Geometrical-mechanical artefacts mediating tangent meaning: the Tangentograph

Abstract

This work deals with the didactical use of geometrical-mechanical artefacts to acquire tangent concept in vygotskian perspective. We adopt Rabardel’s theory on instru-mental approach to distinguish artefacts and instruments specially to evince the history-to-education ontogenesis-phylogenesis process. From this point of view we trace a historical-epistemological pathway for the tangent up to set an ad hoc didactical counterpart. Specifically in this paper we deepen the kinematical properties of the tangent (introducing the XVII century so called tractional motion) designing a laboratorial didactic pathway for 12th grade students with the use of a particular geometrical-mechanical artefact for mediating tangent meaning: the Tangentograph. The paper could be an interesting contribution on the study of the problems related to the tangent meaning and its properties. It can be a first step to the definition of an educational pathway related to the same mathematical content by the use of the tractional instruments that concretely manage it and thus could help the student to explore the tangent meaning.