《数学课程标准(2011年版)》在教学建议中提到:学生获得知识,必须建立在自己思考的基础上。学生面对一个个数学问题,经历一次次思考过程,产生一个个思考的结果。作为教师,我们更多的是看到了学生思考的结果,而容易忽视学生思考的过程。面对大的班额和繁重的教学任务,许多时候,我们面对不“标准”的答案,总会以自己的思考来臆想学生的思考,匆匆地给学生画上了“×”。但有些时候,学生并非如我们所想。当我们放慢脚步,去倾听学生思考的过程,就会发现许多结 “Mathematics Curriculum Standards (2011 Edition)” mentioned in the teaching suggestions: Students acquire knowledge, must be based on their own thinking. Students face a number of mathematical problems, through time thinking process, resulting in a result of thinking one by one. As teachers, we are more likely to see the results of student thinking, and easy to ignore the process of student thinking. In the face of large classes and heavy teaching tasks, many times we face the problem of not “standard” and always think of students’ thinking with their own thinking and hurriedly draw the students “ ”. But sometimes, students are not what we think. As we slow down and listen to our students’ thinking, we find many knots