황동주 김유지 2010-02 10427 https://aurora.ajou.ac.kr/handle/2018.oak/3374 학위논문(석사)--아주대학교 교육대학원 :수학교육,2010. 2 목 차 Ⅰ. 서론························································································· 1 A. 연구의 필요성 및 목적······························································ 1 B. 연구 문제·············································································· 3 C. 용어의 정의··········································································· 3 1. 오류················································································· 3 2. 성취도검사········································································· 3 D. 연구의 제한점········································································· 4 E. 기대되는 효과········································································· 4 Ⅱ. 이론적 배경················································································ 6 A. 오개념·················································································· 6 1. 오개념·············································································· 6 2. 개념정의와 개념이미지··························································· 7 B. 접선에 대해 학생들이 갖는 개념················································· 10 1. 접선과 도함수에 대해 학생들이 갖는 개념·································· 10 2. 우리나라 7차교육과정 교과서에서의 접선의 개념··························· 11 가. 원의 접선····································································· 11 나. 원과 직선의 위치관계······················································· 12 다. 이차 함수의 그래프와 직선의 위치 관계································· 13 라. 할선의 극한, 미분계수와 접선의 기울기·································· 14 C. David Tall의 연구·································································· 17 Ⅲ. 연구방법 및 절차········································································ 22 A. 연구대상············································································· 22 B. 연구도구············································································· 22 1. 접선의 그래프에 대한 인식조사 검사 도구·································· 22 2. 접선과 미분계수 사이의 관계를 측정하는 검사도구························ 24 3. 수학 미분 성취도평가지························································ 25 C. 연구절차·············································································· 27 D. 분석방법·············································································· 28 Ⅳ. 결과 분석················································································· 29 A. 유형별 검사도구에 대한 추리 통계··············································· 29 1. 두 집단 간 차이 검증··························································· 29 2. 접선의 그래프에 대한 인식 조사·············································· 33 3. 접선개념에 대한 오류분석과 접선과 미분계수 사이의 관계 측정········ 39 B. 상관관계 분석······································································· 48 1. 성취도와 접선개념의 이해의 상관관계 분석································· 48 2. 성취도와 접선과 미분계수 사이의 관계측정과의 상관관계················ 54 Ⅴ. 결론······················································································· 58 A. 요약··················································································· 58 B. 결론 및 제언········································································· 59 참고문헌······················································································· 62 [부록-1] 접선의 그래프에 대한 인식 조사지·············································· 64 [부록-2] 접선과 미분계수 사이의 관계를 측정하는 검사지····························· 67 [부록-3] 미분 성취도평가지································································· 69 kor The Graduate School, Ajou University 아주대학교 논문은 저작권에 의해 보호받습니다. 함수의 접선개념에서의 오류분석과 성취도 Thesis 아주대학교 교육대학원 교육대학원 수학교육 2010. 2 Master http://dcoll.ajou.ac.kr:9080/dcollection/jsp/common/DcLoOrgPer.jsp?sItemId=000000010427 함수 접선개념 오류분석 성취도