Well, in a modern context I wish some testing at
degree level was done
without the ability to use a calculator. Mental arithmetic is another
one of those basic skills which does come in handy from time to time,
plus it helps keep the brain sharp.
Another very useful skill is being able to make sensible estimates and
approximations (e.g. \pi^2 ~= g ~= `10. All too often I've had students
give ridiculous errors (I remember one idiot who tried to convince me
that Planck's constant, based on his experimental results was something
around 10^9Js (!)) and not realise that they are _way_ out (in the above
case, the student had dropped many powers of ten in his calculations).
-tony