The goal of any study is to build a mental model in your head. The math curriculum for example is based on analysis so we gain an intuitive feel for physics and engineering. If the utility of building a model for research is low (essentially 0 since the advent of the internet) this should be a specialist skill, not general education.
A general education should focus on structure, all mental models built shall reinforce one another. For specific recommendations, completely replace the current Euler inspired curricula with one based on category theory. Strive to make all home and class work multimedia, multi-discipline presentations. Seriously teach one constructed meta-language from kindergarten. And stop passing along students who fail, clearly communicate the requirements.
I believe this is vital for students. Think about Student-AI interaction. Does this thing the AI is telling me fit with my understanding of the world, if it does they will accept it. If the student can think structurally the mismatch will be as obvious as a square peg in a round hole. A simple check for an isomorphism. Essentially expediting a proof certificate of the model output.
A general education should focus on structure, all mental models built shall reinforce one another. For specific recommendations, completely replace the current Euler inspired curricula with one based on category theory. Strive to make all home and class work multimedia, multi-discipline presentations. Seriously teach one constructed meta-language from kindergarten. And stop passing along students who fail, clearly communicate the requirements.
I believe this is vital for students. Think about Student-AI interaction. Does this thing the AI is telling me fit with my understanding of the world, if it does they will accept it. If the student can think structurally the mismatch will be as obvious as a square peg in a round hole. A simple check for an isomorphism. Essentially expediting a proof certificate of the model output.