Identifying the Co-Construction of Mathematical Practices in Secondary Mathematics Classroom Discourse

• In Event: 14.043 - Roundtable Session 1
  In Roundtable Session: 14.043-14 - Analyzing the Common Core Standards for Mathematical Practice

Abstract

Classroom discourse plays a central role in supporting opportunities for students to engage in mathematical practices (Ellis, 2011; Lampert, 1990; Staples, 2007), such as those set out in the Common Core Standards for Mathematical Practice (SMP). Mathematical practices are socially constructed ways of working (Moschkovich, 2013), intertwined with content (CCSS, 2010), and interconnected (Ellis, 2007). However, prior research has often focused on a single practice, such as justification (e.g., Bieda, 2010) or generalization (e.g., Ellis, 2011), which may hide connections between practices (RAND, 2003). Drawing on data from a project involving urban secondary classrooms, I explore what practices were co-constructed in discussions during the first month of school. This paper focuses on analytic strategies for identifying the co-construction of mathematical practices in discourse in ways that allow for connections among practices.

Data include 30 discussions from four classrooms purposefully sampled (Marshall, 1996) based on teachers’ commitments to cultivating mathematical practice engagement through discourse. Analysis involved segmenting discussions into mathematical practice episodes (Author, 2014). Each episode typically consisted of one or more talk-turns or non-verbal communication. Episodes could be constructed by individuals, but typically were co-constructed by multiple participants. The end of an episode was determined by: (1) teacher reflection on the interaction (e.g., “I like how you gave reasons”), (2) participation in a different practice, or (3) a shift in talk that does not return to that practice. Episodes were coded based on a framework developed from the SMPs. I then identified the moves that initiated, sustained, or reprised these episodes in order to analyze instruction that supported mathematical practice engagement.

Analyses revealed two potential relationships between mathematical practices in discourse: (1) co-occurrence, when the same set of talk turns represents engagement in multiple SMPs simultaneously, and (2) embedding, when one mathematical practice episode is embedded within another. To illustrate this, consider the following discourse focused on part (e) (Figure 1).

Figure 1. Task from a 6th-grade discussion.

Figure 2. Kat’s solution in green and Adrianna’s circled numbers in purple.

Table 1. Examples of co-occurring and embedded mathematical practices.

First Kat explained her strategy (green in Figure 2). Adrianna offered a shortcut, using the base ten structure. This prompted the episodes in Table 1. The blue bracketed text represents co-occurrence of multiple practices: SMP3 (Consider domain in which argument applies) and SMP7 (Make use of structure). In contrast, the discourse bracketed in red represents an embedded episode. This subset represents SMP6 (Communicate precisely to others). Engagement in SMP6 is not at the same level as the blue discourse. Therefore, this represents an embedded rather than a co-occurring relationship.

This study has implications for research that seeks to identify the SMPs in discourse data. First, it offers a unit of analysis that allows for the co-construction of mathematical practices. Second, given a conception of mathematical practices as tightly connected (RAND, 2003), these analyses suggest two possible ways in which mathematical practices might relate in discourse data. Further research can explore other potential analytic relationships between practices in discourse.

Author

• Sarah Kate Selling, University of Michigan - Ann Arbor