Well, I'd say that in the case of the Pythagorean Theorem, we should actually explain it. There's like 100+ different proofs, so there are options to actually explore the methodology of discovering something like this. From a personal example, this year in math class I really wanted to understand math deeply, so I had to ask for a lot of explanations before class and stuff. Like the change of base formula with logarithms. I had no idea why this worked, but when I found the proof in my book and on Wikipedia, I was like "Dang, that's pretty cool." I had fun getting deep into the abstract parts of other mathematical tools, too. That's what had an impact on me, and I've never liked math as much as I do now. As for looking at new ideas, another personal example, if you will. On my test, instead of writing "ln", I wrote Log base e. I understood that more, and I looked at it differently, but I got 3 points off because of it. Maybe I'm bitter, but looking at a formula a different way or finding new ways of doing things shouldn't be discouraged, rather encouraged.