Hi Subbu,
As usual you ask really good and deep questions (which I have a hard time
answering at all, let alone briefly!).
Actually, I passed out several documents to OLPC at a "countries meeting" a few
years ago (a book that we had written for teachers containing about a dozen of
these activities, and a 50 page work in progress document that tried to say a
little more).
We've aimed at 9-11 year olds for this curricula.
First let's take the "math" part (what can be done just by using the computer).
Here we've got something like an artistic medium which can be shaped into forms
and processes. But, since the actual discovery of really powerful ideas has
been difficult for the smartest humans over the last 100,000 years, we do
"carefully guided discovery" in which "carefully guided" and "real discovery"
are both strongly heeded.
A typical activity is in three parts, sometimes stretched over weeks.
1. Show the children how to do the "front part" of an idea
2. Challenge them to figure out some larger part of the idea from what they've
been shown
3. Let them come up with and do their own projects based on what they've just
done
The "idea" has to be some wonderful combination of a powerful idea (like
feedback) and a setting that is deeply within the world of the child.
Montessori is the patron saint here and later Seymour Papert.
For example:
1. Get them to draw a car and a road, talk about how you can make progress
without having full information. Get them to close their eyes and fold their
arms and follow the inside or outside of the classroom or a table just by
bumping and going and turning away and back. Show them how to test a color on
the car against the color of the road to make a simple feedback program that
will get the car to follow the outside of the road in the very same way. No
real discovery here, but the aim is to relate bodily thinking with in the
computer thinkiing.
2. Challenge them to devise a car and road so that the car will go down the
center of the road. With 30 children you will get as many as 7 different kinds
of solutions here, and most of the children will be successful.
3. This will get children thinking their own thoughts about what would be cool
to do. For example, one of the movies from these activities shows Jenny's "Pig
Race" (she like animals rather than cars) and she realized that being able to
drive a vehicle down the middle of something would allow her to make a race
track with lanes. She also needed another powerful idea (random numbers) to
make the races interesting, and these and straight line races had already been
introduced.
All three of these phases are important. And you can tell how well things are
going by the amount of activity using the system in phases 2 and especially 3
(this means they are into the whole process for their own reasons, not just
ours).
I would say that this is quite similar to a good music curriculum (not a
coincidence). Music has similar elements of stuff that has to be guided, and
stuff that needs to be created by the learner, and all points in between. Just
banging away on something whether keyboard, guitar hero controller or computer
misses the whole point.
Another point is that computer tools tend to be more specific than life, so
that bringing an arbitrary idea to a computer for pedagogical purposes usually
doesn't work well. (I see people doing this over and over) What I do is to most
of the time think about what Etoys is good at and how this intersects with
powerful ideas in the child's world, and a smaller percentage of the time to
change Etoys if a wonderful powerful idea doesn't fit and there is a way to
make it fit. What I don't do is to try to bash in a poweful idea that is
awkward (Turing's observations don't apply here).
A lot of the math elements of this kind of curricula came out of the ideas of
Seymour, Mitchel Resnick, Andy di Sessa, our work at PARC, and elsewhere.
Again, one is looking for powerful real math that can work in the child's
sensibilities (some of this will not need the computer to help, and some will
be made feasible only by using the computer). Seymour and I both have math
degrees, and Andy and Mitchel were physicists, etc. It is hard to imagine much
good coming here without the thinkers having a lot of knowledge on the one
hand, and a lot of sympathy for the child's point of view on the other.
The "differential geometry of vectors" is a perfect example, and was first
adapted by Seymour.Quite a bit of the mathematical language of science is in
this form, and it is indeed powerful. As Seymour pointed out, the child is
always at the center of its own coordinate system, and this is the way
differential geometry works. A really important observation is that the
computer can add vectors (a generalization which includes numbers) very
rapidly, so most thiings can (a) be kept just in terms of incremental additions
(human minds can actually grok these) and (b) this allows the whole apparatus
of differential equations (actually "differential relationships" on the
computer) to be used by a 10 year old in the form of "increase by" and simple
loops.
The result is the deep math of calculus and vectors but in a very different
form which does not require algebraic manipulation to use. Its not that algebra
is bad (quite the opposite) but that it often masks the powerful ideas of
calculus (which have nothing to do at all with algebra).
Similarly, trigonometry is really about similar triangles, and much of what is
powerful about it can be taught to children geometrically and in vector form
much earlier and deeper.
As I mentioned, science is the relationships between what we can do with our
representation systems and "what's out there?". So the pedagogy here has to do
with finding stuff in the real world of the child which can be explored in a
deep scientfic way. The gravity activity is a good one because it involves
gross phenomena, is not at all as human common sense would suppose, can be
captured qualitatively (drop two objects and listen) and quantitatively (use a
video camera to get the motion every 30th of a second), mathematically (the
differential geometry of acceleration does a good job of modeling the Galilean
approximation), scientifically (it involves measurements that can't be
completely accurate and thus opens the door to speculation about "what else
might there be there?", and so forth.
One of the exercises that is done well in advance of the actual ball dropping
is to get the kids to try to measure things using different means, and to get
into the philosphy of measuring (that it could very well be the case that we
can't really measure accurately and thus have to temper our "absolute
enthusiasms" with tolerances) -- historically this was the real beginning of
real science in the west, when mariners needed accurate maps, but realized that
accuracy meant including error tolerances with the observations.
Boiling all this down, it's just real math and real science for real children's
minds and using the computer when it really helps.
Cheers,
Alan
________________________________
From: K. K. Subramaniam <subb...@gmail.com>
To: iaep@lists.sugarlabs.org
Cc: Alan Kay <alan.n...@yahoo.com>
Sent: Thursday, July 2, 2009 7:30:27 PM
Subject: Re: [IAEP] Physics
On Wednesday 01 Jul 2009 6:05:08 pm Alan Kay wrote:
> An important part of "ball drop" was the separation of 3-4 months between
> "the math" (scripting various kinds of motion for the children's painted
> cars and dropping markers to reveal the history of their motion), and "the
> science" (handling various 3-4" spherical objects ranging from fruits to
> sponge and croquet balls, and two weights of shotputs; speculating on how
> they would fall relative to each other, coming up with ways to determine
> this, and then a range of experiments in which the janitor dropped the
> objects.
This perspective on doing experiments is missing/too brief in the DVD and the
online clips. What options were considered? Why were some dropped? Why was
this way of learning gravity chosen? Like the first scene in "Designing the
curriculum".
The thinking and planning that goes into such experiments deserves to be
shared and replicated on a whole scale.
Subbu
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