The Trouble with 5 Examples SoCal-Nev Section MAA Meeting October 8, 2005. Jacqueline Dewar Loyola Marymount University. Presentation Outline. A Freshman Workshop Course Four Problems/Five Examples Year-long Investigation Students’ understanding of proof.
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The Trouble with 5 ExamplesSoCal-Nev Section MAA MeetingOctober 8, 2005
Jacqueline Dewar Loyola Marymount University
Is it true that for every natural number n,
If 4 divides n, then n! ends in zeros.
24! ends in 4 not 5 zeros.
From the factors of 10,
so count the factors of 5.
is prime for every nonnegative integer.
Nonstandard problems give students more opportunities to show just how often 5 examples convinces them.
Respond from Strongly disagree to Strongly agree:
If I see 5 examples where a formula holds, then I am convinced that formula is true.
‘Convinced’ does not mean ‘I am certain’…
…whenever I am testing a conjecture, if it works for about 5 cases, then I try to prove that it’s true
Please examine the statements:
For any two consecutive positive integers, the difference of their squares:
(a) is an odd number, and
(b) equals the sum of the two consecutive positive integers.
What can you tell me about these statements?
3 Stages of expertise development
e.g., they lack the confidence shown by experts
With thanks to Carnegie co-investigator,
and Workshop course co-developers,
Suzanne Larson and Thomas Zachariah.
The resources cited in the talk and the Knowledge Expertise Grid can be found at