This disagreement was the point I was trying to make. That sometimes, the right advice is to just get started, such as the guy who thought he couldn’t start programming without learning a bunch of math first that I mentioned in the OP. I actually advised him to just start and backfill later. However, in other cases, it definitely seems right to learn things in order.
I suspect at least one of the failure modes related to not learning things in the right order is slower, more arduous learning that isn’t fun. If you struggle with the whole thing and look up the requisite material as you go, you don’t get a sense for which parts of what you’re learning are interesting results of thattopic as opposed to just requisite knowledge gaps. You don’t have the experience of thinking “that doesn’t sound right...” and then having your confusion cleared up as you keep reading and it is explained. Instead, everything sounds foreign and you don’t appreciate which parts of it are the interesting results of the topic at hand. This leads to poor retention and a low ability to apply what you’ve learned, even if you manage to make it through and “feel like you understand it.”
I suspect at least one of the failure modes related to not learning things in the right order is slower, more arduous learning that isn’t fun.
And if you want everything to make sense anyway, you’re going to learn the prerequisites anyways. So not only are you having more difficulties now, but you’re spending time getting a tenuous grasp on a subject that you’ll want to revisit later anyways once you can put things into a coherent framework.
This disagreement was the point I was trying to make. That sometimes, the right advice is to just get started, such as the guy who thought he couldn’t start programming without learning a bunch of math first that I mentioned in the OP. I actually advised him to just start and backfill later. However, in other cases, it definitely seems right to learn things in order.
I suspect at least one of the failure modes related to not learning things in the right order is slower, more arduous learning that isn’t fun. If you struggle with the whole thing and look up the requisite material as you go, you don’t get a sense for which parts of what you’re learning are interesting results of that topic as opposed to just requisite knowledge gaps. You don’t have the experience of thinking “that doesn’t sound right...” and then having your confusion cleared up as you keep reading and it is explained. Instead, everything sounds foreign and you don’t appreciate which parts of it are the interesting results of the topic at hand. This leads to poor retention and a low ability to apply what you’ve learned, even if you manage to make it through and “feel like you understand it.”
And if you want everything to make sense anyway, you’re going to learn the prerequisites anyways. So not only are you having more difficulties now, but you’re spending time getting a tenuous grasp on a subject that you’ll want to revisit later anyways once you can put things into a coherent framework.