In his wonderful TEDx talk, Dan Meyer, a high school math teacher in Santa Cruz, CA, explains how he gets students who are “mathematically and conversationally intimidated” to formulate math problems themselves — based on their genuine curiosity about the world.
Meyer presents kids with everyday phenomena (like a hose slowly filling a big container in the school courtyard) and asks them simple questions (“How long will it take to fill up?”). Instead of memorizing formulas (or copying them from already-solved examples), his students practice “patient problem-solving.” Slowly, steadily, in small groups, they check out their intuitions and formulate their own reasoning.
Meyer recommends five rules of thumb for math teachers, including “Ask the shortest question you can” and “Let students build the problem.” He asserts: “The math serves the conversation, the conversation doesn’t serve the math!”
It’s another way of saying that Motivation + Deliberate Practice = Mastery.