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Topic: Methods of Comparison
Replies: 7   Last Post: Oct 28, 1995 10:51 PM

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Alfred Barron (908) 704-4102

Posts: 30
Registered: 12/6/04
Methods of Comparison
Posted: Oct 27, 1995 2:00 PM
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Concerning the comparison of learning experiences using
graphing calculators. I'm sure many different forms of
well designed controlled experiments can and have been
conducted. Be careful with the appeal to argument by
analogy with that of FDA's rules for approving a "newly
invented alternate" to aspirin. The rules (procedure)
are complex and involve clinical trials. These trials
are designed so that significant differences (if they
exist) can be measured with credible statistical power.
Even if a manufacturer want's to introduce a different
colored aspirin (let alone a new formulation or variation
of), some form of well designed trial is necessary.

Does it all matter ? People in the industry tell me that
not all aspirins are the same. While they may all deliver
the same therapeutic value for a given set of conditions,
the quality of what happens outside these bounds vary
drastically.

From my own limited experience with graphing calculators,
I know that there are great differnces from model to model.
Not all use the same programming logic (e.g. reverse Polish
logic). Maybe some are more pedagogically sound than others?
Think of all the programming languages available for use.
As technology moves on, less mental labor will be needed to
generate highly informative graphics. Maybe some will soon
deliver in colors.

We need to start teaching about the concepts underlying
the calculations. What is a function ? What do the graphs
of this or that class of functions look like under these
or those conditions... Is there always an asymptote ? etc..
These kind of questions are not answerable by the same
forms of logic necessary to bang out an answer on the
calculator. I'm appealing to the geometric aspect of math-
matics of course. We need to develop our geometric intuition
more. This is occuring more among researchers as they learn
to exploit the power of the computer. Not suprisingly,
geometry has never been a "big" thing in school. We have
algebra I, algebra II, advanced algebra, algebra and trig,
and so on. Have often do you see a geometry I, II, etc ?
Geometry seems to have been on the decline since the 1920s;
maybe earlier. I don't know why. My guess is that our technology
moved in a direction which required the logic underlying
algebraic manipulation. I don't really know. There are many
forms of geometries. With these graphing calculators we have
the opportunity of opening our student's minds to them.

Al Barron
barron@prius.jnj.com







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