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Topic: another "best practice"

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Subject:   another "best practice"
Author: Don Speray
Date: Apr 20 2003
In my previous post, I mentioned a float-to-rational algorithm.  I meant to
say, "of least denominator" rather than "of lowest terms."  My parenthetical
remark will make more sense!  The best practice I had in mind is to hide the
foibles of the underlying software and hardware system, as much as is
reasonable, from students.

For example, other than fraction drill programs and fraction-capable
calculators, one seldom sees rational numbers in general use in educational
software.  It seems once we leave the obvious applications, software reverts to
the simplest (for the developer) numeric representation, floating point, even if
it isn't appropriate.  Read the first chapter in any good numerical analysis
text and you'll understand that floating point numbers leave a lot to be
desired, pedagogically.  Going back to a polynomial program example, rational
coefficients should be an option, both for input and for output if the curve can
be manipulated graphically.  (Imagine snapping the polynomial to the closest one
with rational coefficients whose denominators are, say, less than or equal to
five.  A teacher could use this to "design" examples with nice properties.)
Vieta's relationships among roots and coefficients would be more meaningful
without roundoff errors confusing students.

Another limitation that could be hidden from students is often the standard set
of input/output controls/widgets that a windowing system provides.  Contrast a
typical Windows application with a Labview application (or any computer game!).
Direct manipulation of mathematical entities would go a long way toward
overcoming what I consider the tyranny of the edit box, yet avoid the criticism
of "non-standard" interfaces.

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