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

Research output: Contribution to journalArticle

17 Citations (Scopus)

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 - 2010

Fingerprint

Empirical Study
Strip
student
Essential Component
subject of study
Relationships
experience

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Social Sciences(all)

Cite this

@article{1c4b910c7fa0477ca2f3d6bd5cdde03b,
title = "An empirical study of students' understanding of a logical structure in the definition of limit via the ε-strip activity",
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.",
keywords = "ε-N definition, ε-strip activity, ε-strip definition, Error bound, Limit, Logical structure, Relationship between ε and N, Sequence",
author = "Kyeong Roh",
year = "2010",
doi = "10.1007/s10649-009-9210-4",
language = "English (US)",
volume = "73",
pages = "263--279",
journal = "Educational Studies in Mathematics",
issn = "0013-1954",
publisher = "Springer Netherlands",
number = "3",

}

TY - JOUR

T1 - An empirical study of students' understanding of a logical structure in the definition of limit via the ε-strip activity

AU - Roh, Kyeong

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - ε-N definition

KW - ε-strip activity

KW - ε-strip definition

KW - Error bound

KW - Limit

KW - Logical structure

KW - Relationship between ε and N

KW - Sequence

UR - http://www.scopus.com/inward/record.url?scp=77951877268&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951877268&partnerID=8YFLogxK

U2 - 10.1007/s10649-009-9210-4

DO - 10.1007/s10649-009-9210-4

M3 - Article

AN - SCOPUS:77951877268

VL - 73

SP - 263

EP - 279

JO - Educational Studies in Mathematics

JF - Educational Studies in Mathematics

SN - 0013-1954

IS - 3

ER -