Departmental Bulletin Paper 間接証明カリキュラムの開発に関する研究 : 背理法の学習過程に注目して
A study on curriculum development for indirect proof: understanding and constructing the process of proof by contradiction

早田, 透  ,  上ヶ谷, 友佑  ,  袴田, 綾斗  ,  岩知道, 秀樹  ,  影山, 和也  ,  小山, 正孝  ,  寺垣内, 政一

(45)  , pp.281 - 287 , 2017-03-31 , 広島大学学部・附属学校共同研究機構
The purpose of our study is to develop a curriculum of indirect proof. It aims to increase students’ understanding about indirect proof, and to improve their ability to use logic. Furthermore, we aim to construct a process of indirect proof, as the base of the curriculum. However, as there is no consensus regarding the definition of indirect proof, we only consider proof by contradiction.For this purpose, we designed a lesson in which students will probably be knowing indirect proof and then construct a process of the proof based on their conception (a priori analysis). We conducted the lesson in a 10th grade mathematics class. However, the lesson was not as successful as expected because we overestimated the students’ actual level of cognition. In contrast, most of our analysis of the knowledge is validated. Our future task is to design an improved lesson to deliver to students. We would also need to clarify the validation and limitations of our analysis.

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