I confine myself here to discussion of the effects of two scientific computation environments on two pedagogical environments: the effect of using the so-called `supercalculators', the HP28S and its successors the HP48S and most recently the HP48G, on the teaching of first year engineering mathematics; and the effect of the more powerful and sophisticated environment given by Maple  on the teaching of graduate students in applied mathematics, engineering, and physics.
I will also mention on occasion some observations arising from the use of MATLAB in the engineering numerical methods course: in brief, it turned the course into one on numerical analysis, and allowed introduction of backward error analysis.
We will not discuss the equally fascinating, and perhaps even more important, effects of recent technological developements such as parallel computers, lattice gas methods, or wavelets. A sufficient reason for the omission is that perhaps their full effects are not yet known. The real reason is that I know nothing about them (yet).