For the basis of my research, I have posed the question, "What teacher practices facilitate active learning and student interest in secondary mathematics?" I have based my conceptual framework on the ideas espoused by George P6lya. He was a mathematician and exemplary teacher who strongly believed that activity is the basic principle that drives teaching and learning. The Curriculum and Evaluation Standards for School Mathematics recently published by the National Council of Teachers of Mathematics stresses a similar viewpoint: "In addition to traditional teacher demonstrations and teacher-led discussions, greater opportunities should be provided for small-group work, individual explorations, peer instruction and whole-class discussions in which the teacher serves as a moderator. These alternative methods of instruction will require the teacher's role to shift from dispensing information to facilitating learning, from that of director to that of catalyst and coach" (NCTM, 1989, p. 128). Through my observational experiences at the junior high level I saw some active learning taking place. Questions were asked of the students, however, students who did not offer a , response were left to sit idle. Although games and puzzles were used frequently, these were reserved for extra-credit or Friday afternoon activities. They never served as the foundation for a lesson. I did not observe any group-activities or student-discovery lessons. Although I cannot generalize from these limited observations, my experiences support current research on mathematics instruction. The dominant sequence of activities in the math class is as follows: checking the previous day's homework assignment; a short period of teacher presentation, and students working individually on the next homework assignment. For some students this routine encourages active learning and for some students it does not. Research supports the idea that students are engaging in rote memorization of theorems and algorithms without really understanding why the algorithms work (Fraser & Tobin, 1989).
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