Dojo learning model Updated +Created
Group students by interest, not by age Updated +Created
Grouping by age as done in traditional education as of 2020 is useless.
Rather, we should group students by subject of interest; e.g. natural sciences, social sciences, a sport, etc., just like in any working adult organization!
This way, younger students can actually actively learn from and collaborate with older students about, see notably Jacques Monod's you can learn more from older students than from faculty.
This becomes even more natural when you try to give students must have a flexible choice of what to learn.
This age distinction should be abolished at all stages of the system, not only within K-12, but also across K-12, undergraduate education and postgraduate education.
This idea is part of the ideal that the learning environment should be more like a dojo environment (AKA Peer tutoring, see also dojo learning model), rather than an amorphous checkbox ticking exercise in bureaucracy so that "everyone is educated".
Perhaps, even more importantly, is that we should put much more emphasis on grouping students with other students online, where we can select similar interest amongst the entire population and not just on a per-local-neighbourhood basis.
Learn in public Updated +Created
This is the most extreme and final form of Peer tutoring, it's natural final consequence given the Internet Age.
PROMYS Updated +Created
The good:
The bad: everything else. Closed source learning materials + a university-like selection program. Such a waste of efforts that could benefit way more people with more open resources.
meta.mathoverflow.net/questions/4889/request-to-keep-an-eye-out-for-promys-admissions-problems asking to remove PROMYS problems from MathOverflow. And it seems to have been mostly accepted. Newbs. Any maths problem should be allowed to be askeable online. There are no fundamentally new problems, copyright takedown is just silly.
There is value in tutorials written by beginners Updated +Created
Ciro Santilli is a big believer that there is value in tutorials written by beginners, because beginners are more likely to explain things in a way that other beginners can understand.
Even though they make more mistakes, this more approachable point of view can be very valuable.
And mistakes/omissions can be corrected on comments by people with more knowledge, so that the writer also ends up learning something new.
By other people:
  • jakobschwichtenberg.com/about/ from Jakob Schwichtenberg mentions quotes C. S. Lewis book "Reflections on the Psalms"[ref]:
    It often happens that two schoolboys can solve difficulties in their work for one another better than the master can. [...] The fellow-pupil can help more than the master because he knows less. The difficulty we want him to explain is one he has recently met. The expert met it so long ago he has forgotten. He sees the whole subject, by now, in a different light that he cannot conceive what is really troubling the pupil; he sees a dozen other difficulties which ought to be troubling him but aren't.