I found that when a text requires a second or third reading, taking a lot of notes, etc., I won’t be able to master it at the level of the material that I know well, and it won’t be retained as reliably, for example I won’t be able to re-generate most of the key constructions and theorems without looking them up a couple of years later (this applies even if more advanced topics are practiced in the meantime, as they usually don’t involve systematic review of the basics). Thus, there is a triple penalty for working on challenging material: it takes more effort and time to process, the resulting understanding is less fluent, and it gets forgotten faster and to a greater extent. It’s only worth it if it’s necessary to (passably) learn the material on schedule, or if the material is not of much interest in itself and acts mostly as a stepping stone to more advanced material, or if there is no feasible route that would render the material non-challenging (in which case I’d have to put into it even more work to gain fluency, such as inventing mini-projects, inefficiently studying something not directly useful for my purposes that applies the material and then going back, etc.).
A more efficient path, if the goal is to learn a topic well eventually, is to focus on developing skills that would make the topic easier to learn. Instead of studying the hardest book that you can understand (after three readings and looking things up, etc.), study the easiest book containing something you don’t know very well, that would inform the topic you want to master. Eventually, you get to the book that was originally hard, but it’s now easy and can be mastered reliably.
Personally I find that during study it’s sometimes hard to tell the difference between material that is too challenging and material that is difficult but tractable with some effort. That is, I have to put forth the effort either way and it’s only afterwards that I find out which is the case.
I found that when a text requires a second or third reading, taking a lot of notes, etc., I won’t be able to master it at the level of the material that I know well, and it won’t be retained as reliably, for example I won’t be able to re-generate most of the key constructions and theorems without looking them up a couple of years later (this applies even if more advanced topics are practiced in the meantime, as they usually don’t involve systematic review of the basics). Thus, there is a triple penalty for working on challenging material: it takes more effort and time to process, the resulting understanding is less fluent, and it gets forgotten faster and to a greater extent. It’s only worth it if it’s necessary to (passably) learn the material on schedule, or if the material is not of much interest in itself and acts mostly as a stepping stone to more advanced material, or if there is no feasible route that would render the material non-challenging (in which case I’d have to put into it even more work to gain fluency, such as inventing mini-projects, inefficiently studying something not directly useful for my purposes that applies the material and then going back, etc.).
A more efficient path, if the goal is to learn a topic well eventually, is to focus on developing skills that would make the topic easier to learn. Instead of studying the hardest book that you can understand (after three readings and looking things up, etc.), study the easiest book containing something you don’t know very well, that would inform the topic you want to master. Eventually, you get to the book that was originally hard, but it’s now easy and can be mastered reliably.
Which seems related to building skills in the right order.
Personally I find that during study it’s sometimes hard to tell the difference between material that is too challenging and material that is difficult but tractable with some effort. That is, I have to put forth the effort either way and it’s only afterwards that I find out which is the case.
Thanks. Yeah, this is one of the reasons that I put Model Theory down a little less than halfway through and moved on to a logic textbook.
That makes sense—can you give some examples?