I am a fan of Dan Meyer, ever since I saw his TED talk. His opening is pretty dismal: "I teach high school math. I sell a product to a market that doesn't want it, but is forced by law to buy it. It's a losing proposition." It's good for a laugh, and we come away convinced that he nevertheless remains enthusiastic about changing that. Inquiry followed by learning to formulate problems seems so much more engaging than working through the "paint by numbers" approach in textbooks.
Dan is now working on his PhD in education from Stanford. He blogged recently about how we use abstractions in texts, and it triggered lots of connections with EDUC 402. He is a fan of S.I. Hayakawa, and references his book chapter How We Know What We Know. I like the ladder metaphor, illustrated with his example of Bessie the cow. We often get stuck at a particular rung of the ladder, far from where the student may be. Reminds me of Magritte's pipe that is not a pipe. I think we need to explicitly point out to students that math at the symbolic level is a very high level of abstraction. After the inquiry, and their problem is formulated, they need to understand they are looking at the concrete lower rungs. Now they just need to figure out how to climb the ladder.