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Re: Another Keith Devlin Article on Multiplication
Posted:
Jan 6, 2011 3:38 AM


Jonathan and Anne, thank you
I greatly enjoy this discussion of multiplication. For me the eyeopening moment was Liping Ma's question# for "the other" word problem for 1 3/4 divided by 1/2. It did not take long, but I realized that I was not fit (w/o further training) to teach K4 math. As I quickly realized only after her question, clearly there are at least two different word problems, asking for either of the two factors in a * b = c. Here a = c/b and b = c/a, but a and b have different stories (e.g. number of piles and number of candies in each pile, or, weight/size of each loaf / original loaf and number of loaves, or, as I like better, the magnification factor or the size).
When starting to use CAS in the classroom almost 20 years ago, I first was upset, then loved the idea that the graphs of y=x^2 and y=3x^2 looked exactly the same  not what we were supposed to do according to the syllabus, but a view of the world that might be even more useful (we need both). The factor 3 may be seen just as the scaling, choice of units, the physical object/relation ship is unchanged ...
Matthias *************************************************************** Matthias Kawski http://math.asu.edu/~kawski Associate Director for Undergraduate Programs School of Mathematical & Statistical Sciences kawski@asu.edu Arizona State University office: (480) 965 3376 Tempe, Arizona 852871804 home: (480) 893 0107 ***************************************************************
#Liping Ma http://www.amazon.com/KnowingTeachingElementaryMathematicsUnderstanding/dp/0415873843/ref=ntt_at_ep_dpt_1/18635221530154857



