HPM视角下“导数几何意义”的教学

Teaching of the Geometrical Meaning of the Derivative from the HPM Perspective

极限思想是导数概念的基础，忽视导数概念中的极限思想，是造成未来高等数学学习困难的原因之一．要理解极限思想，需要完成从有限到无限的跨越．借助刘徽的割圆术，在切线的静态定义与动态定义之间架起了一座桥梁，使学生能够自然、顺利地完成从静态到动态、从有限到无限的跨越．实践表明，HPM视角下的导数教学有助于学生对导数与极限概念的理解．

The limit is the foundation of the concept of the derivative, neglect of which will lead to difficulties in learning higher mathematics in the future. To understand the concept of limit, students must make a crossover from finiteness to infinity, which is difficult to implement. Based on the reconstructed history, the Cyclotomic Rule is introduced to construct a bridge connecting the static and dynamic concept of the tangent, enabling students to pass from the finiteness to infinity naturally and successfully. It is revealed through interview and a questionnaire survey that the teaching of the geometric representation of the derivative from the HPM oersoective is conducible to better understanding of the concepts of derivative and limit.