Codeup CEO here: it's the instructors evaluating the students based on their interactions with then and answering the question: how capable is this person of building quality web applications?
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.
That is so subjective that it should be ignored. I've interviewed people who interviewed very well but in practice they failed at basic computer programming concepts and implementations.
We simply do not have an objective measure for program quality and thus do not have an objective measure for programming aptitude.
In the face of this problem we can either give up and not try to measure anything, or we can use an obviously subjective measure and understand where the weaknesses are.
I've interviewed and worked with many people, MANY!, including e.g., Stanford MS CS graduates, who can't write real-world apps. I assume these people can score well on an algebra test. As far as I know, the ability to write non-trivial programs in a commercially relevant time frame can only be judged based on a candidate having already done so. If there's otherwise some way to predict who these people are, I'd love to know what it is.
Social factors in a workplace also seem to be important and hard to predict. Excellent work for one employer isn't necessarily reproducible for another.
These instructors are spending all day, every day with the students as teachers lecturing and helping them through exercises. They're not interviewing them.