I was part of that guessing math thread so I guess I can just jump right into the same discussion here. The problems that were being discussed were not aimed at teaching kids that their primary math skills are worthless and that guessing is the way to go.

They were trying to build something called: DEDUCTIVE REASONING. Perhaps you have heard of it. It is a critical skill for higher level mathematics and it is not something that you learn by just memorizing basic math facts. I will agree that there is probably not nearly enough emphasis on basic arithmetic in our schools and that many of our students are woefully unprepared in math and the sciences but just teaching students how to work a problem alone step by step is not going to let them compete with students from China either. Students must developing reasoning, estimation and various other skills
in addition to their basic math skills. Math can be abstract and fluid. It does not always have to be a rigid science. That does not mean that I think we should teach kids that there is not a right and a wrong answer and it does not mean that we do not need to teach kids the appropriate steps to solve a quadratic equation. However, if we really want our kids to exceed in fields such as mathematics, engineering, chemistry, medicine, etc.. we need to be sure we are building all of their skills not just rote memorization of facts and steps.
I also disagree that we should make math boring. I will admit that some of it is boring and you just have to work your way through it but we should be showing our kids the applications for math and making it interesting. How else do you show them that math is something worth their time and how do you inspire our next generation of scientists? Even from a very early age I think we should show kids the application of math in their everyday lives. Heck, I even do this with my almost 4 year old when we are working on numbers and basic addition.