高等学校数学における理解を深めるための 指導方法に関する研究（Ⅰ） ─ 数学的理解の２軸過程モデルに基づく「図形と計量」の学習指導を通して ─

抄録

　　The purpose of this paper is to examine the effectiveness of lesson organization based on the Koyama’s (2010) “two-axis process model” of understanding mathematics for developing students’ understanding in high school mathematics classroom.　By using the principles and methods for lesson organization based on “two-axis process model”, the authors clarified levels and embodied learning stages for understanding the theorem of sines and cosines as a topic of “Figure and Measurement” in high school subject Mathematics I.　We did an action research with a pretest, mathematics lessons, and a posttest in order to examine the effectiveness of our lesson organization in terms of improving students’ mathematical understanding of this topic.

　　As a result of qualitative and quantitative analyses, the following two points were found out.

(1) About the understanding level of “general mathematical relations”, all students who understand how to prove the theorem can use it in solving mathematical problems, while the opposite is not the case.

(2) In order to shift their understanding up to the level of “general mathematical relations”, beforehand students need to understand the “relations of mathematical entities” at a certain level.

　　The first suggests that it is useful for teacher to make a distinction between understanding the theorem itself and using it in solving mathematical problems at the level of understanding “general mathematical relations” in teaching and learning of mathematical topic in “Figure and Measurement.” The second suggests that it is important for teacher to aim at students’ understanding of “relations of mathematical entities” in order to shift their understanding up to level of “general mathematical relations”.　These findings verify the effectiveness of our lesson organization based on the two-axis process model in high school mathematics classroom.