A world class expert in elementary mathematics seems kind of paradox? A pedagogy expert, sure, but how much expertise do you really need?
>This is basically how we train elite athletes, musicians
... but only after they've proven talent. Children raised to become top athletes aren't necessarily going to be successful, are they?
Simply, the attention afforded to a particular student in a 1:1 setting is an improvement, I agree with that at least.
Beyond basic understanding, teaching elementary mathematics effectively is a difficult job which can take decades to fully master. There are a large number of potential conceptual and procedural errors which various students can make, some of which are subtle and hard to correct. Someone who can perform elementary mathematics is not necessarily able to properly teach it.
As for world-class expertise, that really depends on what our goals are. There are undoubtedly world-class experts in elementary mathematics, who have spent decades doing extensive research in the history and practice, and have thought very deeply about the nature and meaning of numbers and mathematical relations. My comment was about the “ideal” case, if you want the student to learn as fast and effectively as possible.
But you can also get by okay with just a typical trained professional teacher (ideally a specialist in mathematics education).
I recommend Liping Ma’s book Knowing and Teaching Elementary Mathematics for some basic analysis.
Plenty of things do better... if you have much more resources to spend.
The best is 1:1 or 1:few where the 1 is a world-class expert in the field of interest who also happens to be a world-class teacher. Something like a personal tutor/coach. Think Aristotle and Alexander.
This is basically how we train elite athletes, musicians, etc., and how some of the very wealthy provide training for their children. It’s very time-expensive though for the teacher, and doesn’t scale well because there aren’t that many world-class practitioner-teachers out there in any given subject.