2021 Volume 45 Issue 4 Pages 406-420
We often see incomplete proof with inversive inference generated when junior high school students solve the problem of geometrical proof. The purpose of this study is to clarify the reason why incomplete proof with inversive inference is generated. We designed a semi-structured task-based interview survey from the viewpoint of the epistemic value and the status of a proposition, which are components of a proposition’s meaning, and conducted it on 20 pairs of ninth graders. The data from the survey was divided into three types and the frequency of emergence of the codes related to the epistemic value and the status of the proposition for each type was investigated. As a result, the students who generated an incomplete proof understood that the epistemic value based on perception was insufficient and that the epistemic value “necessary” was needed in order to obtain the logical value “true”. Also, it was found that incomplete proof with inversive inference is generated by two patterns, and that some aspects of the epistemic value and the understanding of the status of the proposition generate an incomplete proof. Finally, based on these findings, we provided teaching implications to control the generation of incomplete proofs with inversive inference.
