The days of learning black magic in another world

It's not that Riemann is an expert in pedagogy. His relationship with pedagogy is the same as that of penguins and the North Pole-it has nothing to do with it.After all, he studied mathematics, not mathematics education.

And even when magic is not enough for him to make ends meet, he goes out to teach advanced mathematics instead of elementary school mathematics, but he still has some common sense.

To be honest, he also forgot where this common sense came from, maybe it was one of his college classmates who wanted to change careers to become a teacher?Or it might just be randomly read on the Internet or books and imprinted into his mind, but he does know that if the human brain in another world also follows the development laws of the world he belongs to, then a seven-year-old elementary school student should absolutely not be studying Equational.

If he remembers correctly, children aged 7-11 can carry out simple abstract thinking, but still need the support of concrete things.

So he glanced at the equation on Al's paper.

It says--

"x+y=35"

"2x+4y=94"

(Of course they are not using x and y, but their own symbols)

There are also corresponding answers below. The idea is to use x to represent y and then substitute it into the next equation, the most direct solution.

It is indeed simple enough, because this is the magical core of a ring of magic [Summon Wind], but no matter how simple it is, it is for an adult with hypothetical thinking and abstract logic, not a seven-year-old child.

Riemann glanced at the coefficients of these two equations again.

(1) and (1).

Fortunately, this coefficient is very classic, and it is easy to compile a very classic application background.

"Al, have you ever seen a chicken and a rabbit?"

Little Al shook his head blankly.

Riemann: ... Well, I made a mistake, but it's not a big problem.

"It doesn't matter. Rabbits have four legs and chickens have two. Can you name similar monsters?"

"Oh! Of course, Mr. Riemann! There are two-legged crystal birds, green-winged sparrows, furry birds, and four-legged lizards, fire-breathing beasts, strange fish..."

"Very good!" Riemann promptly interrupted Little Al's endless enumeration with a compliment: "Let's take the crystal bird and fire-breathing beast as examples, they are about the same size, right?"

Al nodded.

"Okay, now imagine such a scene, there are many, many crystal birds and many, many fire-breathing beasts trapped in a very large cage, because they are densely covered with each other, so if we want one by one Is it difficult to count how many crystal birds and how many fire-breathing beasts there are?"

Al imagined that scene for a while, and nodded heavily: "Indeed!"

Riemann continued: "But there are some things we can do. For example, we can count how many heads and feet there are in the cage. You don't need to distinguish who is a crystal bird and who is a fire-breathing beast. Just count, right?"

Little Al nodded again.

"So now we've counted 35 heads and 94 feet in the cage."

Al subconsciously glanced at the questions he wrote down on the paper.

Riemann rubbed his head: "You realize what I'm talking about, right? So smart."

"Now, let the unknown x represent the number of crystal birds, and let the unknown y represent the number of fire-breathing beasts, what is 2x+4y now?"

"It's the number of their feet!"

Riemann rubbed Al's head again: "It's so smart."

"Now let's calculate the number of crystal birds and fire-breathing beasts. Let's put the two unknowns of x and y aside, and simply imagine this picture. Now the crystal birds and fire-breathing beasts are in the cage. It’s a pile, and we can only see a mess when we look at it, only enough to see their heads and feet clearly, then, suppose, outside the cage...for example, a strange-looking monster came..."

"How strange?"

"It's so strange that all the crystal birds and fire-breathing beasts want to watch it."

Al thought about it seriously, and Riemann didn't know what he was thinking about, probably imagining what that strange monster looked like.

"Then now, all the crystal birds and fire-breathing beasts have gathered to the edge of the cage to watch that strange monster. The crystal birds still stand on two feet, but the fire-breathing beasts are so excited that they all lift up their legs. I stretched my two front paws, and lay down on the cage... Of course, there are also those who are squeezed so hard that they can't get on the cage and can only put their front paws on the fire-breathing beast in front, can you imagine this scene?"

Al imagined that scene for a while, and nodded heavily: "Yes."

"Very good, so now, from our point of view, all monsters have only two feet on the ground?"

Little Al thought for a moment, then nodded again.

"Then can you tell me, how many feet are there on the ground now? There are a total of 35 monsters, all of them have 2 feet, and there are a total of...?"

"70 feet!"

"Very good!" Riemann stretched out his hand and clapped Little Al, "A very important step has been completed! Next, I have another question. Since there are only 70 feet on the ground, how can the fire-breathing beast be raised?" How many feet do you have?"

Little Al quickly answered this question: "24."

"Very good, very good. How many fire-breathing beasts are there in the cage?"

Al's face was confused for a moment: "6?"

Riemann:?

Riemann: "Why do you think there are six?"

Al has returned to a state full of confidence after a short thought: "Because the fire-breathing beast has four legs, now there are 24 legs of the fire-breathing beast, so there are six fire-breathing beasts!"

"Stupid! The fire-breathing beast only lifted two feet, so it is 24 divided by 2 twelve!"

The phrase "idiot" was not shouted by Riemann. He has been careful to maintain his friendly attitude, for fear that this child who already has a probability of being forced to be tired of studying by exceeding the schedule will be hit again.

The phrase "stupid" came from a girl who was watching. Uh, in fact, she was not the only one watching. At some point, a group of children had gathered beside the small fire in front of Riemann and Al.

Ayer and that girl obviously got along like this originally, because he didn't show any expression of anger or unhappiness, but clapped his palms suddenly: "Yes! Thank you Missy! It's really you, Mi West!"

The girl named Missy raised her head reservedly: "Huh."

Riemann smiled: "Yes, we now know that the number of fire-breathing beasts is 12, so what is the number of crystal birds?"

"23!" Several children shouted in unison.

Riemann nodded: "Very good, very good, let's go back to these two equations now."

"x+y=35, then 2x+2y is equal to 70, does this formula mean the number of all the feet on the ground after the fire-breathing beast lifts its feet?"

“这时候，我们知道总的脚的数量是2x+4y，喷火兽抬起脚后的地面上的脚的数量是2x+2y，我们用2x+4y减去2x+2y，是不是得到的就是喷火兽抬起的爪子数量？”

"That is 2y. Does it mean that the number of fire-breathing beasts is multiplied by each of them raising two paws?"

“2y等于94-35x2等于24，所以y，也就是喷火兽的数量为24除以2等于12。”

"Should we go back and calculate x and just subtract y from 35?"

The girl named Missy touched her chin like a little adult: "It's very interesting, although the original solution is very simple, but you gave a meaning, well, it's not that I need any meaning, only Al That’s why I keep asking what’s the point of learning this, and what’s the point of learning that…”

Al: "Hey! Is this important to me? I just can't talk myself into doing it if I don't know what it means! I just can't stop wondering what it means!"

"Oh... Poor Al." The little Missy girl looked at him pityingly.

Riemann did not interrupt the conversation between the two of them, nor did he interrupt the thinking process of the thoughtful children beside him. Instead, he looked around and found the person he was looking for.

"Mr. Freddy, can I speak to you in private?"

"Of course, Mr. Riemann, what do you want to talk about?" The big Freddy followed him to the edge of the fire with a confused expression.

"It's like this, I just chatted with Little Al, and I found out that you are... learning mathematics according to the level of magic?"

The confusion on the big Freddy's face became more obvious, and his whole body seemed to be like a big "What else?".

Riemann continued: "If I'm not mistaken, what are the cores of the magic of the first ring, and which topic do you study accordingly? And then the second ring... the third ring...?"

Freddy nodded slowly.

Riemann: "I know that I may be nosy, but I don't think it's a good idea for you to do this. Of course, from a practical point of view, this is indeed the most efficient way. Whichever magic is needed, go to it accordingly. Which magic to study... But this may cause these children to have a poor foundation, so once they encounter more and more difficult questions later, do you want them to build houses on a loose foundation? I think this should be very difficult Come on..."

"No, no, no, Mr. Riemann, please feel free to express your thoughts. You have become a three-ring mage at such a young age. If you are willing to guide us, I wish for it!"

Big Freddy finally came to his senses (partially), raised his sincere eyes, and looked at Riemann.

Riemann: "Then I will be straightforward. I think these children should temporarily forget the practicality of magic and simply learn mathematics, and they must learn systematically. For example, children like Al, he still can't do it well. The reason for understanding those abstract concepts is that he should still be using the state of objects corresponding to numbers, and a child like Missy, who is smart, can understand the essence, and has a natural affinity for logical symbols, let alone waste her time. Talent, if she is properly cultivated, she will be able to solve the core of the third and fourth rings as easily as the core of the first and second rings..."

"...if you don't mind, I can teach them."

Freddy couldn't help hesitating for a moment. Strictly speaking, this was a pie in the sky, and he shouldn't hesitate, but just because it was too "pie in the sky", he couldn't bear the vigilance he had just dispelled. live floating up.

But... no matter what he thought, he couldn't think of what purpose the other party could have - to take them all under him as apprentices?No matter how you look at it, they are taking advantage of it!

And even if there is any danger waiting ahead, it is difficult for him to give up an opportunity to improve the strength of all the clansmen.

Moreover, with the opponent's strength, if he really wanted to do something to them, but he didn't directly use them as experimental materials, Freddy could only think of one possibility—that is, most of them were not strong enough to be the opponent's opponent. For experimental materials, the other party has to bother to train them. In this case, there seems to be no difference between trying to improve your strength on your own in order to get rid of the status quo and trying to improve your strength according to the better route given by the other party.

then--

"Then...thank you Mr. Riemann!"

Riemann thought for a moment: "Wait."

Freddy, who was still thinking about things and being suspicious just now, suddenly became nervous: "You, have you repented?"

Riemann: "Oh that's not true, I just think not only the children, but you have to go back to class."