What none of them can tell you is why they've been taught long division, when short division is faster.
And it's because you need long division to do division in algebra
And it's because you need long division to do division in algebra
After looking at the English Wikipedia I found that
a) what I learned in school is long division
b) the notation with the dividend and the divisor separated by a parenthesis and the result on top of a horizontal bar is totally alien to me
c) I've never seen short division before
d) the German Wikipedia doesn't even have an article about short division
Edit: although if someone else can explain it better I'd really like to know.
From what I have searched,(quickly mind you), it seems to be a mind set.
the "short" notation relies on the ability to squeeze the remainder in between the digits of the dividend. if you have a divisor greater than ten, it's possible to have a remainder with more than one digit. two or more remainder digits is a lot harder to write legibly between the digits of the dividend. you also end up subtracting larger numbers in your head, which is error prone. finally, most people only memorize the multiplication table up to 12x12 or so. once they can't simply do a lookup into their memorized table, they switch to more of a "guess and check" approach, where they will inevitably have to cross out or erase their previous work.
in the end, it introduces a lot of unnecessary opportunities to make mistakes and hides stuff that people can't do reliably in their heads.
I went to school in Sweden where we do teach all this things, but in a strange order.