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Comment by kazinator | Hacker News Reader

> How come we have ten numerals? Could it be because we have 10 fingers?

Objection! Counsel is leading the witness, Your Honor.

Rhetorical questions are really statements in disguise: "The fact is such and such, don't you agree?"

The students should be given an opportunity to form their own hypotheses about why there are ten numerals, otherwise that particular element of the dialog is not genuine "teaching by asking".

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Yes, the questions are logically leading. That is pointed out as what the method is about. That particular question was just to get the discussion started so we could get into "aliens with two fingers" to make it fun for the students to discuss two-digit math (no pun intended, of course). It was not really part of the logic of teaching. It could have been done without reference to fingers at all; e.g., "Could we have a math system if we only used two numerals, 0, and 1?" but that would not likely have piqued the interest of third graders very much. And actually some students might have taken issue with the ten fingers/ten numerals idea, since "zero" as a numeral screws that up. E.g., our number groupings in written, columnar form really go from zero to 9, and then 10 to 19, 20 to 29, etc. You don't count zero things on your fingers....

This one is a particularly weird leading question, since the idea is facially ridiculous. In every human society, we had ten fingers for hundreds of thousands of years before developing a system of ten numerals. We have ten numerals because, when the numerals were developed, we were already using ten-based counting.

> How come we have ten numerals?

By itself, a great way to start the discussion. The art is in knowing what NOT to say.

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