Bell Lab's cardboard computer ( https://en.wikipedia.org/wiki/CARDboard_Illustrative_Aid_to_... ) came to mind, but you are probably right that studying algorithms (and at least something about hardware) is probably the best starting point. As it is some time since I was in school, I am not sure what counts as a good introductory text these days.

This does not give any experience in debugging, which is not taught in books, AFAIK. I am not sure what to do about that...