I heartily second Bill's approach below to problem solving. I did the
same thing as a physics teacher. Setting up the problem, identifying the
relational formulae, and doing the algebra provided the bulk of the
grades. The arithmetic counted but for only a point or two (out of ten).
I also encouraged them to go through the exam and to set up (sketch,
principle, and relational formulae) all the problems they were going do
solve, even before they did any algebra. The algebra and arithmetic were
where math majors are taught to pick up the ball, once the physicists
had done the hard work. (Tweak, tweak.)
Jim
Bill Hooper wrote:
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
==========================
Make It Simple; Make It Metric!
==========================
--
James R. Frysinger
632 Stony Point Mountain Road
Doyle, TN 38559-3030
(H) 931.657.3107
(C) 931.212.0267
