The General Extension of the Sine Theorem Proved by Vector Method in People’s Education A Version (2019)

新课改背景下，《普通高中数学课程标准(2017年版2020年修订)》在课程目标中提出明确要求，学生应通过高中数学课程，获得进一步学习以及未来发展所必需的数学基础知识、基本技能、基本思想、基本活动经验(简称“四基”)；提高从数学角度发现和提出问题的能力、分析和解决问题的能力(简称“四能”)。本文以人教A版(2019)教科书必修第二册正弦定理证明的一般性推广为例，在学生学习教科书基本证明方法，掌握数学基础知识后，本文通过引导学生从数学角度“发现和提出问题”后，采用类比的思想，使用逻辑推理与严格证明的研究方法，通过对教科书的深度挖掘，锻炼学生的基本技能，以数学的基本思想为基石，完成“分析和解决问题”，总结探究活动经验，使得学生实现“四基”、“四能”的培养，进一步培养学生的数学核心素养。Under the background of the new curriculum reform, the “General High School Mathematics Curriculum Standards (2017 Edition, 2020 Revised in 2020)” puts forward clear requirements in the curriculum objectives. Students should obtain the basic knowledge, basic skills, basic ideas and basic activity experience of mathematics necessary for further learning and future development (referred to as the “four bases”) through the high school mathematics curriculum; improve the ability to find and raise problems from a mathematical perspective, analyze and solve problems (referred to as the “four abilities”). This article takes the general promotion of the proof of sine theorem in the second volume of the textbook of People’s Education Edition A (2019) as an example. After students learn the basic proof method of textbooks and master the basic knowledge of mathematics, this article guides students to “discover and ask questions” from a mathematical perspective, adopts analogy, uses the research method of logical reasoning and strict proof, exercises students’ basic skills through in-depth excavation of textbooks, takes the basic ideas of mathematics as the cornerstone, completes “analysis and problem-solving”, and summarizes the experience of exploration activities, so that students can realize the cultivation of “four basics” and “four abilities”, and further cultivate students’ core mathematics literacy.