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Re: numerical methods (was: banning calculators)



I started courses with 739 to the 597'th power just to show how
useless calculators are.

On Fri, 15 Mar 2002, QUIST, OREN wrote:

Yes, these are some good ones.

My other favorite one is to require an answer with more significant digits
than their calculator can provide. e.g. find the square root of 1/(0.98) to
13 (or 14 or 15) places. It's simple to do by expanding it, but students
hate expansions more than they hate to think.

But, I can't think of any real use of such a calculation other than to show
students that their calculators cannot do everything for them.

Oren Quist, SDSU


-----Original Message-----
From: John S. Denker [mailto:jsd@MONMOUTH.COM]
Sent: Thursday, March 14, 2002 9:41 AM
To: PHYS-L@lists.nau.edu
Subject: numerical methods (was: banning calculators)


Justin Parke wrote:

... He wanted to know if long division is still taught in the elementary
schools and how long was typically spent on it. (i.e. do they do division
of a 5 digit number by a 4 digit number or only 3 by 2, for example.) His
thought was to drastically decrease the amount of time spent practicing an
algorithm and use that time to practice estimating what the result of the
division *should* be and then confirming that with the calculator. This is
similar to the idea that students can do integrals while having little idea
of what they mean.

What are your thoughts on cutting instruction on long division in favor of
estimation/prediction?

Tim O'Donnell wrote:

Unfortunately, a student's idea of estimating is doing the
calculation on a calculator then rounding the answer to
the near 1 or 10 or 100, etc.

Then it is the instructor's job to assign problems where
the thoughtless approach doesn't work.

Here is a modest contribution along this line:

Questions:
a) What is 24/25 (to 2 sig digs)?
b) What is 23/24 (to 2 sig digs)?
c) What is 24/25 - 23/24 (to 2 sig digs)? Show your work.
How is this related to answers (a) and (b)?
d) What is 24/25 - 23/24 (to 4 sig digs)?
How is this related to answers (a), (b), and (c)?
e) What is 24*25?
How is this related to answers (c) and (d)?
f) Find a number x such that your calculator cannot accurately
evaluate the expression x/(x+1) - (x-1)/x directly, but
explain how you can use your brain (with or without the
aid of a calculator) to obtain a very accurate result.


--
"But as much as I love and respect you, I will beat you and I will kill
you, because that is what I must do. Tonight it is only you and me, fish.
It is your strength against my intelligence. It is a veritable potpourri
of metaphor, every nuance of which is fraught with meaning."
Greg Nagan from "The Old Man and the Sea" in
<The 5-MINUTE ILIAD and Other Classics>