이차곡선 학습에서 고등학생들의 오개념 분석

The Study on the Analysis of High School Students' Misconception in the Learning of the Conic Sections

이차곡선은 고등학교 기하 내용의 중요한 개념의 하나이다. 그러나 교수-학습 상황에서 학생들은 단순히 대수적인 접근과 해석기하적인 접근만 시도하므로 그 본질적인 기하학적 의미를 파악하지 못하며 단순한 기계적인 계산만을 수행하여 문제를 풀어나가려 하기 때문에 여러 가지 오개념(misconception)을 가지게 된다. 이 논문은 효과적인 이차곡선 교수학습 연구의 일부로, 학생들의 오개념을 인지적 관점, 심리학적 관점, 교수학적 관점에서 분석하고 그 원인을 분석하였다. 연구 결과, 학생들의 직접적이고 다양한 작도 경험의 부재가 오개념의 주된 원인이 되었다. 이차곡선에 대한 교수-학습은 기하적인 관점으로 접근 한 후 대수적인 관점으로 연결시켜야 할 필요성과 오개념에 대한 정확한 진단은 효과적인 교수-학습의 기초가 됨을 확인 하였다.

The purpose of this study is to analyze students' misconception in the teaming of the conic sections with the cognitive and pedagogical point of view. The conics sections is very important concept in the high school geometry. High school students approach the conic sections only with algebraic perspective or analytic geometry perspective. So they have various misconception in the conic sections. To achieve the purpose of this study, the research on the following questions is conducted: First, what types of misconceptions do the students have in the loaming of conic sections? Second, what types of errors appear in the problem-solving process related to the conic sections? With the preliminary research, the testing worksheet and the student interviews, the cause of error and the misconception of conic sections were analyzed: First, students lacked the experience in the constructing and manipulating of the conic sections. Second, students didn't link the process of constructing and the application of conic sections with the equation of tangent line of the conic sections. The conclusion of this study ls: First, students should have the experience to manipulate and construct the conic sections to understand mathematical formula instead of rote memorization. Second, as the process of mathematising about the conic sections, students should use the dynamic geometry and the process of constructing in learning conic sections. And the process of constructing should be linked with the equation of tangent line of the conic sections. Third, the mathematical misconception is not the conception to be corrected but the basic conception to be developed toward the precise one.