Normalising geometrical figures: dynamic manipulation and construction of meanings for ratio and proportion

Abstract

Enlarging-shrinking geometrical figures by 13 year-olds is studied during the implementation of proportional geometric tasks in the classroom. Students worked in groups of two using ‘Turtleworlds’, a piece of geometrical construction software which combines symbolic notation, through a programming language, with dynamic manipulation of geometrical objects by dragging on sliders representing variable values. In this paper we study the students’ normalising activity, as they use this kind of dynamic manipulation to modify ‘buggy’ geometrical figures while developing meanings for ratio and proportion. We describe students’ normative actions in terms of four distinct Dynamic Manipulation Schemes (Reconnaissance, Correlation, Testing, Verification). We discuss the potential of dragging for mathematical insight in this particular computational environment, as well as the purposeful nature of the task which sets up possibilities for students to appreciate the utility of proportional relationships.

Keywords:

• enlarging-shrinking
• dynamic manipulation
• ratio and proportion
• Turtleworlds
• normalising

Notes

1. Turtleworlds is available at: http://etl.ppp.uoa.gr/_content/download/index_download_en.htm