I think we should find a way to take the best content from Math Circles and get that to far more students in a digestible format.
Drilling down even further, if the Question is "what is the _single_ most useful thing that can be done to increase future scientific literacy and accelerate technological progress ?" .. then I think the answer must be to teach multiplication by drawing rectangles.
vis : https://quantblog.wordpress.com/2013/04/13/distributive-rule...
Its a really good antidote to 'math is magic, a set of rules you apply without knowing why'... its based on physical intuition we already have, and it leads very naturally to deeper more abstract thinking :
You can go quickly from counting out areas of integer sides via grouping, to multiplying fractions and decimals, to expanding (a+b)*c, to (a+b)(c+d), you can introduce 1+3+5+7+...+n = n^2 and 1+2+3+..+n=n(n+1)/2 , you can introduce primes as 'non-rectangle' numbers .. all the while improving facility with basic computations, and developing better math intuition.
Kids who believe they are dumb at math can relate to this kind of physical/visual construction - if you play tennis or basketball or fold paper or saw wood you already have a good intuition of area.
It seems not much math is being taught in school before age 12 .. We don't have to wait or invent anything groundbreaking - we can take concrete steps now, we know what works - ie. we have the vaccine, we just need willpower to get it to everyone.