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.
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 [2] https://commoncog.com/tacit-knowledge-is-a-real-thing/
Having no education, I only did menial work for money. Yet in my early twenties, I was contemplating my lack of scholarship and realized I wanted to fill the holes in my education. I went to Khan Academy and, as you did, started with pre-K and worked my way linearly through up to pre-college math. Thankfully, I was soon laid off from my job, which was an opportunity to start attending community college.
I then transferred to a state school and double majored in applied math and computer science. Now I’m doing theoretical research as a PhD student in computer science.
The 8-year path from pre-K math to graduate-level math classes and now being published has been a journey. And I’m deeply grateful for resources like Khan Academy.
Deciding to commit to a daily study of math transformed my life.
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.
I could have easily said "afterwards" and "beforehand", but I like "ex post" and "ex ante" when referring to before/after having access to specific information.
These sets of books are universally considered to be among the best math education resources by mathematicians and others, and they start from the very basic (such as the number line and basic operations), but without the need of practicing elementary school material like counting.
But for anyone who's graduated high school, a lot of it would be at least a second encounter so you'll be reviving forgotten knowledge which is much easier while also diving deeper in your second pass.
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.
https://mathacademy.com/courses/mathematical-foundations-i https://mathacademy.com/courses/mathematical-foundations-ii 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/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.
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...
[2] https://www.edweek.org/teaching-learning/fraction-phobia-the...
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.
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
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.
Try this course: 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
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.
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.
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.
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.
Please let me know if they were helpful!