17 Aug
2005
17 Aug
'05
4:59 p.m.
On Wed, 17 Aug 2005, Tony Duell wrote:
part of why I include the "extraneous" "write it down and turn off the
calculator for 24 hours"
Thrivial example... On most (if not all) calculators,
try something like
1 E 20 [enter] 1 + 1 E 20 -
(Ooops, that's in RPN, I've forgotten how to do it on a normal
calculator, try soemthing like 1 E20 + 1 = - 1 E 20 = )
Explain why the result is not 1 (OK, we all know the answer here...)
An excellent example. Unfortunately, some of them are using cereal box 4
function calculators, some of which won't permit input of 1E20, and may
require different values from one to another.
Hmmmm! If I come up with a similar simple example using the WINDOZE
calculator, then I can kill two birds with one stone.
(I think they fixed the bug in the Windoze calculator that caused the
Windoze 3.1 calculator to come up with 3.11 - 3.10 => 0)
Then take the
number that you wrote down (0.3333333) and multiply it by 3.
EXPLAIN what is wrong with the calculator to not give 1.0."
And hope nobody
has an HP49, which does this _symbolically_ and gives the
exact answer...
More interesting, why do some lesser calculators apparently give the
right answere if you do 1 / 3 = * 3 = ? And why do I object to such
designs ? For non-negative numbers, sqrt and x^2 are inverse
operations. Enter any
number, take the sqaure root 100 times in succession. Now square the
result of that 100 times. For numerical (as opposed to symbollic)
calculators, you'll get an answr of 0 for inputs such that 0<=x<1, and 1
for inputs such that x>=1.
Some of them do just fine and understand what is going on with squaring a
square root. But some of them have SO little actual understanding of math
that they don't get it.
Teaching beginners is incredibly frustrating.
But it makes it all worthwhile if/when they understand.
... and it is FANTASTIC when when SOME of them over the years go on to
exceed my [admittedly very limited] abilities!
--
Grumpy Ol' Fred cisin at xenosoft.com