13 year-olds’ meanings around intrinsic curves with a medium for symbolic expression and dynamic manipulation

We explore how 13 year-olds construct meanings around the notion of curvature in their classroom while working with software that combines symbolic notation to construct geometrical figures with dynamic manipulation of variable. The ideas of curve as intrinsic dynamic construction, and curve as object with properties related to its positioning on the plane were some of those developed. The use of symbolic and graphical notation in conjunction with the dynamic manipulation played an important part in the generation of these ideas, which was interwoven with the activity and the use of the tools. THEORETICAL FRAMEWORK In this paper we report research aiming to explore how 13 year-olds construct meanings around the concept of curvature with ‘Turtleworlds’, a piece of geometrical construction software which combines symbolic notation through a programming language with dynamic manipulation of variable procedure values (Kynigos et al., 1997). The students worked in small collaborative groups in their classroom during a weekly computer-based project-work session established in their school. They were engaged in a project to buil