At least to clear my mind through arguments. That's how I approach forums.
Before ansswering any of your points: I wanted to point out the word "Proof" has two meanings
(1) in non mathematical areas (like biology, economics, etc). There is no absolute proof; They mostly rely on preponderance of evidence.
(2) Math and maybe physics--The proof is absolute (starting from assumptions).
K-12 has enough of (1); If they don't have too much (2) then I wouldn't worry about it. If it was as much as we learned in China, then I would worry it is too much.
Now back to your points:
1 (A) Find the answer to XYZ, and
(B) Prove that the answer to XYZ is W.
Agreed (B) is easier than (A); That means we should give simpler real life problems that uses theoroms rather than proving mathematical thereoms..
2 On various approaches to solve problems and prove theorems.
I believe, finding and confirming answers give anybody approaching the problem more incentive to find more approaches. Agreed that there are people invents different proofs for the same problems--but I'd rather work on unsolved problems than problems with answers.
3. These problems are for the chosen few like yourself. (See point 6 of my OP)
4. In my OP, I wasn't too sure on this point (I said may be high school could have some proofs)
Again, problem solving involves proof--and better; so problem solving should be emphasized more than proof.
