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I currently use "Discovering Geometry" by Micheal Sierra for sophomores in my high school geometry classes. I have the students in groups of 4 to 5. They work through the discovery process as presented in the book, coming up with definitions for geometric figures such as chords, central angles, inscribed angles, diameters, etc. This gives them ownership to the material, because they "discover" the material, as opposed to me owning it and giving it to them through lecture or demonstration. I like the concept. The kids are actively engaged in their learning. Here is my question. Often the definitions they come up with are clumsily worded and although not inaccurate (although sometimes they are) do not make an adequate "working definition". Now, if I close the lesson with a discussion of their definitions, having the groups share their work and then arriving at a good, working definition, many of the students learn that they need not work hard at discovering their own definitions because they will be altered at the end of the lesson anyway. If we do not close the lesson with an attempt to correct and simplify the definitions they arrived at, they walk out of the room with a jumble of words and a jumble of thoughts regarding the concepts they were supposed to master. How do I allow them to discover the concepts and at the same time, make sure they have an acceptable answer from their discovery work? How do I motivate them to continue to work to discover geometry and thereby own the information without stealing the information from them at the end of the period by having them rewrite their work? I would love some working strategies regarding this situation. Thanks.
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