To get this thread back to the point, a student cannot know what data is needed until they have arrived at a solution to the problem. Thus, it is incorrect to say "Students have difficulty knowing what data is important and what data is not." What the students lack is sufficient analytical skill to take the whole of the problem in and through experience and instinct, fashion a solution. It is like playing chess. Before you make your next move you must analyze the whole board and through that analysis you arrive at a strategy and that is when determine which piece you are going to move. Up until that point, when you have settled on a strategy, any piece could be the piece you move.
Dan countered my point with another question, "How much would it cost to wash all of the Windows in Seattle?". I suppose he was thinking that the students would have to go find out how many windows are in Seattle and what size they are. Thus, this would be a "data" driven problem. But this problem, is no different than any other problem. The student would first have to have a model that provides total cost (the goal) and then they would have to do the work to get the data their model requires.
The ability to put mathematics to use relies on the ability to analyze the situation and model it in a manner that fulfills your goal. The ability to do this rests on experience and instincts that are developed over time. Like I said before, teachers may be saying one thing but meaning another, but given that some curriculums focus on data gathering rather than algorithm, I would say that many teachers actually do not understand the cognitive task of solving a problem. The do not understand that the student must actually be able to analyze the problem and arrive at a solution all at once. It is this inability to pull it all together and understand the math in context is what sinks them.
The time that these teachers spend having the students "guess" a solution would be better spent teaching then the art of solving itself. When a student can analyze and solve then they have graduated to the stage where math is useful.