[yt-sdb]

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 [2] https://commoncog.com/tacit-knowledge-is-a-real-thing/

[austinwatkins]

I loved reading your comment. Your story is very similar to my own! A little over 8 years ago, I also started at the beginning of Khan Academy. Due to reasons related to my childhood, I had essentially no education growing up. When I was in my early twenties, I had only an elementary education. The highest level of math I knew was basic fraction arithmetic. I had never written an essay and I did not have a scientific understanding.

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.

[noSyncCloud]

This is really inspiring, thanks for sharing. I should do likewise. I wound up dropping out of school (had kids too early, don't ask), which was... not a good decision. I do work as a developer but I need more domain knowledge in mathematics. Never too late to start, I guess.

[status200]

This is inline with a Zen practice called "beginner's mind", and is so useful in many areas, thank you for this inspiration.

[gareve]

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]

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_]

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'?

[yt-sdb]

"Before" and "after" are generic terms. A car might stop before the crosswalk (space). You might eat dinner after work (time). But "ex ante" and "ex post" specify a relationship to an (random) event or to specific information. For example, a data scientist might compute a quantity "ex ante". This means that the quantity was estimated using only forecast data. No historical data was used. It would not make sense, however, to say that a car stops ex ante the crosswalk.

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.

[hawk_]

Got it. I will try to leverage the synergies between Latin and English ex post.

[timidiceball]

it conveys that you know what ex post and ex ante mean

[jhardy54]

Or, quite often, conveys that you don’t know what they mean.

[gpt5]

If you, or someone else is seriously considering learning math from the basic at a high level, I’d recommend picking up “art of problem solving, pre-algebra” book, and walking up from there.

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.

[jacksnipe]

I think the TAOPS curriculum would be incredibly challenging for somebody who has actively incorrect intuitions about math.

[sn9]

I think if you've literally never seen the material before, you might be right.

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.

[xwowsersx]

What did you do after you completed the K-8?

[yt-sdb]

I worked from the top of this page [1] downwards and ended after algebra 2.

[1] https://www.khanacademy.org/math