Search results for " semiotic mediation"

A geometrical constructive approach to infinitesimal analysis: epistemological potential and boundaries of tractional motion

2014

Recent foundational approaches to Infinitesimal Analysis are essentially algebraic or computational, whereas the first approaches to such problems were geometrical. From this perspective, we may recall the seventeenth-century investigations of the “inverse tangent problem.” Suggested solutions to this problem involved certain machines, intended as both theoretical and actual instruments, which could construct transcendental curves through so-called tractional motion. The main idea of this work is to further develop tractional motion to investigate if and how, at a very first analysis, these ideal machines (like the ancient straightedge and compass) can constitute the basis of a purely geome…

Geometrical-mechanical artefacts for managing tangent concept

2012

Geometrical-mechanical artefacts mediating tangent meaning: the Tangentograph

2012

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 f…