中学校第１学年数学科「多数の観察や多数回の試行によって得られる確率」の授業に関する考察　試行回数と相対度数のばらつきの関係に焦点を当てて

抄録

In school mathematics, it is considered important to learn that the variation of relative frequency of an event is large when the number of trials is small, but that the variation decreases as the number of trials increases (the relationship between the number of trials and the variation of relative frequency), in order to understand the meaning of experimental probability. However, this is not considered very important in current Japanese school mathematics. Therefore, the purpose of this paper is to design a lesson and to examine whether or not the lesson produced learning of the relationship between the number of trials and the variation of relative frequencies of trials. A task was designed based on the hospital problem, and the lesson was designed to achieve learning in the sense of the Theory of Didactic Situations. It was hypothesized that learning of the relationship between the number of trials and the variation of relative frequencies in the sense of the Theory of Didactic Situations would occur through the designed lessons. As a result, we were able to confirm the students’ learning from their utterances and worksheet descriptions during the lesson.