Hasenschule: Was bedeutet das? Bitte erklären das mir. What does it mean? Please explain me that. (1)

When my students asked me a question, I usually answerd the following:

``Was bedeutet das? Bitte erklëren das mir. (What does it mean? Could you please explain me that?)''

I continue as:

``Mathe ist eine Sprache. Es gibt eine Bedeutung. (Math is a language. There is usually some meaning.)''

When I asked my students to explain the meaning of the question, they sometimes answer me, ``You are a teacher, you explain me.'' Well, that's true. But, I want to know they understand the question. I also want to teach them how to explain something. Therefore, I ask them, ``What does the question mean?'', ``Is it true?'', ``Please explain that why.''

Sometimes some students cried saying, ``You didn't teach me an answer.'' or ``You didn't help me. Help me, please.'' I was thinking, ``The answer is not so important. I want to you to learn how to learn by yourself. This is a practice. I wish soon you don't need my help. I want you to practice to solve a new problem. In the future, you will confront a total new problem that no human kind ever met, and you need to solve it. I want to help you to prepare that time because I can not help you that time.'' However, I am also still learning how to solve a new problem. I cannot really teach it since I still don't know it well. Therefore, I said, ``Please don't cry. You can understand if you think slowly, take time as much you need. If you can not do it today, there is a tomorrow. The answer is not so important. The understanding is the most important.'' By the way, in German the word ``correct'' is ``richtig'' and ``important'' is ``wichtig''. I can not say well that ``Richtig ist nicht so wichtig.'' since for Japanese, ``r'' and ``w'' are difficult to pronounce. This makes them laugh.

Five months ago, one student was always crying and her grade was always 5. She got last month 2 in math. I am so happy for her. (`1' is the highest grade in Germany.)

The following articles, I would like to talk about two stories.

Comments

Geometric Multiplicity: eignvectors (2)

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Tezuka Osamu's Black Jack, "Shrinking"

I like several novel authors. My first favorite author is probably Teduka, Osamu. I still love him. The list grows by adding Hoshi, Shinichi, Agatha Christie, Hermann Hesse, and so forth. My first favorite article of Tezuka was Atom as most of the (boy's) Tezuka fans did. But my favorite is Black Jack. I try to summarize one story, it is still quite vivid in my memory. I first read this story when I was 13 - 15 years old. I re-read it at least several times since Black Jack is composed of many short episodes. The title should be "ちぢむ (SHRINKING)" or it might be "縮む(Shrinking)". (It is not so convenient to translate this to English, since English does not have a system to say the exact same word in several ways. So I just simulate it with capital letters.) Black Jack is a genius surgeon, but he does not have the license. In short, his medical activity is illegal. His skill is top level in the world, but, the fee is also out-of-law expensive. In the story ...

Gauss's quote for positive, negative, and imaginary number

Recently I watched the following great videos about imaginary numbers by Welch Labs. https://youtu.be/T647CGsuOVU?list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF I like this article about naming of math by Kalid Azad. https://betterexplained.com/articles/learning-tip-idea-name/ Both articles mentioned about Gauss, who suggested to use other names of positive, negative, and imaginary numbers. Gauss wrote these names are wrong and that is one of the reason people didn't get why negative times negative is positive, or, pure positive imaginary times pure positive imaginary is negative real number. I made a few videos about explaining why -1 * -1 = +1, too. Explanation: why -1 * -1 = +1 by pattern https://youtu.be/uD7JRdAzKP8 Explanation: why -1 * -1 = +1 by climbing a mountain https://youtu.be/uD7JRdAzKP8 But actually Gauss's insight is much powerful. The original is in the Gauß, Werke, Bd. 2, S. 178 . Hätte man +1, -1, √-1) nicht positiv, negative, imaginäre (oder gar um...

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