used properly, technological aids (calculators, software, reference works on-line or in print), are great tools. they increase our "buffer capacity", we don't have to keep so much information in our heads at one time, and can make "just playing around with stuff" easier. it allows one to shift the focus from computational, to conceptual.

if i have to find the gcd of two polynomials, i have no problem at all with using software to check (or even do) my work. i understand what the answer means, and certainly i get what it is i'm looking for faster.

my girlfriend often says to me: "you think everything is just numbers." i have difficulty explaining to her, that math isn't really ABOUT numbers, it's about IDEAS. and these ideas are things you can talk about without ever invoking numbers: symmetry, patterns, do-ing and un-doing. packaging and disassembly. spatial relationships, shapes, forms. a way to make sense out of what at first appears unintelligible. and these are not things that people should be afraid of, they are the natural result of trying to understand ourselves, and the world we live in.