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.