Re: TI-89 and AP Test
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Re: TI-89 and AP Test
When I taught Statistics at the University of Texas at Dallas back in
the mid to late 70s, I permitted the use of calculators on tests. In
fact, I told the students that they would *need* one for the final. I
told them that all work must be shown. That short circuited those who
had calculators which would do linear regression etc, because they
would have no work to show. But in any case, the tests were designed to
test student's mastery of Statistics, not computation. When I taught
Calculus, I did not even have to prohibit calculators. The tests were
such that a calculator would not have been a help, and the students
didn't even try to use them. Answers were expected to be *correct*. If
I asked a question which resulted in the answer sqrt(2), first I would
not accept 1.414 (incorrect answer), and second, a calculator wouldn't
help anyway, since only at the *end* would it show that the result was
sqrt(2), and who would ever punch that up on a calculator to find out
its numerical value for a *calculus* test? It would just be *extra*
effort (engineers always complain that mathematicians hide behind an
integral sign and call it a solution; *they* want numbers!). The hard
part was deciding whether to integrate or differentiate, performing the
operation, and then doing some trig or algebraic manipulations to get
solutions.
That said, however, I must also point out that calculators these days
are getting to where they can perform algebraic, trig, and even some
calculus operations. These I would forbid in a calculus class. Though
not in a stat class. I would probably forbid them in a Stat Theory
class, however. With these the questions are usually something like
"Find the Maximum Liklihood Estimator for <something>. Devise a test for
<blah> using this MLE. Show that your test is Uniformly Most Powerful."
Finding the MLE might be done on a calculator of that sort, which I
would prohibit.
Mike
In article <36E1A1E8.45B2@hotmail.com>,
John Landis <johnlandis@worldnet.att.net> wrote:
)Peter Ammon wrote:
)>
)> The College Board allows the new TI-89 on the AP Calculus AB and BC
)> tests.
)<SNIP>
)> Comments?
)>
)> -Peter
)
) IMHO, this debate is just the tip of a much larger
)question concerning the use of electronic aids
)in the classroom.
)
) From time immemorial, there have been (at least)
)two philosophical factions adressing the use of
)anything other than the student's brain in theprocess of learning , or
)more specifically, the
)verification of that learning. I strongly suspect
)that when writing was introduced, some of the
)Traditionalists decried it as weakening the memory,
)since having a written record of the information
)removed the need to memorize. Likewise with the
)spread of modern arithmetic : the algorithms would
)have displaced rote memorization of the infamous
)" times tables ".
)
) The other side of the argument is that by using
)such " trickery ", a student is freed from the drudgery
)and mistakes which inevitably accompany a lengthy
)recitation or calculation, and is thereby able to devote
)attention to the real point of the subject- be it literary
)or mathematical, or whatever.
)
) The modern gadgets at the heart of these disagreements
)are conceptually no different than the much older methods
)of writing and calculational algorithm ; they just look
)different. Using a calculator to determine trigonometric values is
)exactly the same as looking up the values in a trig table and
)interpolating ; it's just faster and more accurate.I am not saying,
)though, that these devices can or should replace a true understanding of
)the processes involved.It is vital that the student know which
)algorithms to apply, and in what order. The point I make here is that
)while accurate computation ( or spelling) is required, accuracy is
)absolutely no substitute for understanding. Accurately spelled gibberish
)is still gibberish.
)
) As with most similar debates, the antipody is greatly
)exaggerated.Yes, it is essential that a student should be able to
)recognize when a calculation is in error, and should know where the
)process went wrong. It is just as essential, though, that the student
)know when the calculation is required, and should be able to relate why
)a procedure is or is not appropriate to the situation at hand.
)
) These ideas are not unfamiliar to good teachers. Indeed, I would say
)that the problem of integrating technology into the classroom is one of
)the foremost problems confronting educators as the century draws to a
)close.
)
)
)JLandis
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