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I've done this and would echo the good advice you've already gotten about Khan Academy but I think the comments in this thread are skipping over the most import

I've done this and would echo the good advice you've already gotten about Khan Academy but I think the comments in this thread are skipping over the most important part: pace. Work slowly. Don't move on until you really "get" the concept you're working with. Some topics might "click" right away and others might take weeks of bashing your head against the wall until your brain makes sense of it. That's okay. It can definitely be tedious at times (so be kind to yourself!) but a lot of learning happens when you're struggling to make sense of something so it's worthwhile to lean into the trouble you're having and figure out what it is that you're struggling to understand. The downside of formal education is that the teacher has a timeline that needs to be kept and the class will move on without you. It might not seem like a big deal in the moment but in math the foundation is so important because the concepts build on one another. Sometimes in really subtle ways. If you have the motivation (and it sounds like you do!) then the huge upside to self-paced learning is that you can build a really strong foundation and the more complicated advanced topics will be so much easier to master. Khan Academy is really good at breaking subjects down into tiny bites and then slowly building on what you've learned but if you don't quite understand a lesson or if you haven't properly paid attention don't be afraid to do it again. If you guessed the right answer but don't understand why your answer was right, don't be afraid to go back and do it again. So just because one person here could do all of the Khan Academy 9th grade algebra in a week that doesn't mean you should set that timeline for yourself. Everyone is starting from a different place. So maybe it'll take you a day, or a week, or a month, or even months. But however long it takes is how long it takes.

blagie 4y ago
I'll just mention: From a scientific perspective, this is absolutely the wrong advice. If you couldn't understand something yesterday, that's very good evidence you won't make sense of it today. You should work hard, go deep, and try hard problems, but if you fail to understand something after putting in the effort, just move onto something else. Learn a few unrelated things, and come back. Much of the time, if you come back in weeks or months, it will just click into place. You also want to visit topics /many/ times. Truly understanding many topics in math should take months or years. You can do it a lot more efficiently if you visit a topic for e.g. 5 hours each every 6 months over 2 years than a single 80-hour cram. You'll put in less time and understand more deeply. A good starting point for references is Bruner (and specifically under Spiral Curriculum), but there's a whole literature on this. There has been a slow transition from seeing math as a set of bricks which stack on each other to an interconnected network of knowledge. The spacing effect literature is good too.
- jghn 4y ago
  To me, this has been the largest advantage of learning things at my own pace instead of in a classroom environment. Even as a student I recognized early on that topics that'd stump me would often click months later. By then it was too late for my grade, but I'd go back and realize that other things I'd learned in the interim made it easy. So now when I find something blocking me, I just go learn something else instead. And what do you know, some combination of more wisdom, broader knowledge, or perhaps just a different mental state often works.
- elliekelly 4y ago
  Care to share the science? This sounds more like a learner's internal/external locus of control. If you believe you are capable of figuring something out you're probably right and likewise if you believe you can't.
  - blagie 4y ago
    I'd recommend rereading my post. The problem with education research is that there's a hundred years of it. I listed the two in my original post. A longer list: - Bruner's work on spiral curriculum, and follow-up work. Spiral curricula are mis-implemented in most schools which claim to use them; it's not review. It's successive passes going deeper. - Cognitive work on progressions such as surface->deep->transfer learning (Hattie) or chunking - Physics education research on complex multiconcept problems - Spacing effect. You can go all the way back to 1885 with Ebinghaus, but the esoteric author of supermemo seems to have done the best work here. If you prefer the academic establishment, there's a ton. - There's a bunch of science that about 2/3s of what we learn, we're not aware we're learning or teaching. Concepts support each other, deeply. Kaplan, back when Bror was there, did a bunch of nice work there. It's easier to learn long division if you know a bit of algebra, and vice-versa. Chemistry helps learn physics, and physics helps learn chemistry. This was supported with pretty independent methodologies in independent domains (data analysis from tests, cognitive task analysis, etc.). ... and so on. This has very little to do with affect. It's a very well-established, rarely-applied set of results. A complete lit review here would be book-length, at least.
- 4y ago
tzs 4y ago
> Don't move on until you really "get" the concept you're working with. Some topics might "click" right away and others might take weeks of bashing your head against the wall until your brain makes sense of it. Careful. This can sometimes be counterproductive. It is often the case that one concept taught when learning a subject will be applied as part of teaching the next concept. The best way to learn that first concept in many cases is not to focus on it until you really "get" it but rather to just get enough of it for how it is used for teaching the next concept. Then you move on to the next concept and the application of that first concept there gets you experience using the first concept which solidifies your grasp of the first concept and makes you truly "get" it. The application of earlier concepts throughout the subsequent material can be in effect a kind of natural spaced repetition for learning the earlier concepts. I think that deciding when to move on is one of the hardest things in self-learning, especially if the subject is new enough to you that you can't use your experience in a related subject to help guide you. You don't know enough to know when you've learned enough to go on.
dontbenebby 4y ago
Khan has problem sets right? That was always my issue, that and math "teachers" who'd just offer to reread the textbook or point to the index and smirk. But don't feel bad if you struggle, it's really hard to learn math concepts without an incentive. I'd just pick up a book on python and learn algerbra and a few other things along the way.

blagie 4y ago

I'll just mention: From a scientific perspective, this is absolutely the wrong advice. If you couldn't understand something yesterday, that's very good evidence you won't make sense of it today. You should work hard, go deep, and try hard problems, but if you fail to understand something after putting in the effort, just move onto something else. Learn a few unrelated things, and come back. Much of the time, if you come back in weeks or months, it will just click into place. You also want to visit topics /many/ times. Truly understanding many topics in math should take months or years. You can do it a lot more efficiently if you visit a topic for e.g. 5 hours each every 6 months over 2 years than a single 80-hour cram. You'll put in less time and understand more deeply. A good starting point for references is Bruner (and specifically under Spiral Curriculum), but there's a whole literature on this. There has been a slow transition from seeing math as a set of bricks which stack on each other to an interconnected network of knowledge. The spacing effect literature is good too.

jghn 4y ago
To me, this has been the largest advantage of learning things at my own pace instead of in a classroom environment. Even as a student I recognized early on that topics that'd stump me would often click months later. By then it was too late for my grade, but I'd go back and realize that other things I'd learned in the interim made it easy. So now when I find something blocking me, I just go learn something else instead. And what do you know, some combination of more wisdom, broader knowledge, or perhaps just a different mental state often works.
elliekelly 4y ago
Care to share the science? This sounds more like a learner's internal/external locus of control. If you believe you are capable of figuring something out you're probably right and likewise if you believe you can't.
- blagie 4y ago
  I'd recommend rereading my post. The problem with education research is that there's a hundred years of it. I listed the two in my original post. A longer list: - Bruner's work on spiral curriculum, and follow-up work. Spiral curricula are mis-implemented in most schools which claim to use them; it's not review. It's successive passes going deeper. - Cognitive work on progressions such as surface->deep->transfer learning (Hattie) or chunking - Physics education research on complex multiconcept problems - Spacing effect. You can go all the way back to 1885 with Ebinghaus, but the esoteric author of supermemo seems to have done the best work here. If you prefer the academic establishment, there's a ton. - There's a bunch of science that about 2/3s of what we learn, we're not aware we're learning or teaching. Concepts support each other, deeply. Kaplan, back when Bror was there, did a bunch of nice work there. It's easier to learn long division if you know a bit of algebra, and vice-versa. Chemistry helps learn physics, and physics helps learn chemistry. This was supported with pretty independent methodologies in independent domains (data analysis from tests, cognitive task analysis, etc.). ... and so on. This has very little to do with affect. It's a very well-established, rarely-applied set of results. A complete lit review here would be book-length, at least.
4y ago

tzs 4y ago

> Don't move on until you really "get" the concept you're working with. Some topics might "click" right away and others might take weeks of bashing your head against the wall until your brain makes sense of it. Careful. This can sometimes be counterproductive. It is often the case that one concept taught when learning a subject will be applied as part of teaching the next concept. The best way to learn that first concept in many cases is not to focus on it until you really "get" it but rather to just get enough of it for how it is used for teaching the next concept. Then you move on to the next concept and the application of that first concept there gets you experience using the first concept which solidifies your grasp of the first concept and makes you truly "get" it. The application of earlier concepts throughout the subsequent material can be in effect a kind of natural spaced repetition for learning the earlier concepts. I think that deciding when to move on is one of the hardest things in self-learning, especially if the subject is new enough to you that you can't use your experience in a related subject to help guide you. You don't know enough to know when you've learned enough to go on.

dontbenebby 4y ago

Khan has problem sets right? That was always my issue, that and math "teachers" who'd just offer to reread the textbook or point to the index and smirk. But don't feel bad if you struggle, it's really hard to learn math concepts without an incentive. I'd just pick up a book on python and learn algerbra and a few other things along the way.