Technological Support for Reflection and Discussion of What Counts as Math

• In Event: A Framework to Understand the Impact of Technology on Collaborative Learning

Abstract

Students’ beliefs about the nature of mathematics can have a notable effect on their motivation, learning, and trajectories within school math (Boaler, 2008; Schoenfeld, 1991). Students’ lives outside of school comprise rich funds of knowledge for mathematical thinking and problem solving (Esmonde et al., in press; González et al., 2005), yet these experiences are often not recognized as mathematical (Goldman, 2006).
In this paper, we describe a study which explored the potential of web-based collaboration technologies to create opportunities for middle-school students to reflect upon and develop their sense of “what counts as mathematics” in and out of school. Thirty-five sixth-grade students participated as part of their regular math class. The procedure was as follows: Each student rated a set of experimenter-provided photos on whether the activities depicted involved math. Next, students took photographs of objects and activities they thought involved math. They then wrote captions for their photos and viewed and commented on classmates’ photos within a web-based photo-sharing platform. Finally, they discussed the photos in small groups.
A previous analysis of these data showed that when students had more personal experience with an activity, they were more likely to say it involved mathematics. This finding highlights a tension between the personal nature of individual beliefs about mathematics, and the interpersonal nature of discourse about beliefs. Our analysis here considers how the technology helped and hindered students’ efforts to share and discuss their beliefs about mathematics, with a particular focus on efforts to establish shared common ground in support of conversation and argumentation (Clark, 1996).
We focus our presentation on activity categories which saw change in students’ willingness to classify photos as mathematical following the intervention. We examined how students made use of resources for sharing and collaborations (e.g., typed captions and responses) to support their interactions. An initial analysis of students’ use of the web-based photo-sharing platform suggested that it successfully engaged students in interactions around photographs, but encouraged only surface-level discussions of the mathematical nature of activities. A subsequent analysis of the small-group discussion showed that students made use of points of shared reference established during the web-based photo sharing to support more sophisticated argumentation during group discussions. For example, students referred to others’ photos and captions to justify their own arguments. As such, the technology helped students build a bridge between personal experience and the common ground needed in group discourse.
These results show how alternate forms of communication can provide complementary resources for student discussion of and reflection on the nature of mathematics. In particular, they suggest that technology-mediated and “regular” group discussions can provide distinct, yet complementary forms of interaction.
Results also suggest a limitation of the design as implemented, as the web-platform did not encourage rich discourse on its own. We see this study as a small step in considering the ways that technology can support students sharing and reflecting on their epistemological beliefs.

Authors

• Lee Michael Martin, University of California - Davis

• Pamela R. Gourley-Delaney, University of California - Davis