations, please give the variables of the third-order Rubik's Cube."

This is the first question released by Liu, of course, the students dare not slack off, everyone has the psychology of competing for performance, and they have taken out paper and pen to calculate.

After a while, someone raised his hand and reported the results of his calculations.

Liu Fang nodded approvingly: "This classmate's calculation results are completely correct, you are very good." ”

Just a commendation made the student's face flush with excitement, and he didn't know that he thought he had won the Nobel Prize.

Liu Fang continued: "Each side of the fourth-order Rubik's cube has one more square than the third-order Rubik's cube, so please give the variables of the fourth-order Rubik's cube." ”

After Liu released the second question, the students counted it again.

This time it took a bit long, and in the end, a boy sitting in the first row calculated the result first, and after Liu Fang's verification, the answer was completely correct.

Liu Fang seemed to be on the same page as the Rubik's Cube, and he immediately came up with the third question: "Next, please give us the variables of the fifth-order Rubik's Cube." ”

Although the students were puzzled, none of them dared to ask questions, and after a longer calculation, one girl came out on top.

Liu Fang praised the girl twice, wrote the correct answers to the three questions on the blackboard, and then he turned around and asked very seriously: "You have all calculated it yourself just now, do you feel that the number is too big and not easy to calculate?" ”

The students nodded one after another, and Liu Fang smiled and asked, "Then have you thought of using simpler expressions?" ”

None of the people present opened their mouths, and everyone showed expressions that they didn't understand.

Liu Fang explained: "I mean, has anyone thought of using an arithmetic formula instead of an answer? ”

The students shook their heads, and Liu Fang smiled: "From now on, you will try to construct the operation formulas of the three Rubik's Cube variables." ”

The students were busy with their work, and after about two minutes, a boy raised his right hand.

Liu Fang checked it and found that the three formulas listed by the boy were all correct, and he asked with a smile: "This classmate, how much time did it take you to create the first operation formula?" ”

"More than a minute."

"How long did it take to create the second formula?"

"Twenty seconds."

"What about the third?"

"Ten seconds."

"Can you tell me why you're getting faster and faster?"

The boy thought for a moment, and then replied: "Because creating the first operation formula is the most difficult, and the second one belongs to the increment of the first formula, just modify it on the basis of the first formula, and with the previous experience, the third formula is of course faster to build." ”

Liu Fang nodded and said to the others: "When I came out of the question just now, I deliberately paid attention to the time, when everyone calculated the three results in the front, it took seven minutes to add up to the fastest, and when everyone created the formula later, this student only took two minutes, who can tell me, what is the reason for?" ”

A girl raised her hand and said: "The first three questions consume a lot of time because of the large amount of calculation, and when creating the formula later, in addition to the difficulty of the first one, the next two formulas are evolved on the basis of the first, so that the time consumed will naturally be shorter." ”

Liu Fang asked: "If you use an operation formula to represent the result, is this way correct?" ”

The girl thought for a moment and replied, "As long as the answer is not specifically required to be calculated in the question, it is perfectly fine to use the formula." ”

Liu Fang nodded, and said very seriously: "When I asked the first three questions, I didn't ask you to calculate the accurate results, but just asked you to give the variable of the Rubik's Cube, in fact, this variable can be expressed by a formula, but you all answer the questions according to your previous habits, and no one thought of this." ”

The students were ashamed, although they were older than Liu, but no one would really compare with Liu Fang by age difference.

"I said so much, I don't want to embarrass you, but I want to change your inherent thinking, students, when you used to take math class, the teacher adopted a cramming education, I don't agree with this kind of education, the first thing I want to teach you is a change in thinking, so that you can look at problems flexibly, and use flexible ways to solve problems!"

"Mathematics is the basic discipline of the entire science and engineering, whether it is physics or chemistry, even the recent rise of computer science in China, all of which are inseparable from the foundation of mathematics, if the thinking is rigid, it will affect creativity, why so many people in Western countries have won the Nobel Prize, but no one in China has won this award? I don't know what others think of this, according to my own opinion, in addition to the backwardness of our overall scientific research level, another important reason is the rigidity of thinking! ”

"Why do we have the four great inventions of antiquity, and now there are so many of them? The answer is simple, this is also caused by the rigidity of thinking! ”