在《有理数运算》的“学生运算错误原因”典型事件中，在如何认识和理解学生

In the typical event of "Students' Operation Error Causes" in "Rational Number Operation", there are existing experiences and knowledge and updates on how to recognize and understand the reasons for students' operation errors. There are also their and the "Error Cause Distribution Overview" provided by the technology platform. It can be seen from the figure" that "the concept is unclear" and "miscalculation" are the two most common causes of errors. Among them, "miscalculation" is commonly referred to as "sloppy". In the past, teachers' experience in solving "sloppy" is through more practice, but in fact, more practice still does not solve the problem of "miscalculation" very well. In order to further analyze and study the reasons for students' "miscalculation", while conducting interviews with students, combined with metacognitive theory, researchers and teachers believe that students' metacognitive awareness and ability are one of the important reasons for "miscalculation" one. The contradiction between the inherent understanding of the student's reason for computing and the new concept is the third-level contradiction.

In the typical events of "causes of students' operation errors" in rational number operation, there are existing experience and knowledge and updates on how to understand and understand the causes of students' operation errors, and they and the "overview map of error cause distribution" provided by the technical platform. It can be seen that "unclear concept understanding" and "miscalculation" are the two most common causes of errors. Among them, "miscalculation" is commonly referred to as "carelessness". In the past, teachers' experience in solving "carelessness" is through more practice. However, more practice still does not solve the problem of "miscalculation". In order to further analyze and study the reasons for students' miscalculation, while interviewing students, combined with metacognitive theory, researchers and teachers believe that students' metacognitive consciousness and ability are one of the important reasons for students' miscalculation. The contradiction between the inherent understanding of the causes of students' operation and the new concept is the three-level contradiction.

In the typical event of "Reasons for Students' Operation Errors" in Rational Number Operation, there are existing experiences, understandings and updates on how to understand and understand the reasons for students' operation errors, and it can be seen from the "Overview of Distribution of Errors" provided by them and the technical platform that "unclear understanding of concepts" and "miscalculation" are the two most common reasons for errors. Among them, "miscalculation" is commonly referred to as "carelessness". In the past, teachers' experience in solving "carelessness" was through more practice, but in fact, more practice did not solve the problem of "miscalculation" well. In order to further analyze and study the causes of students' "miscalculation", researchers and teachers think that students' metacognitive awareness and ability is one of the important reasons for "miscalculation" while interviewing students and combining with metacognitive theory. Here, the contradiction between the inherent understanding of students' operation reasons and new ideas is the third-level contradiction.