Kenneth Devlin wrote “stop telling your pupils that multiplication is repeated addition” and all hell broke loose.

There was a storm at Let’s Play Math, and then Denise wrote a second post. There is still a storm raging at Good Math Bad Math. And a bunch of places I don’t normally go. And then Josh at Text Savvy has written 11 posts (they start here) - but he disabled commenting, which turns the conversation into an echo chamber. (Josh, it looks bad if you complain about your comments not being published if you run a site where comments are not allowed)

So, my two cents.

Multiplication is not repeated addition.

Multiplication can represent repeated addition.

Devlin’s point was directed to how we teach little kids math, and he blew it. So we stop telling kids that x = + (rep) and we tell them what exactly instead? Don’t ask Devlin. He devoted a second column to the issue, and never got there.

Doubling back, what was his objection? That we say “math is repeated addition” and that somehow this ruins kids’ ability to handle arithmetic: “Multiplication simply is not repeated addition, and telling young pupils it is inevitably leads to problems when they subsequently learn that it is not.” He’s wrong.

What should we do?

Teach multiplication through repeated addition, skip counting, counting arrays, finding unit areas of rectangles, Cartesian product, scaling… That’s too many to start, isn’t it? Pick one, then one more. And tell the kids that multiplication will manifest itself in many other ways as well… Add more… and remind them… No big deal here.

By the way, congratulations to Denise for handling this in an intelligent way. And for, ever so briefly, becoming the central blog in a math ed tempest.