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You probably realize that asking for a definition of a problem-solving approach will yield a variety of responses. In its purest sense, a problem is posed and the students learn the mathematics and other things they need to know in order to solve the problem. (This is sometimes called PBL Problem Based Learning). The best example I currently know of this as a curriculum is the ARISE Project created by COMAP, now published by South-Western Publishing (International Thompson Pub.) under the title <I>Mathematics: Modeling Our World.</I> Contact South-Western Publishing Co. at http://www.swep.com/ For example, consider looking at only a two-dimensional view of a six-pack of cola. Discuss possible definitions of efficiency such as most space covered by the cola cans. Then challenge: is this the "best" configuration for cola cans? What other shapes might they take? What makes them best? How efficient are they? Wonderful kinds of mathematics flow out of such a problem. COMAP itself publishes a quarterly magazine that usually has at least one good problem like the one above. It would help if I knew what area and grade level you are interested in. ARISE is just one of the NSF sponsored projects. It is geared for 8th-11th grade. There are similar programs for other grade levels.
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