[Notatheist]

I've recently gotten back into math and I'm really struggling with your approach. I find it particularly difficult to get an accurate view of how well I'm doing and where I am. Most concepts I ingest easily, and I demolish any exercises in the books I read, find on the internet, ask AI for, or scribble down myself randomly. I repeat them a couple of times to make sure. All is well. Cute green checkmarks abound. Categories marked as mastered. Pride bordering on arrogance. I move on. A week later I'm handed new concepts. The house of cards collapses. I haven't mastered any of the things. There are gaping holes in the information I was given and I wasn't knowledgeable enough to notice.

The author doesn't seem to share my difficulties either. His are of motivation and those seem to maybe be addressed by the resource he used and specifically sharing his progress with other users. For $50 I expect more than polished KhanAcademy, promises like "accelerates the learning process at 4X the speed of a traditional math class" (if anything I want to slow down), and a progress tracker to post pictures of on X. If I wanted to be told I'm amazing, how long my streak is, and to learn nothing I'd use duolingo.

[noelwelsh]

What you describe is entirely normal in my experience learning lots of stuff and teaching many others. It might help you to let go of the idea that learning is a linear process where you master one topic and move on to the next. As I learn more I'm continually getting a deeper understanding of basic material I "mastered" decades ago. I often tell my students I don't think their understanding is complete but it is sufficient to move on, and the later material will help them get a better understanding. And it does!

[mlyle]

> that learning is a linear process where you master one topic and move on to the next.

It's closer to true in mathematics than most other places, but not very close to true.

It's amazing the "layer cake model" of mathematics learning is such a strong idea even among many mathematics teachers.

On the other hand, sometimes a missing concept like cancellation in fractions or just poor proficiency in arithmetic rears its head and makes doing later stuff very hard. Once a student gets used to being and staying confused, it's often game over.

[RealityVoid]

> Once a student gets used to being and staying confused, it's often game over.

I think this is a very good insight, that somehow eluded me. Many many people are OK being confused about things, and I never considered that it's something they learn, but it makes so much sense.

[mna_]

When do you do exercises, do you refer back to sections in the book or examples? If so, this is a bad habit. Try to do exercises without looking back. This will force you to use your memory. Also don't be too quick to check solutions for things you're stuck on.

Everyone who does mathematics feels the way you do when learning something new. It's a normal feeling. Don't get disheartened. Push through it.

[viraptor]

Sounds like you'd really like MA. It will drill you on things until you actually know them. There's no green checkmark as such either - everything will be tested again spaced repetition style. You will be slowed down until you can actually use the previous concepts properly.

[chrisweekly]

Mostly sympathetic here, but your duolingo comment is a bit too harsh. Anecdotal counterpoint: my high-schooler used duolingo last summer to skip a year of instruction and get into AP Spanish as a junior, and got into the Spanish National Honors Society, and earned a fluency certificate. (I know most high school language classes churn out students who can't speak a lick, but her school is excellent and she has working fluency - which she credits largely to using duolingo to catch up.) IOW, YMMV.