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

[ Article ] | |

Journal of Educational Research in Mathematics - Vol. 30, No. 1, pp.89-110 | |

Abbreviation: JERM | |

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

Print publication date 28 Feb 2020 | |

Received 10 Jan 2020 Revised 10 Feb 2020 Accepted 16 Feb 2020 | |

DOI: https://doi.org/10.29275/jerm.2020.02.30.1.89 | |

Analysis of Abduction in Mathematics Problem Posing and Solving | |

Lee, Myoung Hwa ^{*} ; Kim, Sun Hee^{**}^{, †}
| |

*Graduate Student, Kangwon National University, South Korea (hahahoho98@nate.com) | |

**Professor, Kangwon National University, South Korea (mathsun@kangwon.ac.kr) | |

Correspondence to : ^{†}Professor, Kangwon National University, South Korea, mathsun@kangwon.ac.kr | |

Abstract

The purpose of this study was to analyze the abduction in mathematical problem-posing and problem-solving activities. Abduction is more concerned with creating new things than deduction and inductive reasoning. According to the student's rules, abduction are classified as selective and creative. Selective abduction is again classified into ‘manipulative selective abduction’ and ‘theoretical selective abduction’. Creative abduction is again classified into ‘little creative abduction’ at the level of mathematics in school and ‘big creative abduction’ at the level of academic mathematics. Four middle school sophomore students performed problem-posing activities on four tasks. As for the results of analysis on abduction types by problem-posing stages, all four abduction types were observed. But at the problem-solving stages, manipulative selective abduction and theoretical selective abduction were frequently used, while creative abduction was never used. Thus, for the education of mathematical creativity, deepening and expanding problem-posing is necessary that all the type of abduction has been expressed in the problem-posing activity.

Keywords: problem posing, problem solving, abduction, Toulmin model |

Acknowledgments

이 논문은 이명화의 박사학위논문의 내용 일부를 요약, 정리한 것임

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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).