The Emergence of 3D Geometry From Children's (Teacher-Guided) Classification Tasks

Abstract

Journal of the Learning SciencesPublication details, including instructions for authors and subscription information:Geometry, classification, and the classification of geometrical objects are integral aspects of recent curriculum documents in mathematics education. Such curriculum documents, however, leave open how the work of classifying objects according to geometrical properties can be accomplished given that the knowledge of these properties is the planned outcome of the curriculum or lesson. The fundamental question of the present study therefore is this: How can a lesson in which children are asked to participate in a task of classifying regular 3-dimensional objects be a geometry lesson, given that the participating 2nd-grade children do not yet classify according to geometrical properties (predicates)? In our analyses, which are inspired by ethnomethodological studies of work, we focus on the embodied and collective work that leads to the emergence of the geometrical nature of this lesson. Thus, we report both the collective and the individual work by means of which the lesson outcomes-the complete classification of a set of "mystery" objects according to geometrical (shape) rather than other (color, size, "pointy-ness") properties-are achieved. In the process, our study shows how geometrical work is reproduced by 2nd-grade children who, in a division of labor with their teachers, produce a particular set of geometrical practices (sorting three-dimensional objects according to their geometrical properties) for the 1st time.

Children’s Gestures and the Embodied Knowledge of Geometry

“…We surmise that it is these gesticulations serve as another possible site where the emergence of the children's geometrical knowing can be observed ( Table 1). As a means for expressing understanding not only to/for oneself but also making available to/for others, gestures are constitutive parts of conceptual understanding (Roth & Thom, 2009b). Accepting this view of gestures as personally and collectively accessible forms of conceptual understanding (Roth & Thom, 2009a) then suggests there might very well be vast areas of thought that are not directly related to speech.…”

Multimodal Revoicing as an Interactional Mechanism for Connecting Scientific and Everyday Concepts

“…However, they argue that there is much left to uncover about how social interactions between adults and children can create ecologies for scientific and spontaneous concepts to shape one another. Saxe et al [2015] join a growing group of scholars who argue that more microanalytic investigations of the fine details of social interactions are necessary to understand this process [e.g., Macbeth, 2011;Roth & Thom, 2009]. Wertsch [1980Wertsch [ , 1985 long ago argued for the importance of microanalytic investigations of the interactions between adults and children.…”

The Primacy of the Social and Sociogenesis

“…Then, following a pause, Mrs. Winter requests a reason (turn 04). In the very fact that she requests a reason, she also marks the preceding action as insufficient: the "and" (turn 04) followed by a pause, a designedly open statement typical of teacher-student relations (Koshik 2002;Roth and Thom 2009), both accepts what has been done and marks something else that has to be added, which is specified by the remainder of the phrase. It is not that Mrs. Winter has some private wish for the child to add but instead, the invitation to add exists as social fact (in the sense of Durkheim 1919).…”