Building Mathematics Classroom Connectedness Through Dialogue

• In Event: New Frameworks, Methods, and Teaching Strategies for Understanding and Addressing Emotions in Mathematics Classrooms

Abstract

Objectives

In this paper, we explore an interpersonal aspect of mathematics classrooms—what we term classroom connectedness—using social network analysis. Classroom connectedness is the extent to which a classroom collectively values, encourages, and takes care of the individuals within the group (Goodenow, 1993; Strayhorn, 2019). In connected classrooms, members make important contributions to shared goals, purposes, and activities while also depending on one another to achieve those shared goals. To understand how classroom connectedness is built through dialogue, we map whole-class mathematics conversations using networks to visualize who contributes and in what ways.

Perspective

Psychologists argue that connection, or belonging, is a core human need (Maslow, 1943; Ryan & Deci, 2017), and sociolinguists like Halliday (1978) claim that personhood is predicated on membership in a social group, with language being the primary means through which this process occurs. Scholars across disciplines and using various methods of inquiry recognize the importance of forming strong connections to peers and social groups, both for its own sake and because of the relationships between connectedness and other factors like persistence, motivation, and achievement (Goodenow, 1993; Maloney & Matthews, 2020; Noddings, 1984; Strayhorn, 2019). Much of the extant literature conceptualizes belonging as a relatively stable, individual trait, but we conceptualize classroom connectedness differently—as a malleable, social, and discursive construct comprised of moment-by-moment interactions, aggregated over time and individuals, and operationalized using networks.

Methods & Data

We created a directed graph or network for two math lessons from different middle-grades classrooms to explore classroom connectedness (see Figure 1). To represent classroom discourse as a network, a vertex was assigned to every classroom member. For each whole-class turn of talk, an edge and its directionality were assigned on the basis of who (source vertex) addressed whom (target vertex). The size of the vertex was scaled to reflect its degree, or the total number of incoming and outgoing edges, which captured members’ involvement in the lesson. Additionally, we coded all edges for specific types of interaction that scholars have identified as important for creating connectedness (see Table 1 for coding categories).

Results

Visual features of the networks in Figure 1 suggest that Classroom K is more connected than Classroom H (fewer isolated vertices, more student-student edges, and larger student vertices). Network measures such as density—the proportion of edges out of the maximum number of edges—confirm this (.78 and .32). Figure 2 shows simplified networks created using only the subcategory of caring interactions/edges described in Table 1. (For simplicity, multiple edges are combined into one edge whose width reflects the number of caring edges between two vertices/people). Caring interactions simultaneously build mathematical ideas while also communicating to students that their ideas are valued and others are invested in their learning. Hence, they seem to be particularly important in creating connected classrooms.

Significance

This study contributes to the field by (a) providing a new methodological approach to investigate connectedness and (b) conceptualizing connectedness as a malleable, social construct emerging through moment-to-moment classroom discourse.

Author

• Jessica Pierson Bishop, Texas State University