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I just conducted an inservice training for elementary teachers in problem solving. There are many examples you can find in either the NCTM Arithmetic Teacher or the Middle School Journal. Let me say that you don't have to be an expert in problem solving to empower your students to develop problem solving skills! I teach very bright and gifted children and most are smarter than I am. I present a learning environment where they can freely grow and learn. I don't pretend to have all the answers. Sometimes the real learning is in the exploration. For example: Here is a problem. You are given 16 pieces of fence (say 16 toothpicks) and two cows (2 plastic markers). Create the space that will contain the most grass for the cows to eat. Several of the teachers began thinking about the problem, rather than playing with the problem and investigating. Students would probably investigate. Some teachers "already knew the answer," because they were sure the shape had to be a square. Then I asked what about something that would be more rounded? They investigated and discovered that the "circle" would have more area. Then I asked them to convince me. They were not allowed to use area formulas. I guess the problem solving, to me, is the ability to find a way to solve a problem, not so much the solution. Hope this helps.
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