Yes, skipping to the problems is certainly consistent with what I read and hear about how the brain learns and retains information and effective learning. It's when we recall and use the information that we are learning, not when it goes in. I've also heard that having a strong emotion with the content is highly correlated with retention. There's nothing like an "aha!" moment or the joy of solving a problem to cement your knowledge.
I've been coming around more to the problems first approach. When I did LeetCode for a few months, I realized that you could get further with basic algorithms and data structures knowledge than people think. So many online posts would complain that a problem required a specific technique, when really it was just a slight variation on the basics. I always preferred to struggle with the problem for a few hours, or even days, rather than look at the solution to learn that 'technique'.
I don't know that I would *just* do problems though. For example, when I learned linear algebra in school I learned how to do things like multiply a matrix and a vector. But I didn't understand it conceptually as a linear combination of the columns of the matrix until I read Strang's linear algebra textbook after college. Maybe that was a symptom of doing rote exercises which don't fully test understanding. But I do see value in a textbook's prose beyond just using it to get unstuck while doing problems.
I think many people realize that the real learning is in doing the homework. I was certainly told that when I was young. The big issue is that we like what feels easy. Watching a YouTube video or skimming a blog post is fun, quick, and easy, but still feels like learning. And the torrent of novel information on the internet is addictive. Even reading a textbook is easier than struggling with a problem for 3 hours. So it's no surprise that we fool ourselves into not learning effectively. I still do it despite knowing better.
Also, very true. I recall doing very well in an undergrad circuits class only to flail hopelessly when an interviewer asked me the most basic questions of how to design a circuit. I had memorized a procedure without having any intuition about what I was actually doing. That kind of knowledge generalizes very poorly. So, yes, a good intuitive explanation is very valuable. Also we want quality problems that lend intuition and validate more than procedure.
Yes, skipping to the problems is certainly consistent with what I read and hear about how the brain learns and retains information and effective learning. It's when we recall and use the information that we are learning, not when it goes in. I've also heard that having a strong emotion with the content is highly correlated with retention. There's nothing like an "aha!" moment or the joy of solving a problem to cement your knowledge.
I've been coming around more to the problems first approach. When I did LeetCode for a few months, I realized that you could get further with basic algorithms and data structures knowledge than people think. So many online posts would complain that a problem required a specific technique, when really it was just a slight variation on the basics. I always preferred to struggle with the problem for a few hours, or even days, rather than look at the solution to learn that 'technique'.
I don't know that I would *just* do problems though. For example, when I learned linear algebra in school I learned how to do things like multiply a matrix and a vector. But I didn't understand it conceptually as a linear combination of the columns of the matrix until I read Strang's linear algebra textbook after college. Maybe that was a symptom of doing rote exercises which don't fully test understanding. But I do see value in a textbook's prose beyond just using it to get unstuck while doing problems.
I think many people realize that the real learning is in doing the homework. I was certainly told that when I was young. The big issue is that we like what feels easy. Watching a YouTube video or skimming a blog post is fun, quick, and easy, but still feels like learning. And the torrent of novel information on the internet is addictive. Even reading a textbook is easier than struggling with a problem for 3 hours. So it's no surprise that we fool ourselves into not learning effectively. I still do it despite knowing better.
Also, very true. I recall doing very well in an undergrad circuits class only to flail hopelessly when an interviewer asked me the most basic questions of how to design a circuit. I had memorized a procedure without having any intuition about what I was actually doing. That kind of knowledge generalizes very poorly. So, yes, a good intuitive explanation is very valuable. Also we want quality problems that lend intuition and validate more than procedure.