• Title/Summary/Keyword: Steps of Mathematical justification

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Awareness and Steps of the Mathematical Justification of Elementary and Middle School Students (초등학생과 중학생들의 수학적 정당화에 대한 인식과 단계에 관한 실태 연구)

  • Kim, Jeong-Ha
    • Journal of Elementary Mathematics Education in Korea
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    • v.15 no.2
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    • pp.417-435
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    • 2011
  • Mathematical justification is essential to assert with reason and to communicate. Students learn mathematical justification in 8th grade in Korea. Recently, However, many researchers point out that justification be taught from young age. Lots of studies say that students can deduct and justify mathematically from in the lower grades in elementary school. I conduct questionnaire to know awareness and steps of elementary school students and middle school students. In the case of 9th grades, the rate of students to deduct is highest compared with the other grades. The rease is why 9th grades are taught how to deductive justification. In spite of, however, the other grades are also high of rate to do simple deductive justification. I want to focus on the 6th and 5th grades. They are also high of rate to deduct. It means we don't need to just focus on inducing in elementary school. Most of student needs lots of various experience to mathematical justification.

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A Questioning Role of Teachers to Formal Justification Process in Generalization of a Pattern Task for the Elementary Gifted Class (초등학교 영재학급 학생들의 형식적 정당화를 돕기 위한 교사 발문의 역할)

  • Oh, Se-Youn;Song, Sang Hun
    • Journal of Elementary Mathematics Education in Korea
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    • v.20 no.1
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    • pp.131-148
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    • 2016
  • Mathematical formal justification may be seen as a bridge towards the proof. By requiring the mathematically gifted students to prove the generalized patterned task rather than the implementation of deductive justification, may present challenges for the students. So the research questions are as follow: (1) What are the difficulties the mathematically gifted elementary students may encounter when formal justification were to be shifted into a generalized form from the given patterned challenges? (2) How should the teacher guide the mathematically gifted elementary students' process of transition to formal justification? The conclusions are as follow: (1) In order to implement a formal justification, the recognition of and attitude to justifying took an imperative role. (2) The students will be able to recall previously learned deductive experiment and the procedural steps of that experiment, if the mathematically gifted students possess adequate amount of attitude previously mentioned as the 'mathematical attitude to justify'. In addition, we developed the process of questioning to guide the elementary gifted students to formal justification.

Beyond the Union of Rational and Irrational Numbers: How Pre-Service Teachers Can Break the Illusion of Transparency about Real Numbers? (유리수와 무리수의 합집합을 넘어서: 실수가 자명하다는 착각으로부터 어떻게 벗어날 수 있는가?)

  • Lee, Jihyun
    • Journal of Educational Research in Mathematics
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    • v.25 no.3
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    • pp.263-279
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    • 2015
  • The introduction of real numbers is one of the most difficult steps in the teaching of school mathematics since the mathematical justification of the extension from rational to real numbers requires the completeness property. The author elucidated what questions about real numbers can be unanswered as the "institutional didactic void" in school mathematics defining real numbers as the union of the rational and irrational numbers. The pre-service teachers' explanations on the extension from rational to real numbers and the raison d'$\hat{e}$tre of arbitrary non-recurring decimals showed the superficial and fragmentary understanding of real numbers. Connecting school mathematics to university mathematics via the didactic void, the author discussed how pre-service teachers could break the illusion of transparency about the real number.