I feel both human-ability and technological-assitance should go hand-in-hand. We have to give equal importance to making students use a calculator and also learning how to do it by hand. I also feel we should encourage students to use softwares like Mathematica and Matlab. Otherwise, what advantage does a future mathematician have over old-timers!
With this background, I feel there should be a clear emphasis on the interpretation of the results a student obtains on performing a calculation.
'The purpose of computing is insight, not numbers.' -Hamming.
For example, we can use the the series
$\frac{1}{1+x} = 1-x+x^{2}+\cdots,$ for $|x|<1$ to demonstrate the fact that if $|x|<<1$ (|x| is far far less than one) then $\frac{1}{1+x} \approx 1-x$ and show the results in a calculator.
Say, $(1.001)^{-1}$ can be easily seen without the use of calculator as approximately equal $1-0.001=0.999.$ Division problem can be turned into a simple subtraction problem. After showing algebraic manipulation, we can show the calculator result and ask students to interpret the precision and give a good explanation.
We could also enhance Mathlete competitions and make students learn to calculate mentally faster than a calculator, for which we need calculators!
