16 Oct
2011
16 Oct
'11
1:32 p.m.
On Sun, 16 Oct 2011, Tony Duell wrote:
"Because the textbook says, 'PI is about 3.14.16 or 22/7', and therefore
since the textbook said that 3.14.16 is 'ABOUT', but didn't say 'ABOUT
22/7', it is exactly 22/7 ."
The principal did not know better!
My parents knew better, but would not believe my protestations that
disagreeing, and refusing to retract, was all that I had done wrong.
In the eyes of the school system, any kid who knows more than 3 digits of
PI in 5th grade needs to be brought back into compliance with the norm.
(no, that did not remain my only manifestation of maladjustment)
THis reminds me of a related issue :
Since almost everybody uses calculators and computers now, it's often
said that learning things like how to do long multiplication and division
is unneccssary for most people (well, unless they want to end up
designing clacualtors and computers...).
During the span of my teaching, I watched the transition from VERY few
people remembering how to compute a square root ("well, it looks a like
long division") to nobody knowing that a square root CAN be calculated!
Those who "once knew" were grateful when I taught the class progrsessive
interpolation (binary approximation) using squaring a series of "trial
candidates", and now had a way to do it that they "could understand".
But of course such amchines are not mathematically
perfect, there are
rounding erorrs and the like [1]. I feel that if you'r not going to
teach how to do soemthing by hand becuase everybody uses a machine to do
it, you should instead teach why the machine doesnt' always get the
mathematically correct resualt, and how to handle the common pitfalls.
"Get a better calculator/computer/floating point co-processor"
"Just use 'double precision'"
Just making them divide 1 by 3, write down the result, and then multiply
what they had written by 3 actually helped!
As did going over the "rules" for "leap years"!
But, surprisingly, making them convert PI into the bit representation
for IEEE 32 bit floating point, helped them to understand the basic
concept that floating point is a WRONG, but "close enough" approximation.
that PI was
EXACTLY 22/7 ! (half a century ago, in elementary school, I
got into "big trouble" for telling a teacher that PI was NOT 22/7 !)
I
have never understood the windespread use of that approximation. 'How I need a drink, alcholic of course after the
heavy lectures involving
quatnm mechanics'
BUT, you have 3.141592653589 6 9
instead of 3.141592653589 8 9
in spite of presumably knowing a bit about quantum mechanics.
Now, THERE is an argument for bing more careful about speling!