I polled all of our science teachers several years ago and asked them for an
example of where they use a factorable polynomial in science. One
instructor sited an example of a difference fourths that was ocassionally
covered in class. Another instructor thought there was problem he did in
grad school that involved a factorable function but he wasn't sure. Our
recently retired Physics instructor as well as our newer younger faculty
member are sold on the graphics calculators for several reasons--one is
because they as well as the students can input an entire arithmetic
expression on the screen at the same time and then bring the expression back
to edit if something is incorrect. Our retired instructor has expressed
disappointment that his students do not use of calculators (scientific or
graphics) efficiently. To solve a quadratic equation, they calculate the
discriminant, write that down, then calculate the square root, etc.
As a math student in the 60's, I learned a lot about logarithms by doing
numeric approximations of messy arithmetic expressions using logarithms,
dealing with the characteristic, mantissa, and tables. I am not suggesting,
however, that that is the only way to learn and understand logarithms and
would never suggest we bring those problems back. Scientific calculators
have made those calculations so much easier that we no longer need to use
such tedious means for calculations--even though they served an additional
purpose of further teaching the concept of a logarithm and mathematical
thinking. Graphics calculators and computer/calculator algebra systems need
to challenge us to continually redifine mathematics curriculum and re-learn
how to teach mathematical thinking in a high tech world. This is a tough
challenge for math teachers who came from the old school and value our
rigorous education. To learn how to make mathematics relevant and rigorous
in a high-tech world is a much greater challenge than any work we ever did
in graduate school.
Martha
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