Pippy and Calculate - Evolution Solution

[Yoshiki Ohshima]

  Albert,

  Oh, good.  You weren't simply trying to flame the discussion after
all^^; For now, let me just jump to the last part...

> >   Imagine if the functions that are available in the Calculate "mode"
> > (such as sin, sqrt, etc.) are actually defined in a way that kids can
> > understand (for example, the Newton-method for sqrt, or even a
> > graphical version for sin and cos), and if the user goes to the Pippy
> > "mode", the user can look inside the definition and modify them?  That
> > would be very constructionist.
> 
> Dear my. I'm all in favor of supporting the bright kids, but that
> suggestion sounds like grade 12 honors at minimum.

  No no.  Do you have any reason to believe that cannot be done under
grade 12?  (You can't really mean 12th graders... You mean 12 years
old, right?)

  I happen to have a chat with my boss on this topic, and he told me
an interesting experience with a HyperCard stack called "the function
machine" done by a elementary school teacher in LA.  This HyperCard
stack basically has a funny looking picture of machines.  This machine
sucks a number, does something on it and spits out another number.
Kids are first to guess what the machine does inside.  First graders
could do simple additions, and often could do linear relation and with
linear relation with additive part.

  Of course, then kids get to open the "machine" and write the
function (symbolically) in it.  Now, this becomes a sort of quiz; kids
exchange their machines and play with machines made by friends.  This
was largely sucessful with kids from 1st to 4th graders.

  The Newton-method, etc. may be too early for 4th graders, but
understanding the concept of functions is not that magical.  You can
imagine to make a machine with other machines, etc.

  Remember the famous quote from Jerome Bruner:

	We begin with the hypothesis that any subject can be taught
	effectively in some intellectually honest form to any child at any
	stage of development.

  To make this hypothesis stand, the environment and the form have to
be carefully thought out, but like teaching differential vector
geometry with Logo, there are a lot of evidences.

-- Yoshiki