Teachers' understanding of students' conceptions about chance
Zapata Cardona, Olga Lucia
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This study investigated teachersÕ perception of studentsÕ thinking about chance. In particular, the study explored how teachers anticipated and explained studentsÕ difficulties with the ideas of chance, and the strategies teachers claimed to use in order to help students reorganize their thinking. The study was motivated by the literature on reasoning about chance in which researchers present detailed descriptions of the difficulties students have in thinking about uncertainty. Yet little research has focused on teachersÕ practices associated with studentsÕ difficulties. Little is known about how teachers perceive studentsÕ difficulties, how they anticipate studentsÕ struggles, and what kinds of strategies are useful for teachers to deal with those difficulties. Two teachers, one expert and one novice, members of an AP Statistics learning community, participated in this study during fall 2007 and the beginning of winter 2008. They were observed five times in the learning community meetings, and interviewed three times for about 1 hour each. The interviews explored four core ideas in statistics that have been associated with the sources of studentsÕ difficulties about chance: sample space, randomness, independence, and the law of large numbers. The interview protocol included 12 episodes whose tasks had been previously used in research. Data were collected in the form of observations, interviews, and artifacts and then analyzed using grounded theory, interpretativism, and an expert-novice contrast. The results of this study highlighted that the expert and novice teachers exhibited differences in the way they perceived studentsÕ difficulties and in the way they dealt with them. The expert was able to identify studentsÕ difficulties at an early stage in the discussion; the novice, however, underestimated studentsÕ difficulties and needed a longer exposure to the episodes to recognize the difficulties. Data also showed that although the teachers used similar strategies, the way they integrated them differed. The characteristics of expertise in teaching are still murky, but results from this study suggest that novice teachers are more open to considering studentsÕ difficulties when they reflect deeper on studentsÕ struggles. Consequently, teacher preparation and teacher professional development programs should be designed in ways that challenge teachers to reflect on studentsÕ difficulties.