Mistakes are often accompanied by the process of learning.It is very normal for students to make mistakes with mathematics learning and problem solving,further,the effective use of students’ mistake resources will help to improve the pertinence and effectiveness of teaching.Mistakes are stubborn.Many teachers find that similar mistakes are often repeated in mathematics learning.They become a ‘stubborn disease’ which is difficult to cure.For this,it can not be simply attributed to carelessness,the poor foundation,the casual learning attitude and other factors.Instead,we should carry on the thorough analysis to the knowledge understanding,thinking situation,psychological characteristics and other factors when students make these mistakes.What problems do students often make mistakes on? What are the types of such errors? Why do students always make the same or similar mistakes? In view of this,this paper focuses on the stubborn mistakes in students’ mathematics learning.That is the mistakes,for a student themself,showing consistency at different times,which is defined as the repeated occurrence of the same or similar types of mistakes three times or more in mathematics learning and problem solving,and the mistakes still made after the teacher explains them.This paper makes clear the connotation and value of intractable errors through phenomenon observation and literature review.Through interviews with teachers,questionnaires to student groups and case-tracking studies on individual students,according to a large number of students’ resources of intractable errors retained and sorted by taking photos,combined with the results of investigation and research,this paper discusses the common types and main causes of intractable errors in solving mathematical problems in high school students,and puts forward some suggestions for correction.Literature research shows that there are few special studies on students’ stubborn mistakes in mathematics at present,but there are many general studies of problem-solving errors in this respect.The existing practice research on students’ repeated mistakes is more specific,only points out some reasons,the exploration is not deep enough,there is still room for research.The investigation shows that the stubborn mistakes in mathematics problem-solving in high school students are real and universal.In addition,teachers and students have extensive attention and value recognition to stubborn mistakes.Teachers’ classification of stubborn errors is not uniform,and the cause analysis can be divided into six aspects;the attribution of stubborn mistakes in solving their ownmathematical problems in high school students mainly comes from three aspects.For the common types and main causes of intractable errors in mathematics problem-solving in high school students,this paper mainly carries out qualitative research through case study method,assisted by investigation.Then,the following conclusions are drawn:According to the time when the stubborn mistakes occur,they can be divided into two categories: procedural errors and long-term errors.They can be also classified into four categories: knowledge errors,calculation errors,thoughtlessness errors and specification errors,according to the expression form of errors.The main causes of stubborn mistakes are as follows:(1)the causes of emotion,attitude and habit;(2)the causes of cognition,thinking and psychology;(3)the causes of the ways of dealing with errors;(4)the causes of objective aspects.Based on this,this paper puts forward the principle of correction and some suggestions for intractable errors.The principle: identify the cause of the error and suit the right remedy.The suggestions :(1)give positive reinforcement when students first contact with certain knowledge;(2)apply modular teaching appropriately to promote the construction of students’ schema;(3)apply strong targeted treatment of the errors appropriately such as individual tutoring;(4)cultivate students’ efficient management methods of errors. |