대수적 사고의 기원에 관한 고찰

  • 김성준 (서울대학교 대학원 수학교육과)
  • 발행 : 2002.09.01

초록

One of the characteristics of modem mathematics is to use algebra in every fields of mathematics. But we don't have the exact definition of algebra, and we can't clearly define algebraic thinking. In order to solve this problem, this paper investigate the history of algebra. First, we describe some of the features of proportional Babylonian thinking by analysing some problems. In chapter 4, we consider Greek's analytical method and proportional theory. And in chapter 5, we deal with Diophantus' algebraic method by giving an overview of Arithmetica. Finally we investigate Viete's thinking of algebra through his ‘the analytical art’. By investigating these history of algebra, we reach the following conclusions. 1. The origin of algebra comes from problem solving(various equations). 2. The origin of algebraic thinking is the proportional thinking and the analytical thinking. 3. The thing that plays an important role in transition from arithmetical thinking to algebraic thinking is Babylonian ‘the false value’ idea and Diophantus’ ‘arithmos’ concept.

키워드

참고문헌

  1. 대한수학교육학회 논문집 v.8 no.2 Piaget의 개념 발달의 매커니즘과 대수의 역사 민세영
  2. 학교수학의 교육적 기초 우정호
  3. 수학의 역사 Boyer, C;Merzbach, U.C;양영오;조윤동
  4. Approaches to Algebra Bednarz, N;Kieran, C;Lee, L
  5. Approaches to Algebra From Euclid to Descartes: Algebra and its Relation to Geometry Charbonneau, L;N. Bednarz, et al.(eds.)
  6. Approaches to Algebra Placement and Function of Problems in Algebraic Treatises from Diophantus to Viete Charbonneau, L;N. Bednarz, et al.(eds.)
  7. Greek Mathematical Thought and the Origin of Algebra Klein, J
  8. An Analysis of Students' Transition form Arithmetic to Algebraic Thinking Melillo, J.A
  9. Perspectives of School Algebra The Historical Origin of Algebraic Thinking Radford, L;R. Sutherland, et al.(ed.)
  10. Approaches to Algebra The Roles of Geometry and Arithmetic in the Development of Algebra: Historical Remarks from a Didactic Perspective Radford, L;N. Bednarz, et al.(ed.)
  11. Research Issues in the Learning and Teaching of Algebra Algebra: What Should We Teach and How Should We Teach It? Thorpe, J.A;S. Wagner(ed.);C. Kieran(ed.)
  12. Geometry and Algebra in Ancient Civilizations van der Waerden, B.L