조작활동을 통한 분수와 소수 개념의 연결 지도에 관한 연구 = A study on the instructions of connection between ordinary and decimal fraction concepts

다국어 초록 (Multilingual Abstract)

Decimal fractions are the practical system of notations representing real numbers. The set of decimal fractions with the definition of comparison of decimal fractions and the identification of their double representations is essentially the field of real numbers. Decimal fractions are functions from the viewpoint of operator and linearity among the essences of them. Therefore, we have to clarify the cincept of decimal fractions is not easy.
The cause of problematics are as follows. the prior knowledge - whole numbers and ordinary fractions - tackles the acquisition of concepts of decimal fractions. Children learn the concepts of whole numbers, ordinary fractions and decimal fractions in separate situations, different rules and different notational systems, so they can't formalize the connection between them. And they are taught the decimal fractions from not conceptual approach but procedural sense. The symbol manipulation procedures for ordinary fractions and decimal fractions should be related, but, traditional classroom instruction tends to emphasize only the differences between them. This cause some problematics that there is no connection between ordinary fractions and decimal fractions. And, the introduction of decimal fractions are represented by the simple measurement or treated by structuralism.
In this paper, we attempt to eradicate the problematics relevant to the acquisition of decimal fractions discussed above and find the desirable direction of instruction of decimal fractions. First of all, we survey the history of decimal fractions, and then clarify the essence of them - measure function, extension of natural numbers, equivalence class of ordered pair of integers, ratio, operator and linerity. And we compare and analyse the theories about decimal fractions of Resnick and Brousseau. Then, we suggest the efficient instruction methods which are faithful to the essence of decimal fractions and choose some methods among them to plan to the classroom instruction.

목차 (Table of Contents)

• Ⅰ. 머리말
• Ⅱ. 소수와 분수의 출현
• Ⅲ. 소수 지도에 관련된 이론
• Ⅳ. 십진분수를 이용한 소수의 지도
• Ⅴ. 맺음말
• ［참고문헌］
• ［Abstract］