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Re: Another Keith Devlin Article on Multiplication
Posted:
Jan 6, 2011 3:38 AM
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Jonathan and Anne, thank you
I greatly enjoy this discussion of multiplication. For me the
eye-opening 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 K-4 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 85287-1804 home: (480) 893 0107
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#Liping Ma
http://www.amazon.com/Knowing-Teaching-Elementary-Mathematics-Understanding/dp/0415873843/ref=ntt_at_ep_dpt_1/186-3522153-0154857
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