학교 수학에서의 ‘증명’

'Proof' in school mathematics

The purpose of this study is to conceptualize 'proof' in school mathematics. We based on the assumption the following. ⒜ There are several different roles of 'proof' : verification, explanation, systemati-zation, discovery, communication ⒝ Accepted criteria for the validity and rigor of a mathematical 'proof' is decided by negotiation of school mathematics community. ⒞ There are dynamic relations between mathematical proof and empirical theory. We need to rethink the nature of mathematical proof and give appropriate consideration to the different types of proof related to the cognitive development of the notion of proof. 'Proof' in school mathe-matics should be conceptualized in the broader, psychological sense of justification rather than in the narrow sense of deductive, formal proof. 'Proof' has not been taught in elementary mathematics, traditionally. Most students have had little exposure to the ideas of proof before the geometry. However, 'Proof' cannot simply be taught in a single unit. Rather, proof must be a consistent part of students' mathematical experience in all grades, in all mathematics.