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Topic: Rich Imagery in the Math Classroom

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Subject:   RE: Rich Imagery in the Math Classroom
Author: Mathman
Date: Apr 10 2006
On Apr  9 2006, FullerMath wrote:

>using their overhead
> projectors less and less.

When I started teaching about 40 years back, I saw the overhead projector used
then, and vowed never to use one.  I did ...but only once.  It was not
bullheadedness.  I simply did not see any advantage. in fact, the effort to
prepare the materials was sometimes a disadvantage.

>They have dry erase
> boards and use multiple colors as an integral part of
> concepts.

We used coloured chalk.  I'd have liked a dry-erase ...much cleaner!

>They also have changed their langauge about using a
> calculator. For example, which of the following two
> offer a richer learning environment?
<i>Just press STAT 4.</i>
> <i>Let's use statistics to generate a linear regression.</i>

Sorry, but that might not be a best example of your intention?  That choice has
little to do with technology, but has to do with pedagogical approach, and
reflects a dull and boring vs an interested and knowledgeable teacher, not the
choice of instrument; calculator or learned pen and paper techniques.

I taught mathematics, and found a lifetime of "rich imagery" in
Euclid as well as all other studies.  Here's a simple example, and I wonder how
it might be done differently or better without compasses and straightedge:

The problem is to draw tangents to two circles.  If the same size, there is no
problem, the construction being basically a rectangle.  If one circle is
noteably smaller than the other, there is a technique that is not too demanding,
simple in fact.  If the circles are close in radii, but not equal, then the
first is not possible, and the second is not feasible because of limit of
distance required using the same technique, and the problem becomes a pretty
problem [which I had solved and was able to demonstrate or offer to keen

Sorry I can't be more descriptive since binaries are not allowed, but it really
is a problem that contains a wealth of mathematics both analytic and visual.
...and that is only one example.  There are a thousand more.  My point is that
there is "rich imagery" in everything we see around us, if we look.

Perhaps my point is also that those who have learned to graph by hand will find
graphing programs, whether on computer or computerised calculator a great
advantage ...later [I certainly do.]  Those who have not learned to graph by
hand will simply, as you imply, press buttons.


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