糸掛けアートを用いた数学的探究活動 ―SRPに基づく探究過程の事例として―

抄録

　　Recently, inquiry-based learning has become increasingly important in mathematics education in upper secondary schools.  However, compared to science, there are still few practical examples of inquiry-based learning that is purely mathematical.  In this regard, we can point out two issues that need to be resolved. First, although teaching materials for inquiry-based learning in mathematics have been developed mainly through SSH, there is a constant demand for the development of new materials, because materials developed for inquiry-based learning lose their freshness as an inquiry when they are widely disseminated.  Second, because it is extremely difficult to produce truly novel results in pure mathematics, few have experience in actual mathematical research, and even fewer have the knowledge to facilitate inquiry in pure mathematics. Thus, further research in this point is needed.

　　In this paper, we present a case study of inquiry-based learning about string art, which was conducted in a seminar for teacher training students.  First, this paper introduces the content of this inquiry.  The content was structure-oriented, considering the mathematical structure of string arts, rather than an application of mathematics.  The inquiry is within the scope of high school mathematics and can be adapted as a teaching material for inquiry-based learning in high school mathematics.  Second, the process of implementing this inquiry-based learning is analyzed using the anthropological theory of didactics (ATD) framework.  In fact, this practice is based on study & research path (SRP) of ATD, and the Q-A map, an analysis tool of the SRP, is considered to be effective.  Finally, based on the above analysis, we show the characteristics of this inquiry tasks and the inquiry process in this practice, and induce knowledge on how to facilitate inquiry-based learnings.