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Topic: "The Standards are hypocritical" says Andrei
Replies: 10   Last Post: Oct 25, 1995 2:27 AM

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Kreg A. Sherbine

Posts: 26
Registered: 12/6/04
Real World Problems (Again)
Posted: Oct 22, 1995 8:43 PM
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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
sherbine@math.vanderbilt.edu | necessity of reflection. -H. Poincare








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