24 SES 04, Investigating Social Interactions and Classroom Learning from Multiple Perspectives
In this paper I use a methodological instrument to analyze students and teachers' mathematical practices within the mathematics lesson. The context is a study conducted in a laboratory full-equipped with audio and video recording devices, at The University of Melbourne, as part of the Social Unit Research Project, led by Prof. David Clarke. First I use Godino and colleagues' approach (Pino-Fan, Godino, & Font, 2016) to describe and discuss the epistemic configurations produced by a small-group of four students working in an open-ended problem. Through the analysis of the dialogue among the students I intend to identify patterns leading them to solve the task and understand the mathematical concepts, properties and propositions embedded within the epistemological configuration embedded in the task. Interaction is a crucial aspect of learning (Díez-Palomar & Cabre, 2015; Mercer, 2000; Vygotsky, 1978). This study is based on the premise that learning is a social process (Vygotsky, 1978) in which individuals participate in mathematical discourses (Sfard, 2008). Mehan (1979) described a fundamental interaction pattern in typical teacher-guided lessons (initiation-reply-evaluation). Later studies criticized this pattern because it may prevent students developing autonomous thinking and understanding. Researchers introduced a range of different types of interaction, such as the 'funnel pattern', the 'elicitation pattern' or 'real discussion' episodes, to solve the potential limitations of the original construct proposed by Mehan. Recent theoretical developments in the analysis of dialogue points to the central role that dialogic talk (Díez-Palomar & Cabre, 2015) plays in opening opportunities for developing mathematical understanding. I use a communicative methodological approach to look for utterances (characterizing the negotiation events embedded in each episode of interaction), where students use validity claims (in Habermasian terms) to justify, explain, describe, convince, persuade, or, alternatively, make power claims to impose, annoy, insult, disregard. Identifying patterns within the students' dialogue may provide significant information for teachers to take valuable decisions when managing the interaction within classroom episodes of learning in the context of small-group work. This may also contribute to clarify how teachers may scaffold students' reasoning and understanding assuming that learning is a social process based on interactions mediated through dialogue, moving forward previous contributions on the understanding of how learning works (Flecha, 2000; Wood, Bruner, & Ross, 1976).
Díez-Palomar, J., & Cabré, J. (2015). Using dialogic talk to teach mathematics: The case of interactive groups. ZDM, 47(7), 1299-1312. Flecha, R. (2000). Sharing Words: Theory and Practice of Dialogic Learning. Lanham, MD: Rowman & Littlefield. Mehan, H. (1979). Learning Lessons: Social Organization in the Classroom. Cambridge, MA.: Harvard University Press. Mercer, N. (2000). Words and Minds: How we Use Language to Think Together. London, New York: Routledge. Pino-Fan, L. R., Godino, J. D., & Font, V. (2016). Assessing key epistemic features of didactic-mathematical knowledge of prospective teachers: the case of the derivative. Journal of Mathematics Teacher Education, 1-32. Vygotsky, L. S. (1978). Mind in Society. Cambridge, MA.: Harvard Educational Press. Wertsch, J. (1998). Mind as Action. New York: Oxford Press. Wood, D., Bruner, J. S., & Ross, G. (1976). The role of tutoring in problem solving. Journal of child psychology and psychiatry, 17(2), 89-100.
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