### 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 language | English (US) |
---|---|

Pages (from-to) | 217-233 |

Number of pages | 17 |

Journal | Educational Studies in Mathematics |

Volume | 69 |

Issue number | 3 |

DOIs | |

State | Published - Nov 2008 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Educational Studies in Mathematics*, vol. 69, no. 3, pp. 217-233. https://doi.org/10.1007/s10649-008-9128-2

}

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

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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 -