# Analyzing generalizations through discourse

2016-11-03
Strachota, Susanne
İşler Baykal, Işıl
Fonger, Nicole
Blanton, Maria
Gardiner, Angela Murphy
Although generalizing is “intrinsic to mathematical activity and thinking” (Kaput, 1999, p. 137), students struggle to generalize, often make weak generalizations, and rarely justify their generalizations. Supporting generalizing in the mathematics classroom requires a better understanding of the source of students’ generalizing. What are the mechanisms that encourage students’ generalizing? This question is central to our research, which seeks to understand the nature of the discourse that supports students’ generalizing. This study explored the ways in which a fourth grade class generalized and justified their generalizations about even and odd numbers during a lesson. We conducted a multi-level analysis of the classroom discourse, identifying shifts and instances of re-centering. Based on the inferred goal of the speaker, each utterance was coded for purpose and technique for fulfilling that purpose (Gonzalez & DeJarnette, 2012). Additionally, we recorded generalizations (Ellis, 2011), and situated these generalizations in the discourse in order to describe the discursive moves that contributed to and resulted from the generalizations. Two important shifts in the discourse occurred during the lesson. First, the mode of representation shifted from an array to a number expression—a shift in representation that indicates a shift in discourse. Second, after establishing “cubes and left over cubes” as a shared way to describe even and odd number generalizations, students shifted from using “left over/leftover” as a modifier or adjective to using it as a noun, an indication of an evolving understanding of the shared idea. Although five generalizations occurred during the lesson, they all occurred during the second half of the lesson, subsequent to the shifts in discourse. Thus, the results suggest that the shifts in discourse may function as generalizing-promoting actions (Ellis, 2011). We also identified particular discursive techniques, and suggest that future research might focus on these aspects of discourse to further explore generalizing-promoting actions.
38th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (3 - 6 Kasım 2016)

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Citation Formats
S. Strachota, I. İşler Baykal, N. Fonger, M. Blanton, and A. M. Gardiner, “Analyzing generalizations through discourse,” presented at the 38th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (3 - 6 Kasım 2016), Tucson, Arizona, USA, 2016, Accessed: 00, 2021. [Online]. Available: http://www.pmena.org/pmenaproceedings/PMENA%2038%202016%20Proceedings.pdf.