高考向量数量积最值问题分析与研究

Analysis and Research on the Maximum and Minimum Value Problems of Vector Scalar Product in the College Entrance Examination

摘要: 数学思维能力，对于学生形式数学学科素养、提升综合素质至关重要。文章探讨了平面向量数量积最值问题的解题路径与适用情况，并以高考真题为例，多视角解析平面向量数量积最值问题，探究出有关培养学生数学思维能力的教学启示。鼓励教师启发学生多角度思考问题，引导学生寻找不同的解题切入点。教师应丰富学生的思维方式，重点培养学生的发散思维，重视学生思维品质，关注学生数学思维发展特点。

Abstract: The ability of mathematical thinking is very important for students’ formal mathematics discipline accomplishment and improving their comprehensive quality. This paper discusses the solution path and application of the plane vector scalar product maximum and minimum value, and analyzes the plane vector scalar product maximum value problem from multiple perspectives by taking the college entrance examination as an example, and probes into the teaching enlightenment on cultivating students’ mathematical thinking ability. Encourage teachers to inspire students to think from multiple angles, guide students to find different problem solving pointcuts. Teachers should enrich students’ thinking mode, focus on cultivating students’ divergent thinking, pay attention to the quality of students’ thinking, and pay attention to the development characteristics of students’ mathematical thinking.