Getting the student to push a Newton's method button five or six
times during the course of a solution, writing down each iterate,
is much to be preferred to a simple black-box approach. It is
the idea of iteration, after all, that is central to the theory
of dynamical systems. Similarly, step-by-step programs for
linear algebra (exchange this row with that one, etcetera) are
to be preferred at the beginning stages of learning how to solve
linear systems of equations. Get the students to perform more
actions than simply pressing one key.