This generation gap doesn't exist in the sciences and engineering, IMO.
For example, even the crappiest students in my class (in Physics) knew how to do a taylor expansion to approximate the sine of something, and they knew power series and all sorts of other stuff. You have to know how in order to simplify algebra in many cases.
If there is a generation gap, it's because professors aren't strict enough and unwavering on their decisions to not use calculators, or the courses aren't doing hard enough algebra and calculus to really merit not using a calculator. When you get into the really hard stuff, not even Maple can help you half the time.
calculators have been generally available for a long time, well over 30 years
Thirty years before 2011 is 1981. That's not true of graphing calculators generally being in the hands of high school students. By that year, many engineering students at university had calculators that could do calculus (usually with a "solve" algorithm) but the graphics plotting was just beginning for hand-held devices for university students. I was alive and studying math in the relevant years. Four-function or "scientific" calculators in K-12 schooling were just coming in during the 1970s.
After edit: while I disagree that calculators have been pervasive and encouraged in either elementary education or higher education for much longer than thirty years, I agree with the (grandparent?) comment that the curriculum in K-12 mathematics in the United States is lousy, and has been lousy through at least three different eras of curriculum fads, calculators or no calculators. The curriculum is indeed the key issue. Calculators are a useful tool, and today they belong in K-12 and in higher education. For a classic comment on how much calculator technology has progressed in the last fifteen years, see
It is the curriculum.