Students' images and their understanding of definitions of the limit of a sequence

Research output: Contribution to journalArticle

32 Citations (Scopus)

Abstract

There are many studies on the role of images in understanding the concept of limit. However, relatively few studies have been conducted on how students' understanding of the rigorous definition of limit is influenced by the images of limit that the students have constructed through their previous learning. This study explored how calculus students' images of the limit of a sequence influence their understanding of definitions of the limit of a sequence. In a series of task-based interviews, students evaluated the propriety of statements describing the convergence of sequences through a specially designed hands-on activity, called the □-strip activity. This paper illustrates how these students' understanding of definitions of the limit of a sequence was influenced by their images of limits as asymptotes, cluster points, or true limit points. The implications of this study for teaching and learning the concept of limit, as well as on research in mathematics education, are also discussed.

Original languageEnglish (US)
Pages (from-to)217-233
Number of pages17
JournalEducational Studies in Mathematics
Volume69
Issue number3
DOIs
StatePublished - Nov 2008

Fingerprint

student
learning
Asymptote
mathematics
Limit Point
Mathematics Education
Strip
Teaching
interview
Calculus
education
Series
Concepts
Learning

Keywords

  • Asymptotes
  • Cluster points
  • Images
  • Limits
  • Rigorous definitions
  • Sequences

ASJC Scopus subject areas

  • Mathematics(all)
  • Social Sciences(all)

Cite this

Students' images and their understanding of definitions of the limit of a sequence. / Roh, Kyeong.

In: Educational Studies in Mathematics, Vol. 69, No. 3, 11.2008, p. 217-233.

Research output: Contribution to journalArticle

@article{a579968fb916412d8ca090022560d754,
title = "Students' images and their understanding of definitions of the limit of a sequence",
abstract = "There are many studies on the role of images in understanding the concept of limit. However, relatively few studies have been conducted on how students' understanding of the rigorous definition of limit is influenced by the images of limit that the students have constructed through their previous learning. This study explored how calculus students' images of the limit of a sequence influence their understanding of definitions of the limit of a sequence. In a series of task-based interviews, students evaluated the propriety of statements describing the convergence of sequences through a specially designed hands-on activity, called the □-strip activity. This paper illustrates how these students' understanding of definitions of the limit of a sequence was influenced by their images of limits as asymptotes, cluster points, or true limit points. The implications of this study for teaching and learning the concept of limit, as well as on research in mathematics education, are also discussed.",
keywords = "Asymptotes, Cluster points, Images, Limits, Rigorous definitions, Sequences",
author = "Kyeong Roh",
year = "2008",
month = "11",
doi = "10.1007/s10649-008-9128-2",
language = "English (US)",
volume = "69",
pages = "217--233",
journal = "Educational Studies in Mathematics",
issn = "0013-1954",
publisher = "Springer Netherlands",
number = "3",

}

TY - JOUR

T1 - Students' images and their understanding of definitions of the limit of a sequence

AU - Roh, Kyeong

PY - 2008/11

Y1 - 2008/11

N2 - There are many studies on the role of images in understanding the concept of limit. However, relatively few studies have been conducted on how students' understanding of the rigorous definition of limit is influenced by the images of limit that the students have constructed through their previous learning. This study explored how calculus students' images of the limit of a sequence influence their understanding of definitions of the limit of a sequence. In a series of task-based interviews, students evaluated the propriety of statements describing the convergence of sequences through a specially designed hands-on activity, called the □-strip activity. This paper illustrates how these students' understanding of definitions of the limit of a sequence was influenced by their images of limits as asymptotes, cluster points, or true limit points. The implications of this study for teaching and learning the concept of limit, as well as on research in mathematics education, are also discussed.

AB - There are many studies on the role of images in understanding the concept of limit. However, relatively few studies have been conducted on how students' understanding of the rigorous definition of limit is influenced by the images of limit that the students have constructed through their previous learning. This study explored how calculus students' images of the limit of a sequence influence their understanding of definitions of the limit of a sequence. In a series of task-based interviews, students evaluated the propriety of statements describing the convergence of sequences through a specially designed hands-on activity, called the □-strip activity. This paper illustrates how these students' understanding of definitions of the limit of a sequence was influenced by their images of limits as asymptotes, cluster points, or true limit points. The implications of this study for teaching and learning the concept of limit, as well as on research in mathematics education, are also discussed.

KW - Asymptotes

KW - Cluster points

KW - Images

KW - Limits

KW - Rigorous definitions

KW - Sequences

UR - http://www.scopus.com/inward/record.url?scp=53849115008&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=53849115008&partnerID=8YFLogxK

U2 - 10.1007/s10649-008-9128-2

DO - 10.1007/s10649-008-9128-2

M3 - Article

AN - SCOPUS:53849115008

VL - 69

SP - 217

EP - 233

JO - Educational Studies in Mathematics

JF - Educational Studies in Mathematics

SN - 0013-1954

IS - 3

ER -