Academic journal article The Qualitative Report

Using "Tapestries" to Document the Collective Mathematical Thinking of Small Groups

Academic journal article The Qualitative Report

Using "Tapestries" to Document the Collective Mathematical Thinking of Small Groups

Article excerpt

A challenge in mathematics education research has been to document the complex nature of collective mathematical learning. This paper describes a method of data analysis that offers a visual representation of collective discourse during mathematical tasks. Using data extracts from a study of small groups in a middle years classroom, I color code collective utterances to create a "tapestry," a type of transcript that offers researchers the ability to move between individual and collective planes of focus during analysis. The nature of collective thinking is revealed by tapestries, including how utterances bump against each other, the role of utterances evolves as the context of discussion changes, and the potential for self-structuring within collective discourse. Keywords: Collective Discourse, Mathematics Education, Small Groups, Middle Years Students, Collective Understanding

While there have been a growing number of studies exploring the collective nature of mathematical learning (e.g. Bowers & Nickerson, 2001; Clark, James, & Montelle, 2014; Cobb 1999; Davis & Simmt, 2003; Francisco, 2013; Martin, Towers, & Pirie, 2006; Rasmussen & Stephan, 2008; Rasmussen, Wawro, & Zandieh, 2015; Yackel & Cobb, 1996) there is still a need for new analytical models to document the emergent nature of collective understanding (Davis & Simmt, 2008; Francisco, 2013; Towers & Martin, 2015). In this paper, I propose a method of data analysis that offers a visual representation of collaborative discourse through the creation of a "tapestry" style transcript. Using a dialogistic framework, I will discuss how tapestry transcripts developed from data from a study of small groups in middle years classrooms engaged in mathematical tasks (Armstrong, 2013) offer researchers a new way of seeing collective discourse by providing the ability to move between two planes of focus during analysis. I also discuss the nature of collective thinking revealed by tapestries, including how utterances "bump" against each other, how the role of utterances evolves as the context of discussion changes, and the potential for self-structuring within collective discourse.

Studying Collective Thinking

Many researchers (1) have studied group learning over the years (e.g. Cohen, 1994; Webb et al., 2009) in the interest of increasing the effectiveness of small groups in mathematics classroom settings (e.g. Mercer & Littleton, 2007; Rezitskaya et al., 2009). Although in casual conversation one might describe what a certain classroom group thinks, it has been challenging for researchers to conceptualize the group as a unit of analysis, even when the group is small. For instance, if one follows an acquisitionist view (Sfard, 1991) where the mind is seen to function as a container and learning is a matter of pieces of knowledge being transmitted from the teacher's mind, acquired by the student, and then stored in his or her mind, then the idea of group learning makes no sense. Once the group breaks up, as it inevitably must, and the members go their different ways, where does the group's learning go? There is no permanent structure--for instance, a group brain--to contain it. Even when considering learning as adapting to new circumstances, rather than storing chunks of knowledge, the concept of group learning is still "a difficult, counter-intuitive way of thinking for many people" (Stahl, 2006, p. 16) due to the strong association of cognition with an individual psychological process.

Some researchers have tackled this challenge of studying collective learning by considering the development of classroom socio-mathematical norms (Yackel & Cobb, 1996). Bridging the apparent gap between individual and group, the concept of taken-as-shared involves the meaning that develops between individuals through their social interactions, and evolves as students make adaptations "which [eliminate] perceived discrepancies between their own and others' mathematical activity while pursuing their goals" (Cobb, Yackel, & Wood, 1992, p. …

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