"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.
I shouldn't have used the word curriculum. I went to a top university and I know how frequently those prerequisite courses can be totally off base (my degree is chemical/biomolecular engineering). I used the term 'pre-requisite knowledge' because I would prefer a list of what ideas/concepts are needed to be fully understood before taking the course (ex/ instead of saying linear algebra is a prerequisite, say you need an understanding of solving linear equations using matrices but you don't need to understand linear spaces. Then you can focus your effort better and not take a 40 hour pre-req that you only need 4 hours from)
Agree with @flukus. I didn't put anything about pre-requisites because I didn't want to drive anyone away. Anybody seeing these things for the first time can just google it and learn right?
> In a lot of STEM fields there will be one or more required courses in the 3rd or 4th year of a 4 year bachelor's degree program that are significantly harder than anything in the first two years.
Sure, but then the "weeder course" should directly relate to that challenging required material - perhaps by introducing it in a simplified, approachable fashion but with high-standards assessment. The OP's linear algebra class does not seem to be anything like that. I stand by my opinion that the "generic weeder course" pattern is most often a convenient rationalization for what is, at its root, a badly taught course. This doesn't mean it can't become somewhat intentional, but that's secondary.
All of which complexity used to be handled by printing a course guide with a sentence about prerequisites. And perhaps the professor would remind you on day one. This seems like an example of IT not saving anyone time.
the very concept of structured courses in education is because we don't know what to study to understand XXX things.When it comes from a teacher , it comes with a dependency graph drawn by a person who knows the course.If proper knowledge gathering is considered an objective.This dependency is a natural consequence of subject-matter than an optional one .
For e.g. for someone to learn abstract algebra ,its highly suggested that they take up linear algebra first.As for me, i've always the dependency graph quite seriously .May be the gifted brains can leave linear algebra and directly take up abstract algebra , is that so?
If that is a part of the syllabus than okay. But if that isn't clearly stated as a goal of the class at any point than it doesn't make sense.
If the knowledge is necessary, it sounds like there should be an additional class before said class to give knowledge that can be built on in the more difficult advanced class.
A lot just aren't very good but they also tend to make assumptions about prior knowledge in line with what would be typical prerequisites for a class and some degree of guidance.
"A humanities student"? She's a humanities student who had taken up through linear algebra! I have a CS degree and I never learned linear algebra in high school or college--I learned about the topic later!
The idea that a 200-level course should be unapproachable for an interested person with a stronger mathematics background than I have, with an ostensibly mathematics-based degree, is absolutely silly. I took 300 and 400-level classes in economics, in English, in history and philosophy. I never felt unwelcome or incapable.
Such a list is almost worthless without some kind of quality assessment. I skimmed through a few courses and they vary extremely in quality. Some are made by often rather young lecturers who could have prepared better so that they don't have to read their own name from a card. Others are presented by well established researchers who also are excellent teachers. Some courses cover only the basics with the result that in some fields there are a lot courses with about the same content. Other courses go surprisingly deep. A simple list doesn't help you to distinguish between good and bad courses.
You can change it to "courses must be prepared for" and it's still true. Even teaching a course that you know the material for backwards and forwards takes time to prep for - if you want to teach it well.
It isn't currently a requirement, but I assume that this is largely because there isn't a significant supply of potential students who know the fundamentals at the moment.
Increase the supply, and some courses/universities have the option of making it a requirement.
I've never taken a math course that didn't contain some overlap. But you simply can't realistically teach everything from every prerequisite in every class. There may always be some students who snuck through a prerequisite without learning or retaining the info. That's what office hours are for.
My thoughts exactly. The author should reconsider what he means by "mastering" something. Not passing a final exam for an introductory course isn't mastering the topic.
I am totally on board with the idea of seeing how fast someone can complete coursework and push the boundaries of what they can learn in a set amount of time, but name the article about it something other than "Mastering Linear Algebra in 10 Days".
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.
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