中等教育を一貫する数学的活動に基づく論証指導の理論的基盤 ―カリキュラム開発に向けた枠組みの設定―  [in Japanese] Theoretical Foundations of Teaching Mathematical Proof: A Framework for Curriculum Development Based on Mathematical Activities throughout Secondary Schools  [in Japanese]

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Abstract

<p>   The aim of this paper is to find theoretical foundations of teaching mathematical proof for the sake of curriculum development based on the mathematical activities throughout six years of secondary schools in Japan.  To accomplish this aim, we first search for, through the review of related literatures, the principal aspects of proof and proving that should be taken into consideration for the curriculum development.  In particular, we examine the distinction often made in Japan between "proof" (<i>shoumei</i>) and "demonstration" (<i>ronshou</i>), the idea of "local organization" introduced by Freudenthal (1971, 1973), and the idea of "mathematical theorem" proposed by Italian research group (Mariotti et al., 1997).  This literature review shows that proof and proving are often discussed in relation to the propositions to be proven and the system of mathematics within which proof is carried out.  And we consider that three elements―statement, proof, and theorem―that characterize a "mathematical theorem" are principal aspects that evolve throughout the learning in secondary schools.  We then develop and propose a framework that allows us to design a curriculum by studying two questions: what kinds of teaching contents should be included in each aspect?; what kinds of evolution should be envisioned on the nature of each aspect? In this development, we lean on different perspectives such as the viewpoint of mathematical logic to identify different kinds of "statement", Freudenthal's idea of "local organization" and "global organization" to characterize different levels or natures of "theory", etc.  In this paper, we also discuss the relationship between the developed framework and the mathematical activities which is another crucial point to be considered in our curriculum development around mathematical proof. </p>

Journal

  • Journal of JASME : research in mathematics education

    Journal of JASME : research in mathematics education 21(1), 63-73, 2015

    Japan Academic Society of Mathematics Education

Codes

  • NII Article ID (NAID)
    130007580562
  • NII NACSIS-CAT ID (NCID)
    AA11141495
  • Text Lang
    JPN
  • ISSN
    1341-2620
  • NDL Article ID
    026186559
  • NDL Call No.
    Z71-Y908
  • Data Source
    NDL  J-STAGE 
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