"The course prerequisite list is, I think, usually a good balance of the right amount of information."
I strongly disagree with this statement. I see many college curricula as hugely time inefficient. Especially when you want to learn deeply on a specific topic. I personally disregarded the prerequisites for many elective engineering classes because of scheduling constraints. And anecdotally I found you only needed small pieces of the prereq's.
You can argue for a 'foundation' all you want. I was simply stating that I would like a detailed list of knowledge required to take a course instead of a generic 'you need a 100 level linear algebra course.' A detailed list would then allow people to decide if they know/remember enough info or need to learn/brush up on a topic. Speaking of linear algebra, seems like a struck a nerve with my made up example.
I also think it is a disservice to say that you need 'understanding [of] those subjects deeply if you want a high ROI.' These kind of statements discourage learning. I have seen many people struggle with so called necessary prereq's only to flourish in more advanced classes.
Conversely, I see the pursuit of quick and shallow ways of learning advanced subjects as the main reason we see posts like this one frequently posted and voted up.
People who only ever search for the quick secret trick to learning X never end up learning X for anything more complicated than for toy examples unless they already have the technical foundation upon which more advanced courses can rest.
I've seen far more people struggle in courses because of weak foundations of prerequisite knowledge than I have people who were irrationally intimidated by simpler material. Weak foundations are arguably the greatest source of problematic learning outcomes in education.
It seems strange to me that a list of prerequisites isn't sufficient. You can always just pick up some old exams or homework assignments (your own or some publically posted ones) and quickly see if you remember.
The type of person who would be discouraged by the idea that becoming fluent in sophomore mathematics would have a large ROI was never going to learn anything nontrivial without changing their mindset.
So you are arguing that weak foundations are one of the greatest sources of problematic learning outcomes. And yet you are advocating for a system that produces those poor foundations and learning outcomes. I just don't understand why you are so hung up on university/school/establishment dictated 'core/prereq' classes as being defined as the foundation.
I would argue that the current pre-req system is responsible. It lumps a full class as a pre-req. And someone can pass a full class while not understanding pieces of it. Those pieces could be the essential ones needed for the specialty knowledge a person pursues. If instead of saying generally, this requires a 200 level linear algebra course and instead enumerated the topics from that course that were necessary than people would know the foundation that is needed. You saying that 'fluency' is required in some broad course is intellectual elitism.
"I see the pursuit of quick and shallow ways of learning advanced subjects"
Also in what way is clearly defined prerequisite knowledge 'shallow'. And where is this coming from:
"People who only ever search for the quick secret trick to learning X"
You are injecting biases into this debate that weren't there in the first place to make it seem like I am advocating some kind of get rich scheme for learning things. I am actually advocating clearer and more descriptive knowledge ontologies. This would allow for better learning efficiency and overall may benefit the field. People would be able to spend more time on depth in the field they want to pursue.
Also using 'never' in an argument is a habit you need to break. It is hyperbolic and usually trivial to find counter examples.
I strongly disagree with this statement. I see many college curricula as hugely time inefficient. Especially when you want to learn deeply on a specific topic. I personally disregarded the prerequisites for many elective engineering classes because of scheduling constraints. And anecdotally I found you only needed small pieces of the prereq's.
You can argue for a 'foundation' all you want. I was simply stating that I would like a detailed list of knowledge required to take a course instead of a generic 'you need a 100 level linear algebra course.' A detailed list would then allow people to decide if they know/remember enough info or need to learn/brush up on a topic. Speaking of linear algebra, seems like a struck a nerve with my made up example.
I also think it is a disservice to say that you need 'understanding [of] those subjects deeply if you want a high ROI.' These kind of statements discourage learning. I have seen many people struggle with so called necessary prereq's only to flourish in more advanced classes.