20160722 ADDING TOGETHER:

A mystery ghost operation spotted.

US education is practically impossible to discuss. For years, I was trying to figure out about how schools teach multiplication. This helped me understand how to defend the kids from this teaching, but not to explain why do I think I have to defend them. The past observations worth nothing. Next time there will be another school, another teacher and another curriculum. The damage will be done, and only then I will have the valid reasons for defense.

That's why I am going to quote Wikipedia. To preserve their formatting, I captured the following from my browser's window.

My first question is: how multiplication can be defined as elementary if it is made out of additions? Even though, to put it gently, "may be thought as" is not a definition.

US schoolkids are being trained to add using math facts. The statements or expressions like "adding as many copies of them" immediately invoke a question: adding to what?

The example of multiplying 3 by 4 in the following sentence makes the writers change the words: just "adding" became "adding together". I wonder if they actually teach an operation of "adding together". The reason is clear: they claim they add 3 times, but there are only 2 additions. Addition was not working for them. They tried to conjure up something else.

In my engineering view, those "elementary" operations exist only in teachers' imagination. Under the cover of arithmetic, we actually deal with 1s. To add means exactly to bring two sets of 1s together. Positional addition is only a method to handle big quantities of 1s quickly and easily.

Another remarkable aspect of this "definition" is the use of the notion of copying. Copying would make sense for quantities but not for numbers, unless the writers meant photocopying those numbers. A copy of a number is the same number. In multiplication we add the same numbers, not the copies of them.

I have no way to prove where those "copies" came from, but I suspect that they are creations of teachers' guilty conscience. The educators must understand that their elementary operation of multiplication is performing an impossible trick producing the quantities out of thin air. You have 4 dollars and you need more of them. Multiply by 3, and you have 12. "Copying" may be the teacher's way to explain how this can be possible. You just make the copies of your dollars.

The musing about "not very meaningful" distinction between the order of the multiplier and the multiplicand is superb. No, I have no mercy for the people who teach innocent children this stuff. Fortunately, they don't need my mercy.