| Function is a very important part of high school mathematics,and the score in the college entrance examination is also large.The problem-solving error of function has always been a topic that teachers and students attach great importance to.Therefore,it is particularly important to investigate and analyze the problem-solving error of students in high school function teaching.In this study,the first-year students and mathematics teachers in a middle school are selected,and the teachers are mainly interviewed.The test papers made by students are analyzed and combined with interviews.Mainly around the following questions :(1)to explore the regularity of different levels of students' wrong questions,better analysis of different levels of students' cognitive defects and differences;(2)Analyze the underlying causes of typical errors based on cognitive theory.Through this study,students' problem-solving errors are divided into four cognitive components : problem representation,pattern recognition,problem-solving migration and problem-solving monitoring according to the cognitive structure theory of problem-solving.In addition,they are also affected by the knowledge base and problem-solving strategies in long-term memory.The main causes of these errors are :(1)insufficient knowledge and imperfect problem representation;(2)Poor pattern quality and difficult pattern recognition;(3)Mindset,problem solving transfer ability is weak;(4)Poor awareness of problem solving monitoring and difficult problem solving.In view of these errors,this paper puts forward targeted suggestions from three perspectives : scientifically dealing with the errors of different students,making full use of error resource,and reasonably treating function errors.It is hoped that this study can help teachers understand the causes of students' problem-solving errors,optimize teaching design,and help students reduce problem-solving errors. |
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