I think scaling can correspond both to addition and to multiplication. You can scale up and down - also by numbers over and under one if you think more algebraically.
Cheers, Maria Droujkova 1-919-388-1721 Make math your own, to make your own math On Jul 15, 2011, at 9:28 AM, David Corking <li...@dcorking.com> wrote: > Rebecca Hanson wrote (at > http://groups.google.com/group/naturalmath/msg/8fa9efef95a1dd68 ) : > >> Essentially I think there are 3 common primative structures for division: >> >> Splitting/how many each (for one) (e.g. to do 486 divided by 2 - most >> people woudl split 468 into two parts) >> >> Chunking/how many of the divisor in the divident (e.g. in calculation 39 >> divided by 13 most people would think - how many 13s in 39) > > I agree. I read that the terms that some teachers now use are > "partition" (sharing equally among a given number) and "quotition" > (splitting into groups of equal sizes.) > > I found this Australian explanation very helpful: > http://www.education.vic.gov.au/studentlearning/teachingresources/maths/mathscontinuum/number/N22502P.htm > >> Scaling (insights into equivalent divisions - badly neglected in much >> western teaching). > > I feel quite strongly about this, but I won't defend it further here: > scaling is Multiplication. > Division is the Inverse of Multiplication, so it is the inverse of scaling. > > For me, I am afraid I am far too old to recall my childhood > perceptions of multiplication and division. That said, for me, scaling > is the most powerful concept to guide me in extending multiplication, > and division, from natural numbers (1,2,3....) beyond fractions to all > real numbers. > > Regulars at naturalmath and iaep are probably already familiar with > Keith Devlin's 2008 column that inspired my strong feelings: > http://www.maa.org/devlin/devlin_09_08.html > _______________________________________________ > IAEP -- It's An Education Project (not a laptop project!) > IAEP@lists.sugarlabs.org > http://lists.sugarlabs.org/listinfo/iaep _______________________________________________ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep