One of the most important principles in reform mathematics is allowing students to be challenged by mathematics problems (Hiebert et al. 1996). Historically, mathematical problems have required students to apply a known procedure to produce an expected answer. The National Council of Teachers of Mathematics (NCTM 2000) has called for changes in the problems that are typically posed to students, asserting that such problems should instead require students to reason, communicate, represent, problem solve, and make mathematical connections. Posing open-ended, extendable problems allows students to construct their own mathematical learning and understanding by building on previous experiences and making connections among topics and disciplines.
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