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

[David Corking]

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