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Topic: Favorite Elementary Math Problems
Replies: 10   Last Post: May 10, 2000 12:49 PM

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 JEREMY S. FOGG Posts: 37 Registered: 12/6/04
Re: Favorite Elementary Math Problems
Posted: May 4, 2000 4:40 PM
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One nice example to show how a "pattern" may not hold is to ask students
if the function f(x) = x^2 + x + 41 will generate prime numbers--most may
believe this by the fact that f(x) is not factorable over the real
numbers. If I recall correctly, for 0 <= x <= 40, a prime number will
result--establishing a pattern of primes generated. However,
it should be evident that for x = 41, the resulting number is composite
(it will be divisible by 41!).

This may help with getting students to realize that empirical data is not
sufficient "proof" for the general case.

Jeremy Fogg 8)
University of Northern Colorado

On Sun, 30 Apr 2000, Janet Warfield wrote:

> Al,
>
> I have the same question. I use the locker problem in the methods class for
> preservice elementary teachers. The students in that class have taken 9 credits of
> Mathematics for Elementary Teachers taught in the mathematics department. They are
> able to figure out that the lockers with numbers that are perfect squares are the
> ones that are open by looking for a pattern using the first 20 or 30 lockers. But
> when I ask how they know that all of the lockers whose numbers are perfect squares
> are open, most of them approach the question by picking specific square numbers
> and using factors of the number to illustrate that specific locker is open. Many
> don't seem to understand what I am asking when I ask how they know the pattern
> they have found continues. Their answer is that patterns always continue. I want
> to be clear that this is not true of all of the students, but it is for many of
> them. I would appreciate any advise as to how others deal with this.
>
> Janet
>

Date Subject Author
4/28/00 Ronald A Ward
4/28/00 Hollylynne Drier
4/28/00 otto@math.ilstu.edu
4/30/00 Janet Warfield
4/30/00 Wayne Bishop
4/30/00 Janet Warfield
4/30/00 Wayne Bishop
5/4/00 JEREMY S. FOGG
5/5/00 Todd Johnson
5/5/00 Paul S. Ache III
5/10/00 Todd Johnson

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