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

[ Article ] | |

Journal of Educational Research in Mathematics - Vol. 29, No. 2, pp.227-250 | |

Abbreviation: JERM | |

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

Print publication date 31 May 2019 | |

Received 05 Apr 2019 Reviewed 11 May 2019 Accepted 15 May 2019 | |

DOI: https://doi.org/10.29275/jerm.2019.5.29.2.227 | |

Conceptual Analysis for Solving a Missing Value Problem Using a Proportional Relationship | |

Shin, Jaehong ^{*} ; Lee, Soo Jin^{**}^{, †}
| |

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

**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

The aim of this scheme-theoretic study is to present a conceptual analysis on how arithmetic knowledge of whole number and fraction can be used in various solutions to a missing value problem involving a proportional relationship. The missing value problem analyzed in this study is the type of problem in which literature reports that students have difficulties reasoning with quantitative structures embedded. Four schemes (splitting scheme for composite units, iterative fraction scheme, unit-segmenting scheme with a remainder, and general iterative fraction scheme for composite units) and four operations (splitting operation for composite units, splitting operation, unit-segmenting operation, and equipartitioning operation) emerged as essential constructs in solving of the missing value problem using different ways. Our conceptual analysis of the problem suggests that students’ proportional reasoning would be developed as their partitive and quotitive division knowledge is reorganized by embedding the concept of fractions as measurable extents.

Keywords: proportional reasoning, missing value problem, conceptual analysis, schemes and operations, splitting operation for composite units |

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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).