When a teacher says "added x number of times" they write the multiplicand x number of times, not the addition symbol. When I ask you what is the sum of 12, 34, 16 and 7 (4 addends) I am asking what is SUM(12,34,16,7) and the algorithm to do that is to start with 12, then add 34, then add 16, then add 7.
There has to be a word for when people pivot on semantics like this and create problems that aren't even there. I have been calling them "semanticists" but that isn't accurate.
The photocopy example is actually a solution to the problem "1 + x = 4", not "x * 1 = 4".
On Sep 1, 2012, at 1:58 AM, Jonathan Crabtree <firstname.lastname@example.org> wrote:
> P.S. Think of a photocopying machine. You have one letter and you need four altogether. So what button do you press on the multiplication machine? Three! ie k-1 Press the four button and you end up with five.