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non-routine problem-solving
Posted:
Dec 19, 2000 12:39 PM
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The issue of importance to me is not whether a particular problem is routine
to the mathematical community. It is whether we confront students with
problems that are not routine _to them_.
I have seen many texts in which all the exercises are exact copies, except
for the numbers, of one of the examples. Students have only to identify the
appropriate example and then work several exercises in exactly the same way
-- they do not even need to read the problems!
This practice of presenting students only with problems quite close to those
they have seen has, I fear, become quite common. I have had students, even
in non-developmental courses, object that a problem on a test was not like
any example we worked in class. Less commonly, I have had students who
tried to work every problem on a test in exactly the way we worked the last
example in class. These students clearly are not thinking about
problem-solving; they are performing a mindless ritual.
Perhaps this is off the point, perhaps not. A psychologist at my school
recently told me that students who have problems with authority are
frequently very math-anxious. My first reaction was, I had (have) problems
with authority! I always liked math because I didn't need no stinking
authority to tell me what was right.
Another possibly tangential comment. I have occasionally watched a math for
the GED presentation on the state network -- never for long, I admit; it's
just too dull. The teachers do a fine job of explaining _what_ to do; but
as far as I can tell, they never say a word about _why_ we do that.
If I can tie these disparate threads together, it looks to me as though
mathematics education has really lost its bearings. Students are learning
procedures and algorithms that will give the correct answer, but they are
not learning what makes the answer correct or how to judge it correctness
for themselves.
Forsan et haec olim memenisse juvabit.
(Someday even this may be a pleasant memory.)
Aeneid Virgil
> ----------
> From: RWW Taylor
> Sent: Tuesday, December 19, 2000 11:07 AM
> To: mathedcc@mathforum.com
> Subject: A vanishing breed...
>
> Jodi Cotten recently asked on this forum:
>
> > Please give an example of what you consider to be a non-routine
> problem.
>
>
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