Jon McLoone makes a good case for using computers in coursework in “Do Computers Dumb Down Math Education?“, but I’d temper the argument with a bit of teaching experience. There’s a time for hand calculation and simple models–learning the basics with tractable formulas and models–and a (later) time for computation and more complex models.
For example, I put my biosciences students through the paces of simple integration to understand CDFs and expectations–always with integrals having closed forms–so they understand the very different things these integrals represent. But we don’t dwell on advanced integration technique for more difficult functions; instead we proceed to symbolic integration with Mathematica, or numeric integration either canned (that’s what a z-table is, folks) or served fresh, from MATLAB.
However, all this is moot if your students are lacking in basic mathematical skills and intuition. My buddy Jaime is teaching classes to students who are learning basic operations on fractions; they need to learn basic concepts of arithmetic and scale before being turned loose with even a pocket calculator.
You think not? On exams and homeworks, about 10% of my bioscience kids–all of whom are high school science geeks-routinely offer up probabilities outside the range [0,1] and slip the decimal one or more places. Please, God, don’t let one of these bozos become one of my health care providers…