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

Pages (from-to) | 263-279 |

Number of pages | 17 |

Journal | Educational Studies in Mathematics |

Volume | 73 |

Issue number | 3 |

DOIs | |

State | Published - 2010 |

### Fingerprint

### 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

**An empirical study of students' understanding of a logical structure in the definition of limit via the ε-strip activity.** / Roh, Kyeong.

Research output: Contribution to journal › Article

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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 -