Die problematiek van die begrip oneindigheid in wiskundeonderrig en die manifestasie daarvan in irrasionale getalle, fraktale en die werk van Escher
Loading...
Authors
Mathlener, Rinette
Issue Date
2008-02-28
Type
Dissertation
Language
en
Keywords
Limit , Irrational numbers , Fractals , Perspective drawing , Cardinality of sets , Embodied cognition , Conceptual metaphor , The actual infinite (the at once infinite) , The potential infinite (the successive infinite) , Infinity
Alternative Title
Abstract
A study of the philosophical and historical foundations of infinity highlights the
problematic development of infinity. Aristotle distinguished between potential
and actual infinity, but rejected the latter. Indeed, the interpretation of actual
infinity leads to contradictions as seen in the paradoxes of Zeno. It is difficult for a
human being to understand actual infinity. Our logical schemes are adapted to
finite objects and events. Research shows that students focus primarily on infinity
as a dynamic or neverending process. Individuals may have contradictory
intuitive thoughts at different times without being aware of cognitive conflict. The
intuitive thoughts of students about both the actual (at once) infinite and potential
(successive) infinity are very complex. The problematic nature of actual infinity
and the contradictory intuitive cognition should be the starting point in the
teaching of the concept infinity.
Description
Text in Afrikaans
Citation
Mathlener, Rinette (2008) Die problematiek van die begrip oneindigheid in wiskundeonderrig en die manifestasie daarvan in irrasionale getalle, fraktale en die werk van Escher, University of South Africa, Pretoria, <http://hdl.handle.net/10500/1927>