Geometric Modeling of Mesospace Objects: A Task, its Didactical Variables, and the Mathematics at Stake

Abstract

For decades, mathematics educators have been interested in engaging K-12 students in the practice of creating and using mathematical models. What might this look like in the context of geometry? Inspired by claims that students come to secondary school with knowledge of three-dimensional space that can be leveraged to engage them in modeling, we wondered what it would take to have them do so. We designed a communication task aimed at engaging teenagers in the geometric modeling of mesospace objects-three-dimensional objects of scale comparable to that of the human body. Specifically, we asked a group of teenagers to plan and enact the movement of furniture through a narrow staircase in a residential home. In this paper, we present our original design considerations, an analysis of the teens' work, and a set of didactical variables that this analysis led us to believe need to be considered to ensure that such an activity engage teenagers in the geometric modeling of mesospace objects. The paper concludes with a discussion of the implications for research on a modeling approach to the teaching and learning of geometry.