A Study on the meaning of preformal proof and its didactical significance

전형식적 증명의 의미와 교육학적 의의에 관한 연구

The purpose of this study is to verify the meaning of preformal proof and its didactical significance in mathematics education. A preformal proof plays a more important role in mathematics education, because nowadays in mathematics a proof is considered as an important fact from a sociological point of view. A preformal proof was classified into four categories: a) action proof, b) geometric-intuitive proof, c) reality oriented proof, d) proof by generalization from paradiam. An educational significance of a preformal proof are followings: a) A proof is not identified with a formal proof. b) A proof is not only considered from a symbolic level, but also from enactive and iconic level. c) A preformal proof generates a formal proof and convinces pupils of a formal proof d) A preformal proof is psychologically natural. e) A preformal proof changes a conception of what is a proof. Therefore a preformal proof is expected to teach in school mathematics from the elementary school to the secondary school.