I'm working through a 1953 edition of Thomas's _Calculus And Analytic Geometry_. When I work problems, I use Mathematica to type my transformations, and to check my results. I use it for far more, as well; graphing, numerical solutions, etc.
Many years ago I found computers to be a nuisance when it came to math, and more importantly physics. I was contented to have a piece of chalk or a pencil and an eraser, than to have all the computing power in (the) Universe. Time was the only resource I found in short supply.
Now that I have used them for years, I realize that computers can do a whole lot. They can find integrals for equations which I cannot integrate by hand. They can produce graphics which a human could never produce, etc.
I've used a pocket calculator since the 1970's. But, I feel as if I should have learned to work the same problems on my own. I feel somewhat crippled by using it as a crutch.
I'm in a conundrum twixt the use of computers to do my thinking for me, and learning to think for myself. Should a child learn his times tables, or learn to use a computer to do it for him?