An empirical study of students' understanding of a logical structure in the definition of limit via the ε-strip activity

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18 Scopus citations

Abstract

This study explored students' understanding of a logical structure in defining the limit of a sequence, focusing on the relationship between ε and N. The subjects of this study were college students who had already encountered the concept of limit but did not have any experience with rigorous proofs using the ε-N definition. This study suggested two statements, each of which is written by using a relationship between ε and N, similar to the ε-N definition. By analyzing the students' responses to the validity of the statements as definitions of the limit of a sequence, students' understanding of such a relationship was classified into five major categories. This paper discusses some essential components that students must conceptualize in order properly to understand the relationship between ε and N in defining the limit of a sequence.

Original languageEnglish (US)
Pages (from-to)263-279
Number of pages17
JournalEducational Studies in Mathematics
Volume73
Issue number3
DOIs
StatePublished - Jan 1 2010

Keywords

  • Error bound
  • Limit
  • Logical structure
  • Relationship between ε and N
  • Sequence
  • ε-N definition
  • ε-strip activity
  • ε-strip definition

ASJC Scopus subject areas

  • Mathematics(all)
  • Education

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