A. was studying geometry. That time, A Rechtschreibung (spelling) teacher Ms M watched her. The question was how many cross point (Schnittpunkt) of the three lines (Gerade) in the figure. In the question figure, the cross points are emphasized, but, she could not answer the question. Ms M asked me to help her.
As usual, I asked her (A.), ``Could you please explain me what is a line? (Bitte erklären mir was ist Gerade.)'' She answered me ``A line is a line. (Gerade ist Gerade.)'' Well, that's true, but there is no information.
``How the school taught you. A line has an end? Or a line has no end?'' ``A line has no end.'' I see, so I know she learned the difference between line, half line (ray), and segment at her school. ``OK, then what is Schnittpunkt?'' I actually didn't know what is a Schnittpunkt. She answered, ``I don't know.'' So we asked other teacher, what is a Schnittpunkt. It is a cross point of two lines. This actually solved her problem. I think I am better teacher when I teach in German, since my German is not good, therefore, I first need to know whet is the problem. I asked the meaning of the question to my student. I found many students just don't know what the question means. Therefore, many teacher failed to teach. If a student doesn't know the meaning of the question, teaching answer has no meaning.
Now we back to the problem, the question is clear. Then she classified the all cases of the 0, 1, 2, 3 Schnittpunkte correctly.
I asked her what is her mother tongue. She use Spanish and English at home. I should remember I should always first check the question is clear or not. I wish soon she can figure out what she didn't understand by herself.
Today, I asked my students, ``What does this mean?'' Some students think I don't understand math questions. Actually No, I often don't understand the problem. In Hasenschule, when a student became better, she/he usually became both German and math became better.
A few days ago, coincidentally, only A. took a math course. But another teacher was there. So, I just watch how she learn from the other teacher. She learned a calender math. I saw a word ``Schaltjahr'' that I didn't know the meaning. So, I asked her, what is a ``Schaltjahr''. She explained me it well. (Schaltjahr in English is a leap year.) I asked her why it is called ``Schaltjahr''. She didn't know, the other teacher didn't know either. By the way, why leap year is called leap year is an interesting. Japanese leap year is ``閏年'', the character shows `a king is behind the gate.', since that day the king doesn't do the official work. My next question is why such strange year exists? Although, the other teacher seems to continue to teach how to calculate the days, so I didn't have a chance to tell that story. Maybe another time.