HPM视角：“弧田术”在数学教学中的应用研究
HPM Perspective: Research on the Application of “Hutian Shu” in Mathematics Education

文章探讨了数学史与数学教育(HPM)在中小学教学中的应用，以“弧田术”——中国古代计算弓形面积的方法为例进行分析。“弧田术”对后世的弧矢割圆术产生了影响，在数学和天文史中具有重要意义。通过深入剖析，发现“弧田术”的构造原理除了运用“出入相补”原理外，还采用了插值法。这一发现表明，“弧田术”能够有效地将数学史融入教学中，激发学生的学习兴趣，帮助他们深入理解数学知识，发展思维能力，并提升数学文化素养，可为中小学数学教育提供参考。
This paper explores the application of the History and Pedagogy of Mathematics (HPM) in primary and secondary school education, using “Hutian Shu”—an ancient Chinese method for calculating the area of a circular segment as a case study. “Hutian Shu” has influenced later arc and chord division techniques and holds significant importance in the history of mathematics and astronomy. Through in-depth analysis, this paper reveals that the construction principle of “Hutian Shu” employs not only the principle of complementary areas but also interpolation methods. This discovery indicates that “Hutian Shu” can effectively integrate the history of mathematics into teaching, stimulating students’ interest in learning, aiding in their deep understanding of mathematical knowledge, developing their thinking abilities, and enhancing their mathematical cultural literacy, providing valuable teaching references for primary and secondary school mathematics education.