Two aspects of young children’s thinking about different types of dynamic triangles: prototypicality and inclusion

Abstract

This paper illustrates how young children (ages 7–8, grade 2/3) can use the potential of dynamic geometry environments to develop an understanding of, and reasoning about, the properties and behaviours of different triangles (scalene, isosceles, equilateral). It provides a detailed description of a geometry unit, during which children worked both in a whole classroom setting in which they could interact directly with Sketchpad (through an interactive whiteboard) and individually at tables with paper-and-pencil. Using Sfard’s communicational approach, an attempt is made to extend the work of Battista to show how children developed a reified discourse on triangles, which involves inclusive descriptions of classes of triangles (in other words, they thought about equilateral triangles as special types of isosceles triangles). This discourse focused on the behaviour of pre-constructed triangles as the children dragged their sides and vertices, thus generating many non-prototypical examples. During the teacher-led explorations and discussions, the children’s routines moved from informal dynamic descriptions to formal geometric properties as well as from particular to more general discourse about different types of triangles.