最小角定理的理解与解题能力提升策略研究

Study on the Understanding of the Minimal Angle Theorem and the Strategy of Problem-solving Ability Improvement

高中数学新课标人教B版教材选修2-1中,最小角定理仅作为直线与平面成角定义的补充进行了阐述。深入延伸教材中关于最小角的相关内容,引导学生结合实际背景理解最小角概念,运用最小角定理进行变式训练,对学生熟练掌握直线与平面成角的知识点,提高空间思维能力、抽象概括能力、推理论证能力、数据处理能力有较大帮助,是高中数学教学过程中应引起重视的一个知识点。

In Section 2-1 of the PEP B mathematics textbook for new curriculum of senior high school mathematics, the minimal angle theorem is only described as a supplement to the definition of the angle between the straight line and the plane. To extend the relevant content of the minimum angle in the teaching materials, guide students to understand the concept of the minimum angle in combination with the actual background, and use the minimum angle theorem to perform variant training can help students master the knowledge of the angles of the straight line and the plane, and improve spatial thinking ability, abstract summary ability, ability to reason, and data processing skills.It is a knowledge point that should be paid attention to in the process of mathematics teaching in high schools.