How can conservative students be persuaded or motivated to learn computers?

one thing that may work it to bet them they cant do it, try rewarding them after learner things. Mabye they can have pizza day after each big exam on the work they are learning!

By conservative I assume you mean: detail oriented, critical thinkers, and students that have a passion for making sense of academic topics, then applying them to real world situations.

Programming may answer that need.

Programming requires the programmer to make plans, organize them in a logical manner then to carry out those plans in a programming language of their choosing.

Alan Perlis said it best:

It goes against the grain of modern education to teach children to program.

What fun is there in making plans, acquiring discipline in organizing thoughts,

devoting attention to detail and learning to be self-critical?

(Epigrams in programming)