RUME 14 (Volume 1)
2011
Portland, Oregon
USING CONCRETE METAPHOR TO ENCAPSULATE ASPECTS OF THE DEFINITION OF SEQUENCE CONVERGENCE
Page: 39
This study traces how one real analysis student was able to develop a property-based rather than exemplar-based notion of sequence convergence by first instantiating conditions on the parameters of sequence convergence in a metaphorical domain. The analysis uses the radical constructivism framework of cognitive development (von Glasersfeld, 1995). Once he had encapsulated the conditions that related the parameters within the formal definition, he was able to accommodate the conditions into a mathematical schema in which he could reason flexibly about convergent sequences in ways compatible with standard formal practice. I observe his language use and the various lines of reasoning that his concept of the sequence convergence definition did or did not support over the course of a month to identify changes in his convergence schema.