Great work. Have you shared this with the Math Academy folks? I bet they'd love to copy your homework :)
I did a little deep dive into this kind of stuff over the summer. I haven't written it up yet, but I'll share some highlights below.
I realized Anki was optimized for the opposite of the problems I actually had. Anki's optimized to minimize study time. It does this by maximizing difficulty. For me, this means maximizing pain!
I'm not low on time; I'm low on willpower. I need it to be fun and easy! Otherwise, I quit and memory goes to zero. Gwern implies I am typical in this regard; most people who try SRS don't stick with it, even if they want to. So "Minimize Pain" seems like a worthy endeavour here.
So, by necessity, I made the reps easy. By making the reps easy, I realized I had accidentally become much more fluent. [0]
(The "automaticity" you mention, comes from practicing more frequently.) In other words, working hard (suffering more) was giving me worse results. Imagine! (I had a similar experience with complex motor skills, but that's a separate post!)
At some point I realized I could replace my entire flashcard app with a lightly modded Anki: increase target retrievability (to increase frequency), and use latency as the score (easy with a tiny addon, and/or custom card type).
As far as the math goes, I got stuck on generating the cards (past arithmetic). How did you do that? :)
(Also, I'd love to see the knowledge graph! I've been trying to reverse engineer the old one from Khan Academy...)
Speaking of fluency, I think "overlearning" is a misnomer. Our standards are too low and we are chronically "underlearning". Similarly, our "Mastery Learning" is actually Temporary Basic Competence...
Oh, a worthy postscript: Ebbinghaus (of the Forgetting Curves) also discovered the relearning curves. If you've learned something before, it becomes much easier to learn again later.
This is relevant because you can't necessarily apply Very Frequent Reps to your entire knowledge base. There's just not enough time to maintain fluency in everything.
But occasionally, you will want to be fluent in something, which you were once fluent in. Then, you simply shift it into Tier A, spam reps, and rapidly regain what was lost -- for as long as it's relevant to you.
Too much fine print. Trig would be better if it showed the picture of a right triangle with all sides labelled. Giving only the essential information doesn’t help with issues like confusing sine and cosine, which a memorization drill should address.
Basically: add more pictures.
Consider that in applications the names of the variables are different. Not sure that I would change this in a memorization app, but there’s no sign the author is aware of it.
This is a great project to see. I'm also an early fan and customer of Math Academy and am glad to see something like this focused on micro skills. As much as memorization is dismissed, having automatic recall base skills lets you get much further, much faster in harder ones.
Thank you! Yeah, Justin Skycak's writing really turned me on to the benefits of automaticity. Once you're aware of it you start to notice everywhere you lack it and how much it'd help in raising your ceiling.
One small piece of feedback: on my Pixel, the Android keyboard obscures the green button. So when I'm answering a numerical question, I use your number pad to enter the digits, and then use the enter key on my Android keyboard. This feels weird, but I guess with regular use it wouldn't.
Thanks! Yeah, that was a dealbreaker for me since I didn't want to bother with AI slop. So it took a while and a ton of testing/validation, but happy with how it came out.
I made something similar for my partner a while ago for math drills but this is way better (and more comprehensive). I gave up after 3-5 modules. Kudos.
Dude, hell yeah! I was just shopping for this exact thing not that long ago [1]. I've never been great with math and wanted something I could practice with away from my laptop. Love that it works in the browser, too. Well done, this is really nice.
I did a little deep dive into this kind of stuff over the summer. I haven't written it up yet, but I'll share some highlights below.
I realized Anki was optimized for the opposite of the problems I actually had. Anki's optimized to minimize study time. It does this by maximizing difficulty. For me, this means maximizing pain!
I'm not low on time; I'm low on willpower. I need it to be fun and easy! Otherwise, I quit and memory goes to zero. Gwern implies I am typical in this regard; most people who try SRS don't stick with it, even if they want to. So "Minimize Pain" seems like a worthy endeavour here.
So, by necessity, I made the reps easy. By making the reps easy, I realized I had accidentally become much more fluent. [0]
(The "automaticity" you mention, comes from practicing more frequently.) In other words, working hard (suffering more) was giving me worse results. Imagine! (I had a similar experience with complex motor skills, but that's a separate post!)
At some point I realized I could replace my entire flashcard app with a lightly modded Anki: increase target retrievability (to increase frequency), and use latency as the score (easy with a tiny addon, and/or custom card type).
As far as the math goes, I got stuck on generating the cards (past arithmetic). How did you do that? :)
(Also, I'd love to see the knowledge graph! I've been trying to reverse engineer the old one from Khan Academy...)
--
[0] The ancients knew this principle well...
https://en.wikipedia.org/wiki/Precision_teaching
Speaking of fluency, I think "overlearning" is a misnomer. Our standards are too low and we are chronically "underlearning". Similarly, our "Mastery Learning" is actually Temporary Basic Competence...
This is relevant because you can't necessarily apply Very Frequent Reps to your entire knowledge base. There's just not enough time to maintain fluency in everything.
But occasionally, you will want to be fluent in something, which you were once fluent in. Then, you simply shift it into Tier A, spam reps, and rapidly regain what was lost -- for as long as it's relevant to you.
Too much fine print. Trig would be better if it showed the picture of a right triangle with all sides labelled. Giving only the essential information doesn’t help with issues like confusing sine and cosine, which a memorization drill should address.
Basically: add more pictures.
Consider that in applications the names of the variables are different. Not sure that I would change this in a memorization app, but there’s no sign the author is aware of it.
One small piece of feedback: on my Pixel, the Android keyboard obscures the green button. So when I'm answering a numerical question, I use your number pad to enter the digits, and then use the enter key on my Android keyboard. This feels weird, but I guess with regular use it wouldn't.
[1] https://graybearding.bearblog.dev/how-im-teaching-myself-mat...