I regard our conversation as discussion:-)

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.

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• What we see in College is that -trivial- ♀ (1075 bytes) () 01/15/2015 postreply 18:18:37