반영적 추상화와 조작적 수학 학습-지도

• 영문명: Reflective Abstraction and Operational Instruction of Mathematics
• 발행기관: 대한수학교육학회
• 저자명: 우정호 홍진곤
• 간행물 정보: 『수학교육학연구』제9권 2호, 383~404쪽, 전체 22쪽
• 주제분류: 사회과학 > 교육학
• 파일형태: PDF
• 발행일자: 1999.12.31

영문 초록

This study began with an epistemological question about the nature of mathematical cognition in relation to the learner's activity. Therefore, by examining Piaget's ‘reflective abstraction’ theory which can be an answer to the question, we tried to get suggestions which can be given to the mathematical education in practice. ‘Reflective abstraction’ is formed through the coordination of the epistemic subject's action while ‘empirical abstraction’ is formed by the characters of observable concrete object. The reason Piaget distinguished these two kinds of abstraction is that the foundation for the peculiar objectivity and inevitability can be taken from the coordination of the action which is shared by all the epistemic subjects. Moreover, because the mechanism of reflective abstraction, unlike empirical abstraction, does not construct a new operation by simply changing the result of the previous construction, but is forming re-construction which includes the structure previously constructed as a special case, the system which is developed by this mechanism is able to have reasonability constantly. The mechanism of the re-construction of the intellectual system through the reflective abstraction can be explained as continuous spiral alternance between the two complementary processes, ‘réfléchissement’ and ‘réflexion’; réfléchissement is that the action moves to the higher level through the process of ‘intériorisation’ and ‘thématisation’; réflexion is a process of ‘équilibration’ between the assimilation and the accomodation of the unbalance caused by the movement of the level. The operational learning principle of the theorists like Aebli who intended to embody Piaget's operational constructivism, attempts to explain the construction of the operation through ‘internalization’ of the action, but does not sufficiently emphasize the integration of the structure through the ‘coordination’ of the action and the ensuing discontinuous evolvement of learning level. Thus, based on the examination on the essential characteristic of the reflective abstraction and the mechanism, this study presents the principles of teaching and learning as following; ① the principle of the operational interpretation of knowledge, ② the principle of the structural interpretation of the operation, ③ the principle of intériorisation, ④ the principle of thématisation, ⑤ the principle of coordination, réflexion, and integration, ⑥ the principle of the discontinuous evolvement of learning level.

목차

Ⅰ. 머리말

Ⅱ. Piaget의 반영적 추상화

Ⅲ. 반영적 추상화 이론에 입각한 수학 학습-지도 원리

Ⅳ. 맺음말

참고문헌