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> High School Mathematics Whenever I try to catch up with maths (in Khan Academy and elsewhere), I always end up in an awkward state where I keep recursively r

> High School Mathematics Whenever I try to catch up with maths (in Khan Academy and elsewhere), I always end up in an awkward state where I keep recursively researching less and less advanced subjects because of gaps of various sizes in my fundamental knowledge. It's incredibly demotivating.

glass-z13 3y ago
Same for me, let me know if you find the solution! I think it's extremely hard to get into this kind of stuff when you basically have to start from 0 meanwhile everyone else has a better foundation than you
tsingy 3y ago
The book that made things click for me was Maths: A Student's Survival Guide by Jenny Olive. Give it a shot, use a calculator for everything. IMO in the age of computers let computers do the calculations and just learn to have intuitions.
- ghaff 3y ago
  I'd have to be convinced that you can develop those intuitions without basic arithmetic. Mind you, I'm not saying spend a lot of time mastering long division or whatever. (I'd probably have to look up the technique myself.) But I think some level of numeric fluency is probably necessary.
  - 2devnull 3y ago
    “I'd probably have to look up the technique myself.” No offense but I am pretty sure that was the point. If it’s math you forget, it’s not math worth learning. Learn what you want or need to know. The rest is dross.
ranieuwe 3y ago
I have the same problem and have still not found a workable solution. Only one there seems to be is to basically rerun 12 years of math, which is really unpleasant because I know 80% of the work making it unrewarding and slow. I don’t know what I don’t know that is super demotivating, indeed.
vector_spaces 3y ago
I guess first consider that you might have math trauma -- read about it, own it (if it applies, of course), and recognize what it feels like when it rears its head. Lots of people -- mainly in the US, but it's a thing in other countries too -- were taught math in a pretty shitty way, often by people who don't want to be teaching it in the first place because they themselves have math trauma. Then build up fluency in the basic manipulations: do lots and lots and lots of exercises until those manipulations become second nature. You might need to start with fractions[2], and that's fine. One of the nice things about math at the elementary level is that you nearly always are guaranteed to get better with practice. This absolutely isn't the case for proof-based math, where you really need to be intentional about truly digesting the material and thinking careful about the ideas. But if you're shaky on absolute fundamentals, you can get incredibly far with grinding. At some point you'll need to engage with the ideas, but I think that's easier once you've built up some pattern recognition. But others will (surely) disagree [1] https://www.edweek.org/teaching-learning/opinion-how-to-help-students-heal-from-math-trauma/2018/11 https://www.edweek.org/teaching-learning/opinion-how-to-help... [2] https://www.edweek.org/teaching-learning/fraction-phobia-the-root-of-math-anxiety/2015/02 https://www.edweek.org/teaching-learning/fraction-phobia-the...
OwlGoesHoot 3y ago
It would probably be helpful to start at a level above where you left off and look up specific gaps in your knowledge as you find them. It’s always good to come to a topic with the understanding of every previous topic, but often those deeper understandings come from moving into more advanced subjects anyway. It might be more slow and frustrating at times, but it will give you a better understanding of where your specific gaps in knowledge actually lie and you’ll be able to address them as you go.
vidyesh 3y ago
Too many false starts too lead to doing the same fundamentals all over again, making one feels like they are not progressing at all. I remember reading somewhere, do the implementation of it along side fundamentals. The reason you are studying fundamentals to progress ahead, do that course along side too. This helps one grasp the fundamentals quickly and more importantly to know which fundamentals you really need than to try to do everything and forget aspects of it later. That being said, I am yet to implement that concept and get over false starts
yt-sdb 3y ago
Maybe 5 years ago, I was in a similar place. I had a particularly embarrassing moment at work when it clicked that I just... didn't know the basics. I was, to use an overused term, "mathematically immature". So I made a commitment: I decided I would work through Khan Academy math for 1-hour a day for 1 year. I started with pre-K [1] (specifically counting) and watched every video and did every single exercise in order. I focused on mastery. I didn't rush myself, and I did not continue until I felt completely confident in the material. I just did this for a year. I think I go through roughly algebra 2. In my mind, it is critical to combine explicit knowledge (watch videos) with tactic knowledge [2] (do exercises). For example, you need to understand what a logarithm is conceptually but you also just need to do problems to get a feel for it. So this is fundamentally different than learning-by-grazing or just reading a book. I could go on and on, but let me just say that it changed my relationship to math in a deep way. [1] https://www.khanacademy.org/math/k-8-grades https://www.khanacademy.org/math/k-8-grades [2] https://commoncog.com/tacit-knowledge-is-a-real-thing/ https://commoncog.com/tacit-knowledge-is-a-real-thing/
- gareve 3y ago
  if you would have to do it again, would you change something on your methodology? I assume there were some unnecessary time sinks here & there
  - yt-sdb 3y ago
    I don't think so. My problem was that I had a weak grasp of many basics concepts, and more critically I did not know in which areas I was weak. So while it's easy ex post to say "I could skip such and such section", it would have been impossible to make this judgment ex ante. And in fact, I think a failure mode many people make is trying to predict which things they already know and then skipping those. This allows for blind spots to persist. I suppose the one way to skip things correctly would be to have a coach. But that comes at a new cost ($), but maybe that works for some people.
    - hawk_ 3y ago
      I have been seeing more and more usage of 'ex post' and 'ex ante' lately. What do they convey that isn't conveyed by 'after' and 'before'?
Cerium 3y ago
Have you seen "An Infinitely Large Napkin"? I saw it posted here a couple years ago. It is Evan Chen's project "aimed at making higher math accessible to high school students." https://web.evanchen.cc/napkin.html https://web.evanchen.cc/napkin.html
EGreg 3y ago
For what it's worth, if you want to go bottom-up and give yourself a super-solid foundation, go through the videos I recorded several years ago specifically for this purpose. They are for children as well as adults: https://www.youtube.com/@thinkingmathematically https://www.youtube.com/@thinkingmathematically Please let me know if they were helpful!
ke88y 3y ago
Paradoxically, self-teaching is most difficult at the "101" and "pre-101" level. Once you have the basics, self-teaching becomes much easier. Teaching yourself Calculus I and Calculus II after obtaining High School mathematical literacy is not too bad. Teaching yourself Differential Equations or even Functional Analysis after obtaining the pre-reqs is actually quite easy. But teaching yourself high school or especially middle school mathematics requires a TON of dedication. It's not impossible, of course, but "The Basics" are where you really benefit from the help of a professional educator. For this reason, I recommend eschewing self-directed resources and enrolling in an "Applied Math" or "College Algebra" course at your local community college. These courses are basically "high school mathematics for people who never learned or forgot high school mathematics". Depending on where you live, the "College Algebra" course at your local Community College is probably very cheap or free and available as an evening and/or online course. You usually do not need to enroll in a degree program to take the course. Once you make it through "College Algebra" you can return to self-directed learning. Community Colleges are a vastly under-utilized resource, particularly for these "very fundamental knowledge gaps" where self-directed learning is much more difficult.
bovem 3y ago
It might not be the same for you. But this is what I enjoy when I study anything. Filling up the gaps in my knowledge and learning about new ways to think or understand about a concept. Maybe you shouldn't dive so deep into the concepts. Just write all the topics/concepts you didn't understand while learning something and watch one video about each of them.
satvikpendem 3y ago
Why not start from the beginning, ie pre-K on up, as the other commenter mentioned? I've done something similar for teaching myself web development (since it's not taught often in CS degree programs), starting from bare HTML, adding CSS, adding Javascript, adding TypeScript, adding React, and so on. Now I have a good foundation from which to build anything I want. So too with mathematics or really any subject.
poulsbohemian 3y ago
My 13 year old is a very good student, currently taking high school math classes while in middle school... one of the things that the public school system hasn't figured out is how to make any of it relevant. So sure, she's brilliant and flies through the material, but she'd be the first to tell you it's just puzzles, it has no actual meaning to her. I was the opposite - because it had no meaning to me, I couldn't understand it and was a terrible math student. But, once I could view it through the lens of computer science, suddenly it had meaning and I did fine. My oldest daughter was a terrible student. But she would say to me "If they taught history class the way you explain historical events around the dinner table, I would have been a lot more interested in studying." So point being - it's probably not you, a lot of it really is the way we approach k-12 education. In hindsight, I'm not sure college is any better and may be worse what with the approach of hazing and weeding out.
- gnicholas 3y ago
  The Khanmigo chatbot that KA is rolling out supposedly helps with this problem of relevance.
danielvaughn 3y ago
Weirdly enough, mathematics is a very emotional subject for me. I never understood how it was taught in school, and had serious difficulty understanding it. As a result I just ignored it, believing that I didn't have the right brain for it. Even though I taught myself how to code, I never went back and learned math, so my level of knowledge is at a basic high school level. It can be embarrassing at times, and every now and then I think about trying to learn it.
- wonderingwhale 3y ago
  I honestly think this is one of the bigger problems with people who "can't do math", probably most people can learn quite a bit of (at least basic) mathematics. But oftentimes when you did not understand the subject well previously, like in high school because of different interests at the time or a bad teacher or something. And then because of this whenever you see an equation or hear the word 'mathematics' you just shut off your brain. I know some people who can understand me when I explain some physics or mathematics concept without explicit mathematics, but they would be scared off at the first equation.
randmeerkat 3y ago
> Whenever I try to catch up with maths (in Khan Academy and elsewhere), I always end up in an awkward state where I keep recursively researching less and less advanced subjects because of gaps of various sizes in my fundamental knowledge. It's incredibly demotivating. Try this course: https://www.edx.org/course/college-algebra-and-problem-solving https://www.edx.org/course/college-algebra-and-problem-solvi... It uses the ALEKS system which identifies your weak points and brings you up to speed. Take notes during the process so you have something to reference in the future and won’t forget what you learned. After you knock out the algebra course you’ll be ready for the precalculus course: https://www.edx.org/course/precalculus https://www.edx.org/course/precalculus The ALEKS system in the Precalculus course will also remediate anything you forgot from the Algebra course. Hopefully this will help give you the confidence to go after more advanced maths once you finish both courses. Be kind to yourself, math, like anything, is a skill, it takes time and practice.
jayro 3y ago
At Math Academy, we've created a sequence of math courses called Mathematical Foundations I, II, & III that cover everything from 5th Grade Math up through Calculus I & II and will allow anyone to get up to speed on the skills required for university-level mathematics in the most efficient way possible. Our adaptive diagnostic exams will create a custom fit course no matter where you are mathematically and our algorithms will continually adapt to your individual strengths, weaknesses and learning curve. https://mathacademy.com/courses/mathematical-foundations-i https://mathacademy.com/courses/mathematical-foundations-i https://mathacademy.com/courses/mathematical-foundations-ii https://mathacademy.com/courses/mathematical-foundations-ii https://mathacademy.com/courses/mathematical-foundations-iii https://mathacademy.com/courses/mathematical-foundations-iii In addition, we have courses on Linear Algebra and Mathematics for Machine Learning, with more coming soon: https://mathacademy.com/courses/linear-algebra https://mathacademy.com/courses/linear-algebra https://mathacademy.com/courses/mathematics-for-machine-learning https://mathacademy.com/courses/mathematics-for-machine-lear... The system is mastery based, lightly gamified, and completely automated. Our algorithms intelligently apply spaced-repetition to a hierarchical knowledge graph of over 3,000 mathematical concepts to make it substantially more efficient than a traditional course (typically on the order of 4X or more). I'm a founder and would be happy to answer any questions.
xwowsersx 3y ago
Another resource I wanted to mention here is OpenStax. Specifically, their Prealgebra book: https://openstax.org/details/books/prealgebra-2e https://openstax.org/details/books/prealgebra-2e it's a fully online-native book format with exercises, etc.
dghughes 3y ago
That happens to me all the time the solution is I need a push or some deadline. For high school it was a strict (we thought) teacher who brought me from an average of 70% to 95%. For computer programming it was going back to school as an adult and timed in class tests. For music is was paying for lessons at a certain time. If I don't get motivated from some external push I never get past a certain level. Every single thing I do in my life is like that even laundry. I must be chronic or maybe permanent procrastinator.

glass-z13 3y ago

Same for me, let me know if you find the solution! I think it's extremely hard to get into this kind of stuff when you basically have to start from 0 meanwhile everyone else has a better foundation than you

tsingy 3y ago

The book that made things click for me was Maths: A Student's Survival Guide by Jenny Olive. Give it a shot, use a calculator for everything. IMO in the age of computers let computers do the calculations and just learn to have intuitions.

ghaff 3y ago
I'd have to be convinced that you can develop those intuitions without basic arithmetic. Mind you, I'm not saying spend a lot of time mastering long division or whatever. (I'd probably have to look up the technique myself.) But I think some level of numeric fluency is probably necessary.
- 2devnull 3y ago
  “I'd probably have to look up the technique myself.” No offense but I am pretty sure that was the point. If it’s math you forget, it’s not math worth learning. Learn what you want or need to know. The rest is dross.

ranieuwe 3y ago

I have the same problem and have still not found a workable solution. Only one there seems to be is to basically rerun 12 years of math, which is really unpleasant because I know 80% of the work making it unrewarding and slow. I don’t know what I don’t know that is super demotivating, indeed.

vector_spaces 3y ago

I guess first consider that you might have math trauma -- read about it, own it (if it applies, of course), and recognize what it feels like when it rears its head. Lots of people -- mainly in the US, but it's a thing in other countries too -- were taught math in a pretty shitty way, often by people who don't want to be teaching it in the first place because they themselves have math trauma. Then build up fluency in the basic manipulations: do lots and lots and lots of exercises until those manipulations become second nature. You might need to start with fractions[2], and that's fine. One of the nice things about math at the elementary level is that you nearly always are guaranteed to get better with practice. This absolutely isn't the case for proof-based math, where you really need to be intentional about truly digesting the material and thinking careful about the ideas. But if you're shaky on absolute fundamentals, you can get incredibly far with grinding. At some point you'll need to engage with the ideas, but I think that's easier once you've built up some pattern recognition. But others will (surely) disagree [1] https://www.edweek.org/teaching-learning/opinion-how-to-help-students-heal-from-math-trauma/2018/11 https://www.edweek.org/teaching-learning/opinion-how-to-help... [2] https://www.edweek.org/teaching-learning/fraction-phobia-the-root-of-math-anxiety/2015/02 https://www.edweek.org/teaching-learning/fraction-phobia-the...

OwlGoesHoot 3y ago

It would probably be helpful to start at a level above where you left off and look up specific gaps in your knowledge as you find them. It’s always good to come to a topic with the understanding of every previous topic, but often those deeper understandings come from moving into more advanced subjects anyway. It might be more slow and frustrating at times, but it will give you a better understanding of where your specific gaps in knowledge actually lie and you’ll be able to address them as you go.

vidyesh 3y ago

Too many false starts too lead to doing the same fundamentals all over again, making one feels like they are not progressing at all. I remember reading somewhere, do the implementation of it along side fundamentals. The reason you are studying fundamentals to progress ahead, do that course along side too. This helps one grasp the fundamentals quickly and more importantly to know which fundamentals you really need than to try to do everything and forget aspects of it later. That being said, I am yet to implement that concept and get over false starts

yt-sdb 3y ago

Maybe 5 years ago, I was in a similar place. I had a particularly embarrassing moment at work when it clicked that I just... didn't know the basics. I was, to use an overused term, "mathematically immature". So I made a commitment: I decided I would work through Khan Academy math for 1-hour a day for 1 year. I started with pre-K [1] (specifically counting) and watched every video and did every single exercise in order. I focused on mastery. I didn't rush myself, and I did not continue until I felt completely confident in the material. I just did this for a year. I think I go through roughly algebra 2. In my mind, it is critical to combine explicit knowledge (watch videos) with tactic knowledge [2] (do exercises). For example, you need to understand what a logarithm is conceptually but you also just need to do problems to get a feel for it. So this is fundamentally different than learning-by-grazing or just reading a book. I could go on and on, but let me just say that it changed my relationship to math in a deep way. [1] https://www.khanacademy.org/math/k-8-grades https://www.khanacademy.org/math/k-8-grades [2] https://commoncog.com/tacit-knowledge-is-a-real-thing/ https://commoncog.com/tacit-knowledge-is-a-real-thing/

gareve 3y ago
if you would have to do it again, would you change something on your methodology? I assume there were some unnecessary time sinks here & there
- yt-sdb 3y ago
  I don't think so. My problem was that I had a weak grasp of many basics concepts, and more critically I did not know in which areas I was weak. So while it's easy ex post to say "I could skip such and such section", it would have been impossible to make this judgment ex ante. And in fact, I think a failure mode many people make is trying to predict which things they already know and then skipping those. This allows for blind spots to persist. I suppose the one way to skip things correctly would be to have a coach. But that comes at a new cost ($), but maybe that works for some people.
  - hawk_ 3y ago
    I have been seeing more and more usage of 'ex post' and 'ex ante' lately. What do they convey that isn't conveyed by 'after' and 'before'?

Cerium 3y ago

Have you seen "An Infinitely Large Napkin"? I saw it posted here a couple years ago. It is Evan Chen's project "aimed at making higher math accessible to high school students." https://web.evanchen.cc/napkin.html https://web.evanchen.cc/napkin.html

EGreg 3y ago

For what it's worth, if you want to go bottom-up and give yourself a super-solid foundation, go through the videos I recorded several years ago specifically for this purpose. They are for children as well as adults: https://www.youtube.com/@thinkingmathematically https://www.youtube.com/@thinkingmathematically Please let me know if they were helpful!

ke88y 3y ago

Paradoxically, self-teaching is most difficult at the "101" and "pre-101" level. Once you have the basics, self-teaching becomes much easier. Teaching yourself Calculus I and Calculus II after obtaining High School mathematical literacy is not too bad. Teaching yourself Differential Equations or even Functional Analysis after obtaining the pre-reqs is actually quite easy. But teaching yourself high school or especially middle school mathematics requires a TON of dedication. It's not impossible, of course, but "The Basics" are where you really benefit from the help of a professional educator. For this reason, I recommend eschewing self-directed resources and enrolling in an "Applied Math" or "College Algebra" course at your local community college. These courses are basically "high school mathematics for people who never learned or forgot high school mathematics". Depending on where you live, the "College Algebra" course at your local Community College is probably very cheap or free and available as an evening and/or online course. You usually do not need to enroll in a degree program to take the course. Once you make it through "College Algebra" you can return to self-directed learning. Community Colleges are a vastly under-utilized resource, particularly for these "very fundamental knowledge gaps" where self-directed learning is much more difficult.

bovem 3y ago

It might not be the same for you. But this is what I enjoy when I study anything. Filling up the gaps in my knowledge and learning about new ways to think or understand about a concept. Maybe you shouldn't dive so deep into the concepts. Just write all the topics/concepts you didn't understand while learning something and watch one video about each of them.

satvikpendem 3y ago

Why not start from the beginning, ie pre-K on up, as the other commenter mentioned? I've done something similar for teaching myself web development (since it's not taught often in CS degree programs), starting from bare HTML, adding CSS, adding Javascript, adding TypeScript, adding React, and so on. Now I have a good foundation from which to build anything I want. So too with mathematics or really any subject.

poulsbohemian 3y ago

My 13 year old is a very good student, currently taking high school math classes while in middle school... one of the things that the public school system hasn't figured out is how to make any of it relevant. So sure, she's brilliant and flies through the material, but she'd be the first to tell you it's just puzzles, it has no actual meaning to her. I was the opposite - because it had no meaning to me, I couldn't understand it and was a terrible math student. But, once I could view it through the lens of computer science, suddenly it had meaning and I did fine. My oldest daughter was a terrible student. But she would say to me "If they taught history class the way you explain historical events around the dinner table, I would have been a lot more interested in studying." So point being - it's probably not you, a lot of it really is the way we approach k-12 education. In hindsight, I'm not sure college is any better and may be worse what with the approach of hazing and weeding out.

gnicholas 3y ago
The Khanmigo chatbot that KA is rolling out supposedly helps with this problem of relevance.

danielvaughn 3y ago

Weirdly enough, mathematics is a very emotional subject for me. I never understood how it was taught in school, and had serious difficulty understanding it. As a result I just ignored it, believing that I didn't have the right brain for it. Even though I taught myself how to code, I never went back and learned math, so my level of knowledge is at a basic high school level. It can be embarrassing at times, and every now and then I think about trying to learn it.

wonderingwhale 3y ago
I honestly think this is one of the bigger problems with people who "can't do math", probably most people can learn quite a bit of (at least basic) mathematics. But oftentimes when you did not understand the subject well previously, like in high school because of different interests at the time or a bad teacher or something. And then because of this whenever you see an equation or hear the word 'mathematics' you just shut off your brain. I know some people who can understand me when I explain some physics or mathematics concept without explicit mathematics, but they would be scared off at the first equation.

randmeerkat 3y ago

> Whenever I try to catch up with maths (in Khan Academy and elsewhere), I always end up in an awkward state where I keep recursively researching less and less advanced subjects because of gaps of various sizes in my fundamental knowledge. It's incredibly demotivating. Try this course: https://www.edx.org/course/college-algebra-and-problem-solving https://www.edx.org/course/college-algebra-and-problem-solvi... It uses the ALEKS system which identifies your weak points and brings you up to speed. Take notes during the process so you have something to reference in the future and won’t forget what you learned. After you knock out the algebra course you’ll be ready for the precalculus course: https://www.edx.org/course/precalculus https://www.edx.org/course/precalculus The ALEKS system in the Precalculus course will also remediate anything you forgot from the Algebra course. Hopefully this will help give you the confidence to go after more advanced maths once you finish both courses. Be kind to yourself, math, like anything, is a skill, it takes time and practice.

jayro 3y ago

At Math Academy, we've created a sequence of math courses called Mathematical Foundations I, II, & III that cover everything from 5th Grade Math up through Calculus I & II and will allow anyone to get up to speed on the skills required for university-level mathematics in the most efficient way possible. Our adaptive diagnostic exams will create a custom fit course no matter where you are mathematically and our algorithms will continually adapt to your individual strengths, weaknesses and learning curve. https://mathacademy.com/courses/mathematical-foundations-i https://mathacademy.com/courses/mathematical-foundations-i https://mathacademy.com/courses/mathematical-foundations-ii https://mathacademy.com/courses/mathematical-foundations-ii https://mathacademy.com/courses/mathematical-foundations-iii https://mathacademy.com/courses/mathematical-foundations-iii In addition, we have courses on Linear Algebra and Mathematics for Machine Learning, with more coming soon: https://mathacademy.com/courses/linear-algebra https://mathacademy.com/courses/linear-algebra https://mathacademy.com/courses/mathematics-for-machine-learning https://mathacademy.com/courses/mathematics-for-machine-lear... The system is mastery based, lightly gamified, and completely automated. Our algorithms intelligently apply spaced-repetition to a hierarchical knowledge graph of over 3,000 mathematical concepts to make it substantially more efficient than a traditional course (typically on the order of 4X or more). I'm a founder and would be happy to answer any questions.

xwowsersx 3y ago

Another resource I wanted to mention here is OpenStax. Specifically, their Prealgebra book: https://openstax.org/details/books/prealgebra-2e https://openstax.org/details/books/prealgebra-2e it's a fully online-native book format with exercises, etc.

dghughes 3y ago

That happens to me all the time the solution is I need a push or some deadline. For high school it was a strict (we thought) teacher who brought me from an average of 70% to 95%. For computer programming it was going back to school as an adult and timed in class tests. For music is was paying for lessons at a certain time. If I don't get motivated from some external push I never get past a certain level. Every single thing I do in my life is like that even laundry. I must be chronic or maybe permanent procrastinator.