Not sure the history in itself is useful but starting from the beginning is probably a good idea.

A solid grounding in logic should come first. Then we can skip quite a few of the blind alleys because there simply isn't time to cover every byway from Pythagoras onwards.

But always the foundations must be solidly built or we end up with people who can crank the handle on the algorithm they have been taught but can't understand what to do when it doesn't apply.