I agree wholeheartedly that students need to spend more time dealing with the setup of a problem (thinking about how best to express a vague idea mathematically

I agree wholeheartedly that students need to spend more time dealing with the setup of a problem (thinking about how best to express a vague idea mathematically) and in dealing with problems that don't have any known answer. I think this is a huge part of "mathematical thinking skills" that we claim we want to instill in students. It's a sad thing that most people don't really have a good definition of what a "mathematical thinking skill" is in the first place. Figuring out how to adequately and precisely pose questions is one of the MOST mathematical skills, but it rarely shows up in discussions of standards and curricula.