Critical thinking and out-of-the box thinking are two different things. Thinking quickly does not enter into it at all.
Try reading a books like "Why People Believe Weird Things" and "The Demon-Haunted World". That will get you started on the critical thinking part. The book "Goedel, Escher, Bach" was supposed to be about thinking outside of the box, but the book belonged to my roomate and we graduated before I had a chance to finish it.
I've been accused of thinking outside of the box and I'm not sure it is something that can be taught. For the most part, people will fight innovative ideas because, by definition, they will challenge the way they have always done things.
Anyway, I've tried to get others to follow my thought process and the best way I can describe it is with this analogy: When you are looking for something, such as lost car keys, you stop looking once you've found it. Most people are like this with ideas. Once they find a solution to a problem, they stop right there are use their solution. In my case, I've learned to keep looking, hoping to find a better solution that the one I've already found. In other words, just because I have found the 'keys' doesn't mean I stop looking. I know this sounds crazy and it goes against human nature, but then again, I've also been accused of being crazy.