Doctor of Philosophy (PhD)
Educational Theory, Policy, and Practice
Mathematics education reform is informed by constructivist theories that forefront student learning of concepts, and by sociocultural theories whose focus is on students’ mastery of mathematical practices. As Cobb (1994) pointed out, these theorizations are inconsistent with one another, leading to conflict as some theorists seek to promote their approach as the correct one. Alternatively, Cobb, and many others in the social constructivism or the situated cognition camps, seek some sort of integration or balancing of these priorities in pedagogical theorizing. Kirshner (2002, 2004, 2008) argued that instead of either selecting one theory or balancing/coordinating the two theories, we should regard each theory as an independent basis for pedagogical practice, and articulate a separate genre of teaching for each. In that spirit, the current study sought to explore pedagogical methods directed exclusively to enculturating students into mathematical practices, particularly, practices of argumentation characteristic of mathematical proof. The researcher worked with a group of 11 average-ability students in the 11-12 age range, over 24, half-hour sessions. At first, students were called upon to discuss various basic geometric terms, and then to present arguments establishing the truth of 10 basic geometric theorems. Students worked together in groups to discuss the problems, and presented their proofs. All sessions were videotaped and transcribed, and each student’s arguments were coded for sophistication on a 4-level system based on the work of Lolli (2005) and Douek (2009). The results indicated that all students advanced in their level of sophistication, most moving from level 1 in which one understands that an explanation is required, but one does not understand the obligation for the explanation to be logically persuasive to level 3 in which one coordinates the elements of the argument in a way that is consistent with logically sound deductive reasoning. The qualitative analysis of interactional processes illustrates the influence of the group’s level of discourse on individual development.
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Chillara, Indira Venkata, "Enculturational practices in the teaching of proof in mathematics" (2013). LSU Doctoral Dissertations. 745.