Inventing Mapping: Creating Cultural Forms to Solve Collective Problems

Abstract

In this article I detail the conceptual trajectory of a classroom of 2nd-and 3rd-grade students as they reinvent topographical lines to represent height in a map within the constraints of an overhead perspective. In my analysis I pay special attention to the role of social interaction-and in particular the role of the teacher-in the process of knowledge production. First, I demonstrate how the invention of representational forms by individuals occur as part of a larger social process of creating cultural conventions and negotiating a taken-as-shared understanding of these new tools. Second, I show how gesture, as a part of the larger semiotic ecology for meaning making around representations, contributes to creation of understanding. Third, I make some preliminary proposals regarding the process of transforming personal inventions into cultural conventions. The analyses are intended to contribute to our field's growing understanding of young children's activity when inventing representations (i.e., metarepresentational competence), the mechanisms for learning within instructional activities based on the iterative refinement of these representations (i.e., progressive symbolization), and a rejection of the dichotomy between an individual's cognition and her participation within a cultural community.Representation-the act of highlighting aspects of our experience and communicating them to others and ourselves-is one of the fundamental and generative activities that is at the heart of the human experience. Sketches, diagrams, symbols, and so on, are a durable trace of our activity and thought that allow us to abstract, highlight, and coordinate salient aspects of the world around us. In doing so they shape what we and others see and remember about that experience. Though much is known about how students learn how to use various representational forms in

Drawing to Learn in Science

“…"), as well as how representations work more generally (e.g., "The representation was better in this case as it was coherent, compact and parsimonious") (3,14,15). Teachers can guide students to acquire the visual literacies of science at the point when they will see their relevance and appreciate their explanatory power (16).…”

A framework for conceptualizing, representing, and analyzing distributed interaction

“…Microanalysis is becoming increasingly important in computer-supported collaborative learning because a focus on accomplishment through mediated action is necessary to truly understand the role of technology affordances (Stahl, Koschmann, & Suthers, 2006). For examples applied to the analysis of learning, see Baker (2003), Enyedy (2005) Koschmann and LeBaron (2003), Koschmann et al (2005), Roschelle (1996), and Stahl (2006Stahl ( , 2009.…”

Negotiating the “Relevant” in Culturally Relevant Mathematics

“…As such, it might be characterized as using real world contexts that are related to issues that adversely affect the students or their community to promote motivation and engagement. However, current theories of learning suggest that studentsʼ understanding of a tool or concept is dependent upon their understanding of its utility (e.g., why was it developed in the first place and what problems does it help to solve) (diSessa, 2004;Enyedy, 2005). When students donʼt understand the purpose for such concepts, they are less likely to use them effectively.…”