My course started with learning structured programming logic by drawing structograms. From 'what is a variable?' to several sorting algorithms and their time complexity. No keyboard was touched, everything was computed by hand to tables. I found it hugely satisfying and think just doing the thinking-like-a-machine bit is a great addition to any curriculum. It doesn't need to make programmers out of every one, it just needs to show young students that programming isn't this black art only math geniuses can aspire to, because it's too often portrayed that way.