Linear transformation scheme: construction of abstract objects from the internalisation of concrete actions

Abstract

This article show a cognitive model called by the APOS theory (acronym for Action, Process, Object, Scheme) genetic decomposition, which describes the mental structures and mechanisms that a person must develop to understand the concept of linear transformation. We discussed how the functional definition of linear transformation and its matrix and geometric representation are related through the ordered basis concept. Scheme described through the different relationships between mental structures and mechanisms show the importance of actions on concrete objects (graphic representations of plane functions in itself ) to achieve abstract objects. This model allows the construction of a scheme that can evolve thanks to the different experiences of an individual with more sophisticated mathematical situations.