算数から数学への移行について(1) : 代数和の位置づけとその指導

DOI

書誌事項

タイトル別名
  • The Transition from Arithmetic to Mathematics (1) : Focusing on Algebraic Sum and its Teaching

抄録

Most of studies on algebraic area in school mathematics are focused on the understanding of meaning or operation of algebraic symbols, notations or equation. They hardly pay attention to the subtraction of a negative number and algebraic sum. In this study our interest is mainly devoted into two sorts of understanding about positive and negative numbers in order to clarify the transition from arithmetic to mathematics. Arithmetic has no necessity to regard subtraction as addition anywhere. Even if mathematics has necessity to develop it, mathematics teaching could not apply the idea of opposite number and inverse operation to understand the subtraction of a negative number as the addition of a positive number before going to algebra. And there is little room to explain it in arithmetic either. Therefore we use a metaphor to understand the change of subtraction to addition under the virtual reality and the language game. Moreover this idea must be formalized clearly and systematically in the algebraic sum. In this article we showed that the metaphorical understanding of the subtraction of a negative number and the systematic formalization of calculation in algebraic sum were a bridge to introduce mathematics teaching from arithmetic teaching.

収録刊行物

キーワード

詳細情報 詳細情報について

  • CRID
    1390282763087536896
  • NII論文ID
    110009498418
  • DOI
    10.24529/jasme.5.0_85
  • ISSN
    24333034
    13412620
  • 本文言語コード
    ja
  • データソース種別
    • JaLC
    • CiNii Articles
  • 抄録ライセンスフラグ
    使用不可

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