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Myrtle called it The article that launched a thousand posts…, and counting comments on thisandseveralotherblogs, that may not be too much of an exaggeration. Yet the discussion feels incomplete I have not been able to put into words all that I want to say. Thus, at the risk of once again revealing my mathematical ignorance, I am going to try another response to Keith Devlin’s multiplicationarticles. Let me state up front that I speak as a teacher, not as a mathematician. I am not qualified, nor do I intend, to argue about the implications of Peano’s Axioms. My experience lies primarily in teaching K-10, from elementary arithmetic through basic algebra and geometry. I remember only snippets of my college math classes, back in the days when we worried more about nuclear winter than global warming. ....