공과대학 신입생들의 함수개념 연구와 함수 영역의 교육과정에 대한 제안
The Function Concept in Korean Engineering Freshmen and Some Suggestions on the Curriculum in the Function Area
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초록
본 논문에서는 세 가지 관련된 분야의 연구를 통하여 우리나라 대학 신입생들의 함수 개념을 조사하였다: 대학 신입생들은 함수를 어떻게 이해하고 있는가?; 인식론적 장애를 포함한 오 개념에는 어떤 것들이 있는가?; 함수 개념은 어떤 경로를 거쳐서 획득 되는가? 등이다. 이와 함께 대학의 여러 분야에서 함수가 어떻게 정의되고 쓰이는 지를 살펴보고, 미국의 교과서들에 나타난 함수 정의와 도입을 살펴보았다. 설문조사와 이들을 토대로 함수를 대응의 관점에서 도입하는 새로운 교육과정에 대하여 수직선 테스트의 도입을 포함한 몇 가지 제언을 하였다.
Abstract
Many research papers on the college students' functional concept show they have poor understanding on this topic. To compare the results with that of Korean students, four interrelated topics are chosen: How do they understand the concept of function?; what are their misconceptions including epistemological obstacles?; How do the function concepts develop and are acquired? For this a survey has been conducted to 95 engineering students just before they start Calculus course. We have done research on other major areas including psychology, economics and statistics to see how function is defined in these areas. Function definitions from US math text books are also introduced. Based on the these and the survey, some suggestions are made on the new curriculum which treat function as a correspondence relation. Vertical line test should be added to the Algebra II/Pre calculus course to check the univalent property.
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