Some students are like lawn mowers with no gas in them. If you pull the
rope real hard, you can mow the grass in one 21" diameter region. Then
you can move the mower to a new region and pull the rope again. If you
do this enough times, you can mow the entire lawn, but it's horrifically
labor-intensive.
_
(_)
//
//
//
//
.-n---. //
_ _ _|_"_O_|_//_
/ __ __ \
/ / \ / \ /
`-\__/--=====-\__/´
Every so often, though, you find a student who has gas in the tank. You
pull the rope once or twice, and then they go off and mow the entire lawn
by themselves.
I got this parable from Ben Wittner, who attributed
it to his advisor, John Hubbard.
========================================
This is connected to the idea of _retention_. Obviously it doesn't do any
good to teach something if the students aren't going to retain the knowledge.
My point is that mere retention isn't the highest possible goal. Instead,
imagine that you teach for nine months, and then the kids go away three
months of vacation ... and come back knowing _more_ than you taught them.
That's a nice goal to have.
Some people think this goal is over-optimistic (to put it politely), but I
don't think it is completely wacky, and I think it can at least serve as the
starting point for an important discussion. John Hubbard was talking about
graduate students, but I've seen enough self-propulsion in teen-aged kids to
know it is possible.
1) For example, a couple of weeks ago I was looking over the shoulder of a
12-year-old kid (soon to be 13) whom I had taught to write computer programs
(using gamemaker). He was editing the image of a sprite (i.e. moving object)
to be used in a game he was working on. I noticed that the image editor was
set to 1024x1024.
jsd: What are you doing, making a reeeally big sprite?
kid: Huh?
jsd: 1024 by 1024?
kid: Oh, no ... I scale it down to 32x32 before I use it. But I do the
drawing at 1024 by 1024, because it gives me more control......
jsd: Hmmm, that's a really good idea. Let's talk about that.........
I didn't teach him that. I didn't teach him anything remotely like that.
I didn't even mention the image editor; I told them to just scrounge for
images using http://images.google.com/. I'm virtually certain the importance
of scaling isn't in the manual, and I'm virtually certain the kids haven't
read the manual anyway. (It's 223 pages and not very well written.)
He figured it out.
I hope you can appreciate that this scaling trick is (a) really useful,
and (b) nonobvious. I can explain if anybody is interested in the next
level of detail.
2) I also found out that one of my students turned around and taught one
of his 13-year-old friends how to use gamemaker.
I figure if he's at the point where he can teach it, I don't need to
question whether he really understands it, or whether he will retain it.
============
I mention this because it cracks me up when I read that "research shows"
that young kids are incapable of abstraction, incapable of symbolism,
devoid of imagination, devoid of creativity, and almost incapable of
anything we would recognize as thinking. Phooey!
It takes a goodly amount of symbolism and abstraction just to be able
to play the sort of games we are talking about ... and then the process
of /creating/ the games is another level entirely:
-- the game concept requires lots of imagination, and
-- the implementation requires layers upon layers of abstraction; I'm
talking about object-oriented event-driven real-time programming.
There is another side to the argument: Of course kids will not
/exhibit/ much (if any) powers of abstraction, imagination, thought,
etc. if they are not interested in the subject.
Also, I am aware that some people have serious cognitive impairments.
Oliver Sacks writes books about this. If you show me somebody who
is so impaired that they cannot play video games, because they cannot
understand the relationship between the symbols and the things
symbolized, then I'll agree that such persons should not be enrolled
in physics. Such persons *will* be "left behind" if we set the goal
high enough that abstraction, symbolism, imagination, and thinking
are required in school ... but what's the alternative? We do a
treeeemendous disservice to the other 99+% of the students if we do
not expect and demand abstraction, symbolism, imagination, thinking,
et cetera.
We tell ourselves that physics class is important, partly because of the
physics-related domain-specific facts that are covered, but also because
physics class traditionally/supposedly teaches important thinking skills.
(Note that traditional HS geometry is another class where the thinking
skills are more important than the domain-specific knowledge; knowing
how to do a _proof_ is far more important than knowing the area of a
parallelogram.)
We now come to some questions where I don't know the answers ... and probably
these are not even exactly the right questions.
Since it appears that students will exhibit imagination, creativity, symbolism,
abstraction, thinking, etc. if and only if they are interested, how do we make
our teaching sufficiently interesting? Can we make HS physics as interesting
as a video game?
a) If not, why not?
b) If not, should we perhaps change tack and teach something more interesting
instead, even if it means giving up a large part of the traditional HS
physics curriculum? There's no point in teaching the domain-specific facts
if they are not going to be retained, and if the thinking skills are what's
important, we are free to look for other ways of teaching those skills.
By way of example (not the only possible example), we might consider the
possibility that a course in game programming could take the place of HS
physics *and* HS geometry. Obviously there is a great deal of Cartesian
geometry involved in moving stuff around on the screen. It is amusing to
see kids who will not take HS geometry for several years but are already
conversant with dot products, such as taking the dot product of the velocity
vector with the separation vector. Also there is a certain amount of
physics involved, including collision physics, Galilean relativity, etc.
(You can imagine that I have a rather math-intensive and physics-intensive
programming style, and I'm not shy about passing it on.)
There is also the notion of "provably correct" code. The standards of
rigor required for such a proof are at least (!) as high as the standards
of HS geometry class.
There other thinking skills involved. Debugging a big computer program
demands serious thinking. It's fun to watch kids racking their brains.
They go through the same steps that big people do.
All this involves setting high goals. But why should we not set high goals?