The more it changes, the more it becomes the same: The development of the routine of shape identification in dynamic geometry environment

The overall aim of our research project is to explore the impact of dynamic geometry environments (DGEs) on children's geometrical thinking. The point of departure for the study presented in this paper is the analytically and empirically grounded assumption that as the geometric discourse develops, the direct visual identification of geometric shapes gives way to discursively mediated identification, that is to a process in which one needs to perform a discursive procedure, prescribed by a formal definition of the shape, in order to ascertain the name of the shape. Previous research, conducted in static geometry environments, has already shown that many children, even in the middle school grades, rely on static, visual prototypes when identifying geometric shapes and that formal definitions, even if known, play no role in this process. Our study aimed at testing the conjecture that DGEs, in which the shapes can be continuously transformed, may flex the routine of identification, allowing for greater diversity in the shapes recognized as deserving a given name (e.g. triangle). This, we believed, would be an important step toward the discursively mediated routine of identification. The study, conducted among 4–5 year-old children working with Sketchpad, furnished some supporting evidence. In this paper, the focus is on one 30-min lesson during which the children observed, described, created and transformed triangles of different sizes, proportions, and orientations. During this one meeting the children's thinking evolved, in that the diversity of three-sided polygons they were prepared to call ‘triangle’ grew substantially. Not surprisingly, however, this rapidly-induced change was local and object-level rather than meta-level: it changed the children's use of a specific word rather than causing a transition to a discourse-mediated routine of identification.

► Our study aimed at testing the conjecture that DGEs flex the routine of identification.
► We see thinking as a form of communication and levels of thinking as levels of discourse.
► We observed children's transition from purely visual to discourse-mediated identification.
► The teacher models the way in which mathematical narratives are being endorsed.
► The development of geometric thinking occurs in “patches”, varying across geometry.