Constructing Different Concept Images of Sequences & Limits by Programming

(formerly from) Mathematics Education Research Centre Chengdu University University of Warwick Chengdu Coventry, CV4 7AL P. R. China United Kingdom As a transition between an informal paradigm in which a limit is seen as a never-ending process and the formal ε–N paradigm we introduce a programming environment in which a sequence can be defined as a function. The computer paradigm allows the symbol for the term of a sequence to behave either as a process or a mental object (with the computer invisibly carrying out the internal process) allowing it to be viewed as a flexible procept (in the sense of Gray & Tall, 1991). The limit concept may be investigated by computing s(n) for large n to see if it stabilises to a fixed object. Experimental evidence shows that a sequence is conceived as a certain kind of procept, but the notion of limit remains more at the process level. Deep epistemological obstacles persist, but a platform is laid for a better discussion of formal topics such as cauchy limits and completeness.