I have been teaching for 10 years now, and have always pursued math. Over the past 6 years I have pushed more and more technology in my classes, but always struggle with useful integration. I have developed very interactive power-points but they are still limited as presentation tools. Recently I have started using PearDeck which is a great response tool, but still has it's limitations. I basically want to find the best way to get my students to learn and interact, but still value teaching as the "sage on the stage."
I think this could go two ways, both of which are very very useful for our students. 1. Perseverance through a no win scenario, and then recap with them how the struggle, and how you take control of the struggle (even if you can't change the outcome), affects their personal development.
2. Sometimes ingenious thinking can 'cheat' your way around or through a situation that was supposedly impossible.
I like both aspects, provided they have oversight and decompression at the end, as the would greatly help our students in their future struggles.
As far as those entering college, I would love to see a college application process set up as one of these. At least for me, I would rather see how a student does in the face of defeat rather than what they have to say about themselves. It would give you a much better idea of who they are, and what they can do. It is a slant connection, but there was an article I read at some point over the weekend about how Walt Bettinger (the Charles Schwab CEO) takes his candidates out to eat, and tells the staff to mess up the candidates order, to see the reaction.