I'll tell you what's wrong: the mentality of the author of this text
Multiplication has started as repeated addition. That's where the idea came from.
> It is as if there were two types of addition: regular, random, “wild” addition and the specially-bred variety of addition to which we give the name multiplication.
Nobody. Literally nobody said that
Of course, you'll need to forget a bit the idea of repeated multiplication when you get into the rationals/reals/complex numbers, but even there it kinda makes sense
So no, I think this is the kind of teacher that makes the students even more confused and prone to hating math
Now that's an interesting point, did it start as repeated addition?
It is just as conceivable that people were faced with a problem like 'each person needs 2 apples, we have 5 people, so we need 10 apples'?
In this case repeated addition is a perfectly fine algorithm to calculate the product but the product itself is not defined as repeated addition, it's the solution to a particular type of problem.
Your problem just reinforces the notion that multiplication is repeated addition. "So we need 2 for him and 2 for her and 2 for him and 2 for him and 2 for her. 2+2+2+2+2 = 5 x 2 = 10"
I disagree, translating from "2 for (him + her + him + him + her)" to "2 for him + 2 for her + 2 for him + 2 for him + 2 for her" is using the distributive property of multiplication.
The sentence "2 for him and 2 for her and 2 for him and 2 for him and 2 for her" is unnatural and not the way people generally think (unless they're just tallying up but then we're not even talking about multiplication anymore, a tally rarely consists of all equal numbers)
Multiplication has started as repeated addition. That's where the idea came from.
> It is as if there were two types of addition: regular, random, “wild” addition and the specially-bred variety of addition to which we give the name multiplication.
Nobody. Literally nobody said that
Of course, you'll need to forget a bit the idea of repeated multiplication when you get into the rationals/reals/complex numbers, but even there it kinda makes sense
So no, I think this is the kind of teacher that makes the students even more confused and prone to hating math