[IAEP] [NaturalMath] Looking for Concrete "Fraction Experiences"

Maria Droujkova droujkova at gmail.com
Sun Jul 17 21:55:35 EDT 2011

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.

Maria Droujkova

Make math your own, to make your own math

On Jul 15, 2011, at 9:28 AM, David Corking <lists at 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
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