The goal of K-12 CS education
Alan Kay
Alan.Kay at squeakland.org
Mon Jul 30 17:05:58 UTC 2001
For a minute let's not worry about satisfying official school
systems, and worry just about teaching "real math" and "real
science". (I use these terms because in the US "math" and "science"
have been "colonized" to actually mean "fake math" and "fake
science". And let's suppose we are interested in having the children
actually learn a strong combination of the two.
There are some very interesting implications that arise from these
goals. One is that we should try to help children develop "uncommon
sense" (instead of the 80,000 year old common sense that most
cultures bestow). We especially would like the uncommon sense to
include both the epistemological stance of science towards knowledge
and knowing, and also a large toolbox of modern heuristic methods for
thinking, having ideas, and colliding theories.
If we could come up with a "new math" that included the (a) new math
of complex internally interacting systems, and (b) a new math for
differential vector geometry and quasi-linear relationships, whose
foundations can be taught to children as play, then we might be able
to make some progress.
Simply put: objects in relationship is a nice way to do (a), and
turtle geometry with costumes is a nice way to do (b).
Where the play gets applied and transferred is in the gradual
escalation of the systems that can be modeled. Just the simple car
with "car forward 5, car turn 5" is the differential vector geometry
expression of a circle (as can easily be seen if the pen of the car
is dropped). Each constant differential vector is added (the loop
acts the part of the integral sign) and the result is an expression
for constant curvature (a circle) whose derivative, the change in
curvature, is 0.
Now the few children who even get to calculus do not usually learn
this in the US because the pathway is Cartesian coordinate, numeric
and algebraic. What Papert proposed to do years ago was to simply
start the kids off on the precursors for modern mathematical thinking
in science.
When the child hooks the steering wheel into the car (via dragging
the "steer's heading" tile into the "car turn by 5" tile) they are
painlessly learning about variables and why variables are a great
idea.
When the child makes the car into a robot car that can follow a track
by itself, they are learning the powerful idea of feedback that is so
central to animal and mechanical controls systems that don't have
complete knowledge. The next stage of this is to make a gradient
follower and now they can model what salmon, clownfish, and ants do
in critical phases of their existence.
The combination of science (trying to understand cause and effect
"out there") and math (trying to model useful and interesting
relationships) is extremely powerful.
So the possibilities for transfer are both large and successful if
the further curriculum is also in accord with modern math/science.
(We have been doing this for 30 years now and have seen much
convincing evidence.) The difficulty with getting this stuff going in
the US has primarily been the lack of any kind of math preparation on
the part of K-8 teachers. (Also, for political reasons the math and
science groups do NOT cooperate in the US very much.) This is a huge
problem.
In any case, those who are interested in this stuff will find quite a
bit in the current Squeak to this end.
Cheers,
Alan
At 4:08 PM +0200 7/30/01, G.J.Tielemans at dinkel.utwente.nl wrote:
>-----Original Message-----
>From: Alan Kay [mailto:Alan.Kay at squeakland.org]
>Sent: maandag 30 juli 2001 16:12
>To: squeak-dev at lists.squeakfoundation.org
>Subject: Re: The goal of K-12 CS education
>
>
>Do you folks realize that every Player (the automatic wrapping of a
>morph for kids) in Squeak is a turtle? Get the handles by cmd-click,
>then click on the blue eye to see the viewer, then look in the
>category called "pen use". Change pen down to true.
>
>Cheers,
>
>Alan
>
>> OK Alan, the problem of transfer: Suppose I learn in Squeakland to build a
>car and automatic run a track with the color-under-command. Where can I
>apply this knowledge outsite track-racing or other kinds of mazes (like the
>moving robot.) What can help me to come to better transfer from this
>knowledge-molecule?
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