If thinking was to be described the way electrical circuits are, then we would have two basic type of thinking; series and parallel.
Series thinking, is something which we all do. Most of us are coded from birth this way, we learn to go for logic, for logical steps, from one point to next in the line, and thus we always proceed in that fashion, anything that falls out of that order is dismissed as illogical and focus is kept only on the logical queue, which makes most sense.
And the other is parallel thinking, few of us are left as we are born maybe. As one isn't born skilled or dumb, likewise, one isn't born to think a certain way. A newborn mind is a blank mind & that’s the last stage, one will witness a blank/white mind, ever.
Now, since we humans evolved, we learnt, applied and corrected the leaning to apply it again, and so happened the circle of life. We moved, sequentially, logically, weeding out things not contributing to what we wanted as outcome, and kept going. It has worked neatly, no doubt. Although, how can one question, until one doesn't have anything to compare to? & to compare this thing we are in, are you kidding!!… To compare such a humongous theory of learning, of logical precedence… what will you compare it with?! Our math, our physics, our chemistry, our biology… our entire learning is based on the logical series thinking!! What tool can one get to put against this and say, hey this doesn't sizes up!!
I believe, there’s this, “parallel thinking” too, it must be. Maybe from my finite vision and understanding, it’s 
something like this: When understanding geography one can relate and understand physics as well, then it’s parallel thinking. Makes any sense? ……..exactly!, from series viewpoint one will never make any sense of something which first breaks the very first principle of their existence – logic.
“Dismissed, it doesn't makes any sense, he has gone mad.”
Well, on a lighter note, mad is good, when everyone around seems to be intelligent then the other and are hell-bent to prove. we need a bunch of mad people around, to balance it out. :)
Coming back to topic, our intelligence, our logic, our reasoning, seems to be in series. Our roots are balanced upon logic – one directional perhaps. Our numbers, are based on that same logic and so is our everything else. So, if I am an enemy, then I just got one thing to take care of – “logic”! Just blow it up and you are already defeated without a war!!
And since this is the thing at “the scratch”, the basic principle of how we think and work, we need to put the 
solution at “the scratch” as well. To address this, and to develop parallel thinking, fresh minds, needs to be addressed with a complete different strategy. Nothing should be taught the way we do it, but in a new invented way. I already feel the goose bumps of the heart, mind and intelligence at that level, of someone my age.
Update: I read a news article of a Russian mathematician, who solved a 100 year old "Poincaré conjecture" math problem. After reading articles on him including on Wikipedia, I cant stop thinking the way he thought and comprehended things.
http://www.guardian.co.uk/world/2010/mar/23/grigory-perelman-rejects-1m-dollars
http://en.wikipedia.org/wiki/Grigori_Perelman
http://techland.time.com/2011/05/03/math-genius-solves-100-year-old-problem-then-refuses-million-dollar-prize/
http://windowstorussia.com/wp-content/uploads/2011/04/Grigori_Perelman_Interview.jpg
@ Amazon: Parallel Thinking, by Edward de Bono
