Mediating artifacts and interaction in a computer environment – An exploratory study of the acquisition of geometry concepts

Nine dyads of twelve-year old students were engaged in collaborative small-group activity in order to find a way to determine the area of a parallelogram via a computer program. The program introduced two models or metaphors of a parallelogram, one changing the perimeter with a constant area ("the deck-of-cards model"), the other changing the area with a constant perimeter ("the frame model"). By changing the form and size of a displayed parallelogram the students had the opportunity to explore and obtain the characteristics of the parallelogram. The interaction between the students and their interaction with the computer were registered for analysis. After twenty minutes work with the computer, only one dyad failed to obtain the idea of the area determinants. The students' discussion, characterized by active inter- pretation and mutual adoption in combination with the deck-of-cards model as medi- ating artifact, established a situation in which the students acquired the conception that the area remained invariant through a specific kind of transformation. This know- ledge was then used to draw a rectangle with the same area as a given parallelogram.