It was interesting to read the 1st four chapters of The Art of Possibility by Rosamund and Benjamin Zander. I liked the idea in the first chapter where it is said "We see a map of the world, not the world itself. But what kind of map is the brain inclined to draw?" As a Social Studies teacher, I am constantly working with map a intangible items that I need to make tangible to my students. Yes, these items exists, but I cannot physically bring the White House and the Capitol building into my classroom when I talk about the separation of powers. This is the big picture that I got from these chapters. We have to think outside of what we perceive and look at the bigger picture. The exercise of the nine dots is a perfect example. To be able to connect all the dots with four straight lines, you have to do something unorthodox. You have to, as the authors state "extend beyond the borders that confine us to our everyday reality." This is an important concept that we can instill in our own classrooms.
I agree, those intangible things are difficult to bring into the classroom. Trying to find a way to get the students to think on a more abstract scale is something that works amazingly well, but very difficult to implement. Your reference to the four straight lines is a great point. Doing something unorthodox is not only hard, but we are almost trained NOT to think in those terms. So not only is it a challenge to learn in a different way, it is so to teach in a different way, especially when you were yourself taught in that same way.