Inventing Mapping

This project was focused on designing and analyzing the conceptual trajectory of a classroom of second and third grade students as they invented ways to represent large scale spaces. The focus of the research is the role of social interaction—and in particular the role of the teacher—in the process of knowledge production.

1. 1.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.
   

2. 2.How personal inventions are transformed into cultural conventions.
   

3. 3.How gesture, as a part of the larger semiotic ecology for meaning making around representations, contributes to creation of understanding.
   

Here are three examples of student’s preliminary ideas on how to represent height:

A step pyramid represented with shadows and a map of Southern California generated by a commercial GIS package.

Here is a short analysis of the students Debate facilitated by the teacher:

There are now three proposals for representing height on the table, or in this case the whiteboard. However, the process of invention, at least in the context of a classroom oriented towards the production of knowledge, does not end with an act of creation. Debate contributes to the elaboration and clarification of an idea. Debate also can contribute to the stabilization and propagation of the ideas.

In Excerpt 4 the teacher begins the debate by a restating Matthew's idea and adding a visual and gestural elaboration that forges the connection between the concentric circles and several slices of the cone. However, Chris, who had invented the Cartwheel method, immediately challenges the representation. In this case, the debate is facilitated by the fact that both Chris and Matthew have chosen to represent the same object, the cone. Having the same physical referent allows the students to more easily compare different aspects of the representation and perhaps to better see the flaws of the alternative representations.

In this exchange we can see that one result of Chris's critique is actually a further elaboration of Matthew's idea. The teacher's gestures both in line 12 and 19 of excerpt 8 also help to clarify how the circles represent height by re-inserting into the interactional space exactly what is missing from the two-dimensional representation-the physical height of the cone. In line 12, Ms. Adis positions her body in the bird's-eye-perspective and uses her fingers to physically create circles that are fitted over different heights of the actual cone. Upon completion of the turn she points to the graphic display of concentric circles that Mathew had created. Gesture and body position are being used temporally juxtapose a set of resources, which may help the students create a web meaning that binds these resources together into a whole. The body position invokes the classes shared history of looking down and drawing maps (as was discussed previously). The teacher's gesture of fitting circles over the cone is timed with her statement, "it kind of looks like a lot of little circles," binding together an element of the picture with an element of the physical space. Finally, the point at the end connects the whole turn to Mathew's representation.

Enyedy, N. (in press). Inventing Mapping: Creating cultural forms to solve collective problems. Submitted to Cognition and Instruction.