Involving students in open exploration and a search for patterns and relations is a very exciting and rewarding experience. These activities promote stimulating discussions, the application of known skills and relations to unfamiliar settings, and the development of what the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) has called "mathematical power"—the ability to probe and connect and to reason both inductively and deductively. Involvement of this kind can also lead to findings that capture the imagination and that foster a lasting interest in mathematics and an appreciation for its beauty.
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