A Study on the Nature of the Negative Numbers and the Teaching of Them by Formative Approach

음수의 본질과 형식적 접근에 의한 음수지도에 관한 고찰

In school mathematics, the negative numbers have been instructed using the intuitive models such as the number line model, the counting model, and inductive-extrapolation on the additionand multiplication and using inverse operation on the subtraction and division. Theseinstructions on the negative numbers did not present their formal nature and caused the difficulty for students to understand their operations because of the incomplete function of the intuitive models. In this study, we tried to improve such problems of the instructions of the negative numbers on the basis of the didactical phenomenological analysis. First of all, we analysed the nature of the negative numbers and the cognitive obstructions through the examination about the historic process of them. Second, we examined hew the nature of the negative numbers were analysed and described in mathematics. Third, we explored the improving directions for them on the ground of the didactical phenomenological analysis. In school mathematics, the rules of operations using the intuitive models of the negative numbers have been Instructed rather than approaching toward the nature of them. The negative numbers have been developed from the necessity to find the general solution of equations. The study tries to approach the operations instructions of the negative numbers formative]y to overcome the problems of those that are using the intuitive models and to reflect the formative Furthermore of the negative numbers. Furthermore, we examine the way of the instruction of the negative numbers in real context so that the algebraic feature and the real context should be Interactive.