As mathematics teachers, we want students to understand mathematics, not just to recite facts and execute computational procedures. We also know that allowing students to explore and have fun with mathematics may not necessarily stimulate deep thinking and promote greater conceptual understanding. Tasks that are aligned with the NCTM's curriculum standards (NCTM 1989) and that are connected to students’ lives still may not challenge students to build more sophisticated understandings of mathematics. The actions of the teacher play a crucial role.
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Elham Kazemi (1998) studied this question.
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