[drcomputer]

I'm just wondering whether the model of which they base their programming problems for web apps is isomorphic (structurally preserving) to algebraic concepts.

Computer science and development in school is very different from computer science and development in the real world. You don't get to know what you have to know before you know it - that information doesn't exist in the ether of the collective consciousness anywhere. You have to draw it out from yourself.

You might not even know the words for the concepts you have to create in the real world - because they aren't defined, and it's different from pattern matching, finding invariants, optimizing around invariants, simplifying semantically and forming relational constructions. It's different from probabilistic modelling and inference. It's different from a machine doing all those things and a human reasoning on top of it, turtles all the way down (or up, rather).

If you really want to teach people, you have to be able to believe that every person has the capacity to exceed their boundaries and even perhaps demonstrate that you can exceed your own.

This is really philosophical at this point, but don't make the mistakes I've seen tons of educational institutions make. Don't define your students before they learn how to define themselves. Coding at it's core is a creative endeavor. If you want to build robots, code. If you want to build students, learn.