高等学校における定積分の探究型授業の実践とその分析―教授人間学理論を拠り所にして―

抄録

Our study investigates the potential of inquiry-based learning for teaching definite integrals in Japanese senior high schools. We developed a sequence of lessons based on the Reference Epistemological-Didactic Model (REDM) of definite integrals, which illustrates how this mathematical concept can be studied and taught. The lesson sequence was designed and implemented at a senior high school, with data systematically collected and analyzed using the tools proposed by the Anthropological Theory of the Didactic. The analysis revealed substantial insights: Firstly, students encountered different kinds of the mathematical knowledge pertaining to definite integrals that they were supposed to learn in the curriculum within a meaningful context highlighting their practical and theoretical importance. Furthermore, the inquiry process expanded as students explored various quadrature methods, enhancing their understanding and appreciation of the subject matter. Second, the inquiry process was further enriched by active student interactions with their milieus, promoting deeper engagement with the mathematical concepts. These findings affirm that inquiry-based learning is a viable and effective approach for teaching definite integrals, providing students with a robust framework to actively explore and understand complex mathematical concepts.