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Re: NEGxNEG=POS:Once more with feeling
Posted:
Apr 3, 1996 7:07 PM


Even in 2*3, the 3 refers to the number of objects, while the 2 refers to the number of groups of 3. So the interpretations of the two numbers are necessarily different even with whole numbers. When considering (2)*(3), the 3 refers to a directed amount, and the 2 refers to a "directed number" of groups of 3. (Refer to my exciting post from yesterday about the mathematical basis for integers, and how integer multiplication is not the same as whole number multiplication.) I continue to argue that the conceptual basis for this is nontrivial, and many of us (myself included) have rather tentative understandings of integer multiplication. Which is why we have a tough time teaching it. Gary
At 3:10 PM 4/3/96, Lou Talman wrote: >Tim hendrix wrote: > >> An important part of the Postman approach or any other story >> approach to unearth the concept of offsetting properties of multiplying >> two negatives is that each integer in the product must have a different >> interpretation: > >This observation is itself important; it ties in nicely with my observation >about the way we overload the "" sign in our discussions of arithmetic with >signed numbers. The fact that we must give different interpretations to the >"" signs when we give plausibility arguments to justify ()*() = (+) is an >indication of the fundamental artificiality of those plausibility arguments. >Notice that in my earlier post I *did not* overload the "" sign. I used "" >as the unary negation operator *only*. That's one of the reasons I say that >this is the "real" reason why ()*() = (+). > >Lou Talman
W. Gary Martin Curriculum Research and Development Group University of Hawaii



