On 2007 Dec 3 , at 11:26 AM, Mike Millet wrote:
... I'm struggling in the class because there is no consistency
between problems, they all use different measurements, ...
Math is difficult enough that I think it's doing a disservice to
people to make it unnecessarily harder by flipping units around.
The math is not difficult; just the unit conversions are.
There's a way around it, some of it anyway.
Solve the problems entirely algebraically. That way, you don't need to
enter ANY units and as a matter of fact you don't have to enter any
numbers either.
At the end, there will be only two steps left to do; plug in the
values (simple substitution) and do the arithmetic. You can and
should, really, substitute the values in the given units even if they
are not coherent in order to demonstrate that you know which values
are represented by which algebraic symbols but carrying out the
arithmetic will not give the right answer until the units are in a
coherent set.
At that penultimate point, you have done all the really important
science and engineering of the problem and that there are only two
relatively unimportant steps to go:
(1) converting the given values to a coherent set of units (SI
metric being best) and
(2) carrying out the trivial step of doing the arithmetic on your
calculator,
You should persuade the professor that leaving out those two minor
steps should not cost you more than a point or two out of the whole
problem. That gives you time to work on the important aspects of the
other problems on the test at the cost of a mere point or two on the
first problem. Losing no more than a point or two here and there
should still allow you to get an A on the test.
If you have time at the end of the test, when you have zipped through
all the other problems by this simplified method, you could go back
and try to recoup the couple points initially lost by not completing
the trivial unit conversions and calculator arithmetic.
I suggest this to you as a student but I also suggest it to any of you
who are or may become teachers. It is the way I taught my physics
courses (algebraic based and calculus based). Of course I never gave
them values in Ye Olde English units. (Oh, OK! Yes I did before 1975.)
But I did tell my students that plugging in the numbers and doing the
arithmetic were trivial parts of any problem and that I would never
take off more than 1 point for failing to carry out the arithmetic or
doing it incorrectly. (I did insist that they plug in the numbers just
to show me that they knew what went where.)
I even went so far as to suggest that sometime I might give a test on
which the directions would tell them to carry out the entire problem
without substituting any values until the last step AND that after the
substitutions were made, I would REQUIRE that they NOT carry out the
arithmetic. I would DEDUCT points if they did carry out the arithmetic
which meant that I would deduct points even for the right answer.
I never actually gave such a test, but I regret that I did not. I
should have done so at least once so I could say that I did it.
Throughout all this, my mantra was:
"Answers don't count, METHODS do. Yesterday's answers may not be
correct in tomorrow's world, but today's methods will still work
tomorrow to solve tomorrow's problems."
Of course, the purpose of learning the methods in the academic world
is to prepare you to find the FINAL answers in the real world.
However, that final step of doing the unit conversion (if necessary)
and arithmetic are things that can be turned over to junior staff
members and their calculators. We must learn to do that, too, but it
is a relatively routine thing to learn to do. The real science and
engineering, however, comes before that.
Regards,
Bill Hooper
Fernandina Beach, Florida, USA
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Make It Simple; Make It Metric!
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