On the Meaning of 'Activity' in Mathematical Cognition

수학적 인식에서 '활동'이 갖는 의미에 대한 고찰

In this study, I consider the meaning of activity as the source of mathematical knowledge. Mind-body dualism of Descartes which understands that knowledge precedes activity is somewhat overcomed by Ryle who understands that knowledge and activity are two sides of the same coin. But his discussion cannot offer the explanation about the foundation of rightness or the development of rules which can be expressed propriety of activity or rationality. Contrary to these views, Piaget solve this problem by the reasonability of 'the whole system of activity'. The theory of Dewey can be evaluated as an origin of activism of Piaget. Piaget considers knowledge as the system of activity itself, whereas Dewey considers knowledge as 'the result of activity'. This view of Dewey is related to the view of pragmatism which considers 'practice' is more important than 'theory'. The nature of 'activity' in this study has to be understanded as the interaction or the relation between the subject and the object. If we understand activity like this, we can explain that the whole structure of activity has the 'wholeness' that cannot be simply restored to the sum total of 'parts' and the new structure is a self-regulative transformation system which includes former structure continuously.