## 2012-09-24

### Can you say ``equal to''?

What I first asked to children is
Kannst du ,,gleich'' sagen?
(Can you say ``equal to''?)
Because many children say
Eins plus zwei ist drei.
(One plus two is three.)
Of course it is no problem if the children know the difference. But when a child use ``ist (is)'' I am not sure they know what the 1 + 2 = 3 means. Therefore, I asked often children to say,
Eins plus zwei (ist) gleich drei.
(One plus two equals to three.)
But if I force this, children might hate mathematics, so I only ask this sometimes. I am afraid they hate mathematics. If they hate, it doesn't matter what is correct.

By the way, I just thought that does usual grown up know the difference? I asked some of colleagues, though, they earn money by doing mathematics, so they knew it. (Maybe wrong samples.)

The problem is how to explain this to 8-11 years old. I explain as the following. All the children said ``I see''. But still some children forget to say ``equal to'', so I am not yet sure.
7 is equal to 2 + 5.
2 + 5 is equal to 7. These are both correct.
Hitoshi is a Japanese.
A Japanese is Hitoshi? There are other Japanese names.
Therefore, ``Hitoshi is equal to Japanese.'' is wrong. ``A Japanese is equal to Hitoshi.'' is also wrong.
Another example.
Daniel is 160 cm (tall).
160 cm is Daniel? 160 cm is a length, a length is not Daniel.
Therefore, ``Daniel is equal to 160cm.'' is not correct.
Equal things can be exchange-able.
Can you see ``ist (is)'' is not equal to ``gleich (equal to)''?
So far, I explain a concept ``gleich (equal to)'' as ``austauschbar (exchange-able)''. This works numbers, money, length, and so on. But when a quartic object (e.g., area) is shown up, I have a problem. In fact, in ancient Greek (if my memory is correct), x*x = x can not be a computable equation. Ancient Greek people thought the left hand side is an area and the right hand side is a length. How can you exchange area with length? The concept of ``equal to'' is not so simple.  But I think this is fine for the first step.

In my case, I even can not speak the correct German, so I hope my students think I am not always correct. I wish my students think me as: the teacher is usually correct, but sometimes makes mistakes.