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Curiosity.
Galileo had curiosity for all things natural. After aiming his newly refined
"telescope" at the cosmos, he turned it around and looked at the tiny creeping
things that plagued his garden, pronouncing the flea "terrible," and the
mosquito "beautiful." When cosmology became politically dangerous--the
Inquisition was a newly-formed office of the Church--Galileo put that study
aside, and extended the study of motion to such a degree that Newton's law of
universal gravitation seems now to be almost a shallow afterthought. Galileo
determined that bodies in freefall did not fall at a uniform rate, but that
the distance they fell was a function of the square of the elapsed time. He
did this without the help of an accurate timepiece, as none existed! Moreover,
he did this all with only Euclidean geometry and a rudimentary knowledge of
what we now call algebra. Simple tools and a curious mind can work wonders.
I wonder if the writers of the AIMS exam understand this.
Creativity. Galileo epitomized creativity in his approach to engineering tools
to help him explore the world. Take the case of the telescope/microscope
mentioned earlier. While an eye for aesthetics may not be in the Standards
(certainly beauty is in the eye of the beholder), what kind of person would
have thought to turn the darned gadget around and use the same principles of
optics that enable a human being to discern the moons of Jupiter 700 million
miles away to describe the beauty of animals literally right underfoot?
Today, discerning such principles and exploiting their properties in new and
unanticipated fields is a hallmark of the New Economy. What assessment system
is in place that helps us understand how well we are doing promoting our
children's creativity with things scientific, mathematical, and technological?
Not the AIMS test.
Perseverance. Galileo, in spite of political opposition, lack of
technologies, and again, armed with only rudimentary mathematics by modern
standards, engaged his mind in solving fundamental problems that took years to
develop any semblance of resolution. While I cannot, in good conscience,
advocate this level of problem solving as the basic unit of a high school exit
examination, at least the problems should involve more than one step, have
more than one pathway to a potential solution, and require that the solution
be justified through mathematical means. Many of the released items of the
AIMS exam do not even address fundamental conceptual knowledge, let alone
require students to think deeply about those concepts. Note that difficulty
of items and conceptual depth are not the same thing. Items may be
exceedingly difficult, but only address shallow-level thought: Recognizing
the secant of a circle, for example as illustrated in AIMS item 18, as opposed
to reasoning with the concept of secant to determine properties of a curve.
Galileo, a thinker who is admired 400 years after his discoveries, wouldn't
have passed the AIMS test. Who determines the degree to which a test measures
potential for contribution to a vital economy? Granted, Galileo's
contribution was in another time and another place, but I submit that it was
his curiosity, creativity, and perseverance that were the earmarks of his
successes, and not the range of his mathematics. After all, Descartes was a
contemporary of Galileo's, and he was certainly a better mathematician.
However, Descartes' contribution to the world outside mathematics and
philosophy cannot be said to be more profound or impactful than that of
Galileo's. Both are heroes of mine, but for different reasons. Mathematical
sophistication is one avenue to success in the modern world, but there are
other values, perhaps as vital as knowledge of that hallowed content, that
make men and women successful. Wouldn't it be a shame to artificially
eliminate so many from the New Economy merely because they had the one, but
not the other?
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