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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:
schools and how long was typically spent on it. (i.e. do they do division
... He wanted to know if long division is still taught in the elementary
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.
estimation/prediction?
What are your thoughts on cutting instruction on long division in favor of
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.