I have seen a great many students of the type described by Gary
Hemminger, and tested many hundreds more in high schools and colleges of
all types. They are not over calculused and under algebra-ed. They are
over calculus-ed, often over algebra-ed (though they don't understand
it), and woefully under arithmetic-ed (to coin several horrifying
verbs). Thus the example quoted by Gary of being unable to do 0.6/0.3
without a calculator (or sometimes WITH a calculator, because they can
punch in the numbers in the wrong order and be unable to tell that the
answer is not sensible). At Lehman College in New York (CUNY) an
embarrassing fraction of physics students can not do:
"Divide .738 by .9"
I would add that my diagnostic test shows that a large majority of the
elementary school teachers, who taught arithemtic to these students, are
in the same condition -- or worse.