Dynamic manipulation schemes of geometrical constructions: Instrumental genesis as an abstraction process

Abstract : Dynamic manipulation of geometrical constructions enabled by a specially designed computational tool, called variation tool, is studied during the implementation of proportional geometric tasks in the classroom. The analysis combined the use of two theoretical frameworks: instrumental genesis and situated abstraction. The Dynamic Manipulation Schemes (DMS) developed by 13-year-old students based on the use of the variation tool are reported in the paper. It is indicated that situated abstraction may complement instrumental genesis in analysing the links between student's behaviors and expressions of mathematical ideas within particular computational settings.