基于一道课本例题的探究与拓展

Based on a Textbook Example Question to Explore and Expand

摘要: 中学数学课本中的例题具有示范性、典型性和探究性，是课本的精髓。浏览近几年全国各地的高考数学试卷，很多试题来源于课本，“题在书外，根在书内”。本文选择人教A版必修二“平面向量数量积的坐标表示”的习题中的拓广探索进行探究，分别从选题意义、试题分析、解题思路、价值与拓展和高等知识的联系等方面进行分析。

Abstract: The examples in middle school math textbooks are exemplary, typical and exploratory, which is the essence of the textbook. Browsing the recent years of national college entrance examination math papers, many questions from the textbook, “the problem is outside the book, rooted in the book”. This paper selects the extension exploration in the exercise “coordinate representation of plane vector dot product” of compulsory A edition of Human Education, respectively from the significance of topic selection, analysis of test questions, problem-solving ideas, value and expansion and the connection of higher knowledge.