• 대한수학교육학회지:학교수학
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• 제9권4호
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• pp.487-506
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• 2007

본 연구는 14명의 중학교 2학년 수학영재들이 아르키메데스 다면체를 소재로 한 공간기하과제를 해결하면서 보여주는 정당화 유형과 수학적 표현에 대한 연구이다. 문헌 연구를 통해 정당화 유형과 수학적 표현 분석을 위한 분석틀을 마련하고 이들의 다양한 반응들을 분석하였다. 정당화 유형에서는 부분적인 분석을 통해 형식화를 추구하는 학생과 비형식적이며 경험적인 정당화이지만 모든 구성요소를 고려하여 전체적 정당화를 시도하는 두 반응간의 비교를 통해 비형식적 정당화의 유용성에 분명한 주의를 기울일 필요가 있었다. 수학적 표현에서 시각적 표현은 문제해결을 위한 아이디어를 찾고, 구조를 파악하는데 유용한 역할을 하고 있었으며, 기호적 표현을 점진적으로 발전시키는 과정에서 수학적 개념을 표현 속에 함축시키고 정제시켜 정교한 기호(Harel & Paput. 1994)를 창출하려는 욕구를 발견할 수 있었다.

• 한국수학교육학회지시리즈A:수학교육
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• 제45권2호
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• pp.191-204
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• 2006

Computer technology has a potential to change the contents of school mathematics and the way of teaching mathematics. But in our country, the problem whether computer technology should be introduced into mathematics classroom or not was not resolved yet. As a tool, computer technology can be used by teachers who are confident of the effectiveness and who can use it skillfully and can help students to understand mathematics. The purpose of this study was to investigate the effective way to introduce and utilize computer technology based on the status quo of mathematics classroom setting. One possible way to utilize computer technology in mathematics classroom in spite of the lack of computer and the inaccessibility of useful software is using domain specific simulation software like 'Polyhedron'. 'Polyhedron', as we can guess from the name, can be used to explore regular and semi regular polyhedra and the relationship between them. Its functions are limited but it can visualize regular polyhedra, transform regular polyhedra into other polyhedra. So it is easier to operate than other dynamic geometry software like GSP. To investigate the effect of using this software in mathematics class, three classes(one in 6th grade from science education institute for the gifted, two in 7th grade) were chosen. Activities focused on the relationship between regular and semi regular polyhedra. After the class, several conclusions were drawn from the observation. First, 'Polyhedron' can be used effectively to explore the relationship between regular and semi regular polyhedra. Second, 'Polyhedron' can motivate students. Third, Students can understand the duality of polyhedra. Fourth, Students can visualize various polyhedra by reasoning. To help teachers in using technology, web sites like NCTM's illuminations and NLVM of Utah university need to be developed.