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In my tireless pursuit of the question raised this past summer by Keith Devlin in a series of columns in the MAA MONTHLY (" It Ain't No Repeated Addition " (June 2008); "It's Still Not Repeated Addition" (July-August 2008); and " Multiplication and Those Pesky English Spellings " (September 2008)) regarding the potential harm of leaving students with the belief that multiplication is nothing more than repeated addition, I am doing extensive reading about how children learn about, think about, and are taught to think about mathematics and the connection amongst and differences between the operations. One leg of this journey brings me to consider division. There are a number of ways to think about division, but the two "big ideas" looked at in school mathematics are the partitive or "fair sharing" model and the quotative or "measurement" model. Partitive Division With Whole Numbers As a quick overview or review, let...

A recent post on the continuing conversations, fights, and debates inspired by Keith Devlin's recent trio of columns on problems he and some mathematics educators (in England, if not elsewhere) see with teaching multiplication-as repeated-addition (or, variously ONLY teaching it that way and never leading students to see that multiplication either is not repeated addition or is a lot else besides repeated addition) to elementary students, let me to write a response that gets at some of what I've been thinking about as I read those British researchers. Below is a re-edited version of my reply: A crucial point I've tried to make previously in various places: there is a serious problem with the absolutist language a lot of folks in this debate insist upon using and which Prof. Devlin falls into at times (and hardly just at math-teach: check the comments at lets play math ; good math, bad math , and any number of other blogs where this issue has been debated for several month...