Abstract
In this paper, I investigate a conception of a proof of junior high school students (214 students). I think there are three levels of proof and four categories in a preformal proof.(fig.1) I study that how junior high school students understand what is a proof. The findings are the followings. (1) About a half of students consider "proof" as an experiential explanation and a deductive inference simultaneously. (2) Ca.20% of students consider "proof" exactly from a point of generality of a proposition and deductivity of inference. (3) Ca.60% of students consider a preformal proof as a proof. Ca.20% of students understand a preformal proof as a proof from a point of generality and deductivity. [figure] (4) 11% of students consider a paradigmatic proof as a proof to give a conviction of it, 23% of them consider a action proof as such proof. (5) Students consider a action proof more understandable than a paradigmatic proof. (6) In a case of understanding a proof, ca.50% of students are influenced by a formal expression.
