수학화 교수․학습을 위한 소재 개발 연구

• 영문명: A study on developing material for teaching and learning mathematising: the number of unit squares a diagonal passes through for an m by n lattice rectangle and its generalization
• 발행기관: 대한수학교육학회
• 저자명: 박교식
• 간행물 정보: 『수학교육학연구』제13권 1호, 57~75쪽, 전체 19쪽
• 주제분류: 사회과학 > 교육학
• 파일형태: PDF
• 발행일자: 2003.02.28

영문 초록

The goal of this paper is to offer material which make mathematising Fruedenthal(1991) proposed be experienced through the process of teaching and learning mathematics. In this paper, the number of unit squares a diagonal passes through for an m×n lattice rectangle is studied and its generalization is discussed. Through this discussion, the adaptability of this material is analysed. Especially, beyond inductional conjecture, the number of unit squares is studied by more complete way, and generalization in 3-dimension and 4-dimension are tried. In school mathematics, it is enough to generalize in 3-dimension. This material is basically appropriate for teaching and learning mathematising in math classroom. In studying the number of unit squares and unit cubes, some kinds of mathematising are accompanied. Enough time are allowed for students to study unit squares and unit cubes to make them experience mathematising really. To do so, it is desirable to give students that problem as a task, and make them challenge that problem for enough long time by their own ways. This material can be connected to advanced mathematics naturally in that it is possible to generalize this problem in n-dimension. So, it is appropriate for making in-service mathematics teachers realize them as a real material connecting school mathematics and advanced mathematics.

목차

Ⅰ. 서론

Ⅱ. 격자 직사각형의 한 대각선이 지나는 단위 정사각형의 수

Ⅲ. 격자 직육면체의 한 대각선이 지나는 단위 정육면체의 수

Ⅳ. 4차원 직육면체로의 일반화

Ⅴ. n차원으로의 일반화

Ⅵ. 결론

참고문헌

키워드

수학화 일반화 격자 직사각형 격자 직육면체 mathematising generalization lattice rectangle lattice rectangular parallelepiped