For the benefit of Andrei and others who need examples, here are a few real-world problem samples straight from the C&E Standards: 1. page 164, the Ferris wheel problem 2. page 79, the survey reporting problem 3. page 45, the cost-sharing problem 4. page 85, the pattern problem 5. page 174, the gas consumption problem 6. page 117, the room measurement problem
I could continue, since all I've done to find these is to go through the Standards and look for bold print. "Real-world" is in the interpretation, i.e., what is real-world for one person is quite different from what is real-world for another. What is real to Judy and Andrei would be totally fantastic to a typical elementary school student (I speak of the high-level math research these folks do); what is real to Mike may be totally meaningless to some of the rest of us (I speak of Michigan football and snow in November); what is real to the most street-hardened of Dan's kids may have no relation at all to what is real to a farm boy in rural Carolina.
I doubt that the authors of the Standards failed to recognize this. Instead, I suspect that their impetus for including repeated reference to real-world problems was to encourage teachers to relate the mathematical content they teach to the everyday lives of *their students.* This returns to Susan's comments on educational constructivism: this theory says that every kid must sleep, eat, and learn for himself or herself. The extension of this related to real-world-ness is that every kid must eat, sleep, and learn in the context of his or her everyday experience.
And I really don't think that the NCTM would have us abolish problems dealing with money. The point they try to make (by using the phrase "topics to receive decreased attention" rather than the phrase "topics to be ignored altogether") is that coin and work problems have, in many classrooms, been the *only* sorts of problems ever posed. By decreasing attention to these sorts of problems, there can be room for more and more detailed work on other sorts of problems.
Finally, although I think I written it before here, "real-world" can change from student to student and from day to day, and even from moment to moment. In fact, that's sort of the point of one form of mathematical problem-solving: we start with a relatively concrete situation, and as we make generalizations and proofs and refutations, we begin to operate more fully in a realm independent of the initial problem. We can always return to it, but we can also go beyond it. When this happens, the solution really *isn't* the answer, and the understandings that students take away from such sessions are mathematically valuable in the sense that meaningful mathematical thought occurred.
Kreg A. Sherbine | To doubt everything or to believe Graduate Student | everything are two equally convenient Vanderbilt University | solutions; both dispense with the firstname.lastname@example.org | necessity of reflection. -H. Poincare