I have always tried to “Build Small Skills in the Right Order”, but I think it has been detrimental or even crippling to my learning process in some cases.
I’m pretty good at math, but I haven’t studied advanced math and would like to begin a program of self-study. I have started a few times, usually reading the first couple of chapters of a high-level calculus book (Apostol or Spivak), or something at a similar level.
I already know calculus well, having used it as a physics major in college and taught it as a private tutor for high school students, but I am not completely familiar with all the subtleties, such as why Taylor series converge and under what conditions. Reviewing calculus before diving into an advanced book on real analysis seems like a good idea because I know I can understand the calculus book, and reading it will prepare me to study more challenging material.
Nonetheless, what usually happens is that I get impatient at the slow progress, bored with the material, and want to jump straight to the more difficult book. If I do, I feel like I am “doing it wrong” by ignoring the small skills, but if I don’t, I wind up abandoning the program of study. I think I would have learned much more than I have by now if instead of a schedule of small skills, I’d simply opened advanced books to whatever section interested me and started plugging away, going back to review as necessary.
Similarly, early when I was a competitive distance runner, I read scores of books and internet forums for advice on training, then designed detailed training programs with careful “periodization” which would gradually build up my total amount and speed of running to the right quantities at the right time of the year. I also had many different gym exercises to do to build all requisite fitness before I could undergo the hardest training.
The result was that I was overly worried about whether my training was “correct”, frequently got worn down or injured, and didn’t perform well. Later, when I stopped worrying about all the small skills involved and simply ran every day for an amount that felt right to me, I improved a lot.
These examples aren’t intended to contradict the advice to build small skills, but to point out that even if a skill is both small and helpful to your larger goals, it is not necessarily the right skill to work on. In one case, the skills I chose were actually too small; in the other they were distracting.
This is how I prefer to learn as well. I call it “Immersion Learning”.
For example, during my first year of Algebra, I carried a Calculus textbook with me to class, and read whenever I was bored. I read through the whole textbook that semester, and understood maybe 20%. I didn’t bother doing any problems, and when I tried I was totally incapable, but that was OK. The next semester I read through a Calc II and Calc III textbook. Afterward I decided I was going to take the AP Calculus exam. I bought a prep book and started doing calculus problems for the first time in my life, and found that mastering the techniques came naturally. A few weeks later I passed the AP exam.
I think this works because knowledge (at least as it exists in brains) is not highly structured. It’s a giant associative mess. As with learning a language, the best way is to be immersed, and let the entire associative mess emerge simultaneously.
Learn the shape of the forest before the lay of the trees. Afterward you can do targeted study to patch up your makeshift map.
A question: Is ‘Immersion Learning’ a term that you have coined? If not, does this have anything to do with Luis Von Ahn’s immersion concept on duolingo?
Ah, I should have guessed that ‘Immersion Learning’ had been co-opted a few times before. My above use is my own coinage. By it I just mean jumping in and being exposed to everything you can and letting your brain sort it out, rather than methodically building a cathedral of understanding, one block at a time.
This seems like a useful counterpoint. The idea of leaping in, realizing what you don’t know, and then backtracking to cover the fundamentals seems useful. I recently decided I wanted to learn advanced math, grabbed some sample calculus problems, and failed them so hard that I’m now doing a methodical go-through of Algebra before I even try again.
I’ve found that, for some of the exercises, and realize I’ll completely forget the material in a week because it seems “irrelevant” to me and is easy to relearn. For others, I just skim over them because I already know how to do it, or because it’s simply irrelevant to what I want to learn. Taking the time to at least skim each section has definitely helped me, though, as I get little reward boosts of “oooh, I already know this!” and I’m making myself aware of skills I might need to review if they become relevant.
I have always tried to “Build Small Skills in the Right Order”, but I think it has been detrimental or even crippling to my learning process in some cases.
I’m pretty good at math, but I haven’t studied advanced math and would like to begin a program of self-study. I have started a few times, usually reading the first couple of chapters of a high-level calculus book (Apostol or Spivak), or something at a similar level.
I already know calculus well, having used it as a physics major in college and taught it as a private tutor for high school students, but I am not completely familiar with all the subtleties, such as why Taylor series converge and under what conditions. Reviewing calculus before diving into an advanced book on real analysis seems like a good idea because I know I can understand the calculus book, and reading it will prepare me to study more challenging material.
Nonetheless, what usually happens is that I get impatient at the slow progress, bored with the material, and want to jump straight to the more difficult book. If I do, I feel like I am “doing it wrong” by ignoring the small skills, but if I don’t, I wind up abandoning the program of study. I think I would have learned much more than I have by now if instead of a schedule of small skills, I’d simply opened advanced books to whatever section interested me and started plugging away, going back to review as necessary.
Similarly, early when I was a competitive distance runner, I read scores of books and internet forums for advice on training, then designed detailed training programs with careful “periodization” which would gradually build up my total amount and speed of running to the right quantities at the right time of the year. I also had many different gym exercises to do to build all requisite fitness before I could undergo the hardest training.
The result was that I was overly worried about whether my training was “correct”, frequently got worn down or injured, and didn’t perform well. Later, when I stopped worrying about all the small skills involved and simply ran every day for an amount that felt right to me, I improved a lot.
These examples aren’t intended to contradict the advice to build small skills, but to point out that even if a skill is both small and helpful to your larger goals, it is not necessarily the right skill to work on. In one case, the skills I chose were actually too small; in the other they were distracting.
This is how I prefer to learn as well. I call it “Immersion Learning”.
For example, during my first year of Algebra, I carried a Calculus textbook with me to class, and read whenever I was bored. I read through the whole textbook that semester, and understood maybe 20%. I didn’t bother doing any problems, and when I tried I was totally incapable, but that was OK. The next semester I read through a Calc II and Calc III textbook. Afterward I decided I was going to take the AP Calculus exam. I bought a prep book and started doing calculus problems for the first time in my life, and found that mastering the techniques came naturally. A few weeks later I passed the AP exam.
I think this works because knowledge (at least as it exists in brains) is not highly structured. It’s a giant associative mess. As with learning a language, the best way is to be immersed, and let the entire associative mess emerge simultaneously.
Learn the shape of the forest before the lay of the trees. Afterward you can do targeted study to patch up your makeshift map.
A question: Is ‘Immersion Learning’ a term that you have coined? If not, does this have anything to do with Luis Von Ahn’s immersion concept on duolingo?
Ah, I should have guessed that ‘Immersion Learning’ had been co-opted a few times before. My above use is my own coinage. By it I just mean jumping in and being exposed to everything you can and letting your brain sort it out, rather than methodically building a cathedral of understanding, one block at a time.
Maybe he coined it, but it’s not new:
http://www.alljapaneseallthetime.com/blog/
(Just pointing out one popular example of immersion learning.)
This seems like a useful counterpoint. The idea of leaping in, realizing what you don’t know, and then backtracking to cover the fundamentals seems useful. I recently decided I wanted to learn advanced math, grabbed some sample calculus problems, and failed them so hard that I’m now doing a methodical go-through of Algebra before I even try again.
I’ve found that, for some of the exercises, and realize I’ll completely forget the material in a week because it seems “irrelevant” to me and is easy to relearn. For others, I just skim over them because I already know how to do it, or because it’s simply irrelevant to what I want to learn. Taking the time to at least skim each section has definitely helped me, though, as I get little reward boosts of “oooh, I already know this!” and I’m making myself aware of skills I might need to review if they become relevant.
Each new skill needs to be a challenge. Ideally, a very easy challenge.