TED occasionally has question and answer sessions with their speakers who really ignited something with their presentation, and Sir Ken recently did this. (Here's the article.) He addresses math specifically:
It's not hugely original, but it's nice to get confirmation of things we believe from outside sources. He touches on engagement several times in the Q&A, and I do believe that's the central issue in teaching, and I love to ponder what is the key for math. Going to more and more of these reading conferences, I am insanely jealous of the teachers who talk about the book that turned a student on to reading. Problems don't seem to have the same effect.
"If you want to promote creativity, you need, firstly, to stimulate kids minds with puzzles and questions which will intrigue them. Often that's best done by giving them problems, rather than just solutions. What often happens in classrooms is, kids sit there trying to learn in a drone-like way things of not much interest that have already been figured out.
The best math teachers I know, like the best English teachers, are always giving kids puzzles. They're given things to work on where math skills are required but may not be the focus of the activity. There giving them problems to solve. Or they're made to engage with age-old mathematical problems. For example, I'm thinking about the problem of latitude. How do you go about measuring the planet? I mean, somebody had to do that. How do you do it? Professional mathematicians have such a cornucopia of fascinating puzzles, questions, proposals and conundrums. A great math teacher really has endless opportunities to stimulate kids minds and get them engaged with things they'd probably never thought about before. Rather than just giving them techniques." -Ken Robinson