Structuralist view of Knowledge and the Structure of Knowledge in Mathematics

지식에 대한 구조주의적 관점과 수학에서의 '지식의 구조'

Structualist view distinguishes structure(reality) from phenomenon(appearance). Phenomenon is the outside aspect of structure and structure is the inside aspect of phenomenon. From the structualist view, the knowledge could e divided into two parts, the appearance of knowledge(the outside aspect of knowledge)and the structure of knowledge(the inside aspect of knowledge). Structualist view advices teachers to understand knowledge more totally from the inside-outside viewpoint, and not to teach mere the one aspect of knowledge, especially the outside aspect of knowledge, that is, the written expressions in textbook, but to teach the inside and outside aspects fo knowledge totally. In the history of mathematics education, the attempts to teach the structure of knowledge were flourishing in the period of discipline-centered curriculum. 'New Math movement' represents the attempts. The advocators of New Math, however, did not succeed sufficiently to understand the inside-outside view which the term the structure of knowledge represents, and failed to make mathematics teachers to understand the view well. Their attention was put on to introduce the modern mathematics to school math rather than to understand the educational and epistemological perspective which the term the structure of knowledge represents. To teach the structure of knowledge, mathematics teacher should be able to understand mathematical knowledge more totally from the inside-outside viewpoint. Especially, s/he should not regard the outside aspect of mathematical knowledge written in textbook as the totality of knowledge, but inquire into the inside aspect of mathematical knowledge from the outside aspect of mathematical knowledge.