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Topic:  Using the Math Tool for various ability levels within one class 
Related Item:  http://mathforum.org/mathtools/tool/13171/ 
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Subject:  RE: Using the Math Tool for various ability levels within one class 
Author:  Mathman 
Date:  Aug 10 2006 
As an application/tool designer, I'm
> curious to know if teachers would prefer a generic tool that they
> can develop a problem around, as described above, or multiple tools
> designed for a certain student ability level.
There may be a need for both. The differences between those of one capability
and the other can be far too wide to try to rely upon one single tool for all,
but some initial studies might have a use. Some problems require simple
mechanical solution. Others require great insight and a wide, general knowledge
base. Differences can be subtle. Change a simple problem even slightly, and it
ccan become most difficult, or wellnigh impossible. One tool can not account
for all of these differences.
Students of mathematics who show great insight would do well to encounter
problems typically of the competition level. Students encountering great
difficulty need much repetition of basic technique. There is a world of
difference, and one tool can not possibly satisfy the needs of all.
Not a great example, but there is a technique in geometry for bisecting any
angle. There is software to do that as well, perhaps more easily ...perhaps
not. Now, suppose an angle is drawn then the paper is ripped across the arms
leaving only two nonparallel lines that lead to the edge of the tear. Now,
the question is how to draw that same angle bisector without resorting to taping
extra paper and so on, but resolving as is. Whether or not one uses an old
tinbox geometry set or software, the problem remains [at first], "Now what?"
The point is then what the software is intended to convey and accomplish.
For the curious, the solution to that one involves recalling that the angle
bisectors of a triangle are coincident.
More keen students need a constant supply of such challenges, and more found in
competitions and olympiads.
David.
 
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