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Journal of Educational Research in Mathematics -
Vol. 30 ,
No. 2

[ Article ] | |

Journal of Educational Research in Mathematics - Vol. 30, No. 2, pp.281-305 | |

Abbreviation: JERM | |

ISSN: 2288-7733 (Print) 2288-8357 (Online) | |

Print publication date 31 May 2020 | |

Received 06 Apr 2020 Revised 13 May 2020 Accepted 14 May 2020 | |

DOI: https://doi.org/10.29275/jerm.2020.05.30.2.281 | |

Relationship Between Proportional Reasoning and Covariational Reasoning of 7^{th} Grade Students | |

Park, JongHee ^{*} ; Lee, Soo Jin^{**}^{, †}
| |

*Teacher, Cheonan Yonggok Middle School, South Korea (cyber-iris@hanmail.net) | |

**Professor, Korea National University of Education, South Korea (sjlee@knue.ac.kr) | |

Correspondence to : ^{†}Professor, Korea National University of Education, South Korea, sjlee@knue.ac.kr | |

Abstract

To understand the relationship between students’ proportional reasoning and covariational reasoning, clinical interview was conducted with four 7^{th} grade students. Students participated in four interviews each of which took about three-four hours. The analysis of the data suggests the following results: First, all four students conceived ratio as ‘internalized ratio’ but how they reasoned with the ratio concept were somewhat different, which were categorized into three different types of proportional reasoning. Secondly, there were differences in how the four students conceived two quantities in graph construction and interpretation tasks. Specifically, two of the four students showed ‘coordination of values’ level, one showed ‘chunky continuous covariational reasoning’, and the other showed ‘smooth continuous covariational reasoning’. Thirdly, there was little relationship as to how students conceived ratio and how they reasoned with quantities in function task. All four students perceived the continuity of function in various ways. We have finalized our study by suggesting students' ways of partitioning and iterating of two quantities in proportion and function tasks as potential theoretical constructs to distinguish how students reason.

Keywords: proportional reasoning, covariational reasoning, proportion, function, constant comparative method |

Acknowledgments

본 연구는 제1저자의 2019년 박사학위 논문의 내용을 토대로 재구성, 수정 및 보완하여 작성하였음.

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Submitting manuscripts for peer review as well as other correspondences can either be made via online by an email (ksesm@daum.net) or sending a mail at Secretariat of

Journal of Educational Research in Mathematics, #1305 Daewoo The'O Ville, 115 Hangang-daero, Yongsan-gu, Seoul, 04376, Republic of Korea (Tel: +82‐2‐797‐7780, Fax: +82‐2‐797‐7750).