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Re: Technology In Education
Posted:
Dec 5, 2007 1:53 AM
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On Dec 4, 2007, at 7:57 PM, Haim wrote:
> When I look at your animations I can understand the powerful
> attraction of technology in education. It his hard to believe that
> your animations do not help in student understanding. And yet,
> that seems to be the general experience with technology in education.
In these animations, my use of technology is substantially different
from what most people think of when they think of "use of technology
in education". People usually think of students doing interactive
stuff with computers. I think there's a place for that---maybe even
a preeminent place. But when I developed the techniques that led me
to these animations, technology wasn't capable of making them
interactive and delivering them over the Web. Although some of what
you see on my Mathematics Animated site (<http://clem.mscd.edu/%
7Etalmanl/MathAnim.html> for those who missed it earlier) could now
be made interactive with, say Java applets, a lot of it can't because
the computational burden is still too heavy: three-dimensional
animations require quite a bit of calculation. (Note that some of
those animations were made in the late '90's, when almost none of
what you see on the site could have been interactive.) In the near
future, I expect that I will make some of this stuff interactive; I
believe that interactive demos are likely to be more effective.
John Clement has told us that students don't appear to learn from
demos---but he was talking about classroom demos presented by an
instructor who did not provide student interaction. These video
demos don't quite fall into that category. Of course, they can be
projected onto a screen in a classroom. But students can acquire
their own copies and view them repeatedly as they wish. They can
(now---the reorganization is complete, except for the missteaks that
I missed and others will find) study the explanatory notes as they
wish. And I will expand those notes as I think of new or better
things to say and find the time to do so. So I think the jury is
very much still out for this kind of thing.
And I think that in your analysis you've overlooked the student who
would, in years past when people still gave a lot of C grades, have
earned a "gentleman's C", possibly with great effort. These
students, I believe, are likely to profit from more ways of
apprehending ideas. And, especially in multivariable calculus,
students who are poor at visualizing things in three dimensions can
use animations such as mine not only to see what they couldn't see
otherwise but to begin learning to visualize in three dimensions. In
this particular topic, my dream is to be able to give the user a
joystick and let him fly around a three-dimensional surface as he
chooses. We still aren't there by a pretty long shot, though we're
noticeably closer than we were 10 years ago.
And, of course, there is the fact that teachers seem to find these
things entertaining---if not fascinating. I've spent more time that
I'll admit just watching some of those videos play and replay; some
of them even *surprised* me when I first saw the finished product
run---see the Hyperbolic Reflector. ("How to Make a Contour Map" is
my current favorite.)
And there is an application you've overlooked. We require our majors
to learn something about using Mathematica. In the course where we
teach them how to work with this tool, I sometimes show them one of
these animations and tell them to produce one like it. They can
learn not only the programming, but a substantial amount of
mathematics. Try producing a reasonable picture of the surface z = 5
x^2 y/(x^4 + y^2) near the origin, and you'll see what I mean. (See
"A Singular Surface in Three Dimensions" for my rendering of this
surface. If you can find a better one on the Web, I'd like to see it.)
- --Lou Talman
Department of Mathematical & Computer Sciences
Metropolitan State College of Denver
<http://clem.mscd.edu/%7Etalmanl>
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