I agree that an understanding of the basic concepts of programming languages is vital to becoming a successful programmer; but man, would you really want to work your way through every single concept before ever writing your first program? It sounds like an awfully painful method to bootstrap your way into writing code. (And besides, I'm not sure there even is a book or a website out there that describes the fundamentals of coding completely outside the context of a programming language...)

If you've got a computer sitting in front of you, I see no reason not to use it every step of the way. For each concept taught to a student, have that student put it to practice immediately, and see the results; at the very least, that seems a more enjoyable way to learn a subject.