《数学课程标准(2011年版)》明确提出:“认真听讲、积极思考、动手实践、自主探索、合作交流等,都是学习数学的重要方式。”可见动手操作在学生学习中的重要性。但在课堂教学实践中,很多时候教师给了大量的时间让学生操作,却没有收到应有的效果。究竟是什么原因呢?通过观察研究发现:很多教师忽视了操作与思维的紧密结合;操作过程中关注外显的操作,忽视内隐的思维,使操作仅停 The Standard for Mathematical Curriculum (2011 Edition) clearly states: “Listening carefully, thinking positively, practicing, exploring independently, and cooperating and exchanging are all important ways to learn math.” "The Importance of Hands-on Operation in Students’ Learning . However, in classroom teaching practice, teachers often give students a lot of time to operate, but they do not receive the necessary results. What is the reason? Through the observation and study found that: many teachers ignore the close combination of operation and thinking; the operation of the focus on explicit operation, ignore the implicit thinking, the operation only