I can confirm that my maths teachers at primary school were terrible: if you stepped a little bit outside what's in the book, they were absolutely lost.
They were a lot better in secondary school, possibly because they had a much stronger mathematical education (secondary school teachers usually have a university degree in the subject they teach or in a closely related field, at least in my country).
I also absolutely agree with what you say about overconfidence and the need to revisit a subject / layer instead of thinking "it's over for good".
If 'what are you doing?' generalises, I'd say people would end up answering just the same way people answer to 'how are you?' or 'how are you doing?'.
In fact, in Spanish '¿qué haces?' or in Greek 'Τι κάνεις;' (both literally meaning 'what are you doing?') can be used, depending on formality and closeness, as greetings, and the usual answers are as shallow as 'fine'.
In other languages, 'where are you going?' is a customary greeting and again it's not expected to be answered with an honest description of where you're physically going to, but rather with another more or less fixed expression similar to 'fine'.
Here's one article which shows a different view on this:
FWIW, my experience is that I learn better going up and down the different layers, rather than exhausting and completely "automating" the lower layers before attempting to go to the advanced material on the upper layers.
Plus, some experience with something what you're learning is useful for is a great motivator and can help focus.
You have an idea of how likely something is to happen, or an estimate of a figure, or a model of something in the real world (e.g: Peter is a guy who loves cats). You happen to get new information about this something (e.g: you see Peter viciously killing a cute kitten).
You'd most likely update, with both epistemical consequences (you'd probably stop believing Peter is the cat-loving guy you thought) and instrumental or practical consequences (you wouldn't ask him to look after your cats while you are away on holiday).
The way I see it, Bayes' Theorem tells you how much you should update your beliefs to take into account all the evidence you have, to be right as much of the time as possible, given the limited information you have.
Obviously, as they say about information systems in general, "garbage in garbage out", which means you should worry about getting reliable information on the things you care most about, because even with the best possible update algorithm, if the information you get is biased, your beliefs and actions will not be right.
I don't know if your criticism of the importance attached to Bayes' Theorem is because you feel other aspects are neglected or what exactly is your rant. Could you please elaborate a bit?
I'd be curious to know if you kept on doing that and, if so, what the results were.
A similar approach has worked for me better than a more split-time approach.
I'm aware of the forgetting curve and I certainly forget a lot of the contents afterwards, but the global structure seems to remain in the brain and changes to the way of thinking or of solving problems after these intense study sessions also seem to remain for longer than the details.
I've also tried doing some incremental reading / incremental learning and although the contents stay for longer, I don't feel the same kind of enlightenment or learning taking place. It feels a bit like wasting time, even if I'm learning.
I don't know how you'd approach maintenance for skills you acquired but forgot. Sometimes I've learnt something which has the skill I want to review as a prerequisite, using the same method, but reviewing the old material as needed, and it sort of did the trick.
Thank you for the interesting article. I completely agree that curiosity ("the spark") is an important component of learning, and no technique will give it on its own.
Have you experimented with learning one textbook or article at a time vs learning several concurrently (alternating between them)? If so, what are your conclusions on this?
I know the relevant results of spaced repetition, the test effect, distributed practice vs massed practice, interleaving... but in practice how does it translate to a sustainable learning routine? How often do you change subjects when studying more than one thing at a time?
Your comment looks surprisingly fit for https://www.lesswrong.com/posts/SfbesWBQQY3RJkJKa/what-would-you-store-to-maximize-value-in-100-years-a, which makes me think your intention may have been to submit it on the other post.
I'd say 'anger', as many other such psychological constructs, is ambiguous and can refer either to a trait / feature (an anger-prone person, a person who tends to become angry easily) or to a state (a person who is momentarily angry).
The same distinction can be made vis-à-vis other emotions (sadness, happiness, disgust, anxiety...) and perhaps personality traits.
I'd propose the terms 'momentarily angry' and 'anger-prone' (and similarly for the other emotions: momentarily sad and sadness-prone, etc) if there's a need to disambiguate, but not being a native English speaker I'm not really sure of them being fit.
Duolingo now has more languages than when the OP was written, among them Mandarin Chinese.