An operation is a process that takes some input(s) and gives back an output(s). Many of these operations (especially arithmetic) are some type of relation (typically binary relations like functions). If we look at multiplication from this perspective, yes, multiplication is not repeated addition, however, we can define multiplication BY repeated addition. I say “by” because, yes, in some ways, Devlin’s slightly overzealous argument is correct, it is not defined AS repeated multiplication. In math, that tiny word change can alter the meaning completely. The other thing that everyone seems to over look is where are we using it. Multiplication being taught as repeated addition works when we are discussing natural numbers, and for a child it should work fine.

I do not support Devlin’s opinion that we should alter the education systems so multiplication isn’t taught as repeated addition, however I also feel some pedagogical bias to treat multiplication as only repeated addition. I think that the system we have in place is fine as long as we get the point across that multiplication ISN’T repeated addition. It is just EQUAL (equal for many of you who have forgotten, means they are the same but not necessarily the same thing) to it with natural numbers.

In summary (partially because I would much rather the majority of articles and comments have conclusions):

Multiplication is NOT repeated addition;

Multiplication is DEFINED its EQUALITY to the the repeated addition of numbers;

I feel the educational system in place currently works fine, albeit could use some clarity that multiplication is BASED on repeated addition;

This issue is just a confusion in semantics, either sides are sort of right and wrong