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Topic: [math-learn] Re: can any one solve my challenge. lets see.
Replies: 2   Last Post: Dec 27, 2010 11:43 AM

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Ralph A. Raimi

Posts: 724
Registered: 12/3/04
Re: [math-learn] Re: can any one solve my challenge. lets see.
Posted: Dec 27, 2010 11:43 AM
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On Mon, 27 Dec 2010, Ron wrote:

> What I think Ralph suggested (with tongue firmly in cheek?

Correct.

Of course I did "figure out" that "a.p." meant "arithmetic
progression", though that is probably by now an archaic designation for
what these days are usually called "arithmetic *sequences*". Once Ms Marx
(the author of that problem) limited it to being about an a.p. she was of
course right in getting the value of a(88), for in the case of arithmetic
sequences it takes only two terms to determine all the others uniquely.

But I pretended ignorance of the meaning of "a.p." in order to
deliver my short lecture on the indeterminate nature of problems of this
type, frequently found in elementary textbooks, and exams, too, where it
is expected the student will *deduce* from the first few terms what the
nature of the sequence must be. Well, he can guess, or read the mind of
the person who set the problem, but students ought not to be subject to
arguments that begin, "Well, you can tell from the differences ..." A
*mathematical* question doesn't allow such observations as proofs.

Ron Ferguson quite correctly elaborated this point.

Over the years that I have seen problems of the incomplete kind
(such as asking for the next term of a finite list of numbers, without
fully stating the rule that makes an answer possible) I have come to the
conclusion that the authors might in many cases be aware that "if you want
to be fussy" there is no unique answer, but are also aware that the
children giving the expected answer will have guessed what was in his
mind, while the other students, less skilled at solving exam problems, are
not catching on. Thus such "problems" are considered worthy in that they
do what exam questions ought to do, which is to distinguish those students
who have learned their lessons from those who have not.

Well, yes, but those particular "lessons" ought not to be taught.


Ralph A. Raimi Tel. 585 275 4429 or (home) 585 244 9368
Dept. of Mathematics, Univ. of Rochester, Rochester, NY 14627
<http://www.math.rochester.edu/people/faculty/rarm/>




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