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Journal of Educational Research in Mathematics -
Vol. 29 ,
No. 3

[ Article ] | |

Journal of Educational Research in Mathematics - Vol. 29, No. 2, pp.283-299 | |

Abbreviation: JERM | |

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

Print publication date 31 May 2019 | |

Received 10 Apr 2019 Reviewed 04 May 2019 Accepted 10 May 2019 | |

DOI: https://doi.org/10.29275/jerm.2019.5.29.2.283 | |

A Study on the Meaning of Similarity in School Mathematics | |

Yoo, Jae-Geun ^{*} ; Park, Moon Hwan^{**}^{, †}
| |

*Teacher, Hongcheon Middle School, South Korea (kuki122@chol.com) | |

**Professor, Chuncheon National University of Education, South Korea (pmhwan@cnue.ac.kr) | |

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

Abstract

The 2015 textbooks on school mathematics explain ‘the meaning of similarity’ as ‘figures that are stretching or shrinking at a constant rate’. The method of ‘stretching or shrinking at a constant rate’ can be interpreted in various ways. When interpreting the meaning as ‘the ratio of the length of the corresponding side and size of the corresponding angle are invariant’, the ‘meaning of similarity’ and ‘property of similar figure’ falls into the recursive argument. In order to find an alternative, the Euclid’s ‘Elements’ and Clairaut’s ‘Elements of geometry’ were compared with contents that are related to the similarities. Based on this, the 2015 textbooks were analyzed. Since the method of ‘stretching or shrinking at a constant rate’ was not clarified, the possibility of the recursive argument was confirmed. In order to avoid the recursive argument, a search for a manner to specify the ‘the meaning of similarity’ based on Clairaut's approach is necessary. ‘The meaning of similarity’ can be avoided in the recursive argument by interpreting the meaning of ‘stretching or shrinking at a constant rate in the horizontal and vertical directions’. In particular, it was confirmed that it is possible to intuitively develop similarity in school mathematics.

Keywords: Euclid, Clairaut, Meaning of similarity, Property of similarity, Recursive argument |

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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).

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).