| Function is one of the core teaching contents of high school mathematics.It covers many mathematical thinking methods and has high requirements for students’ ability.The application ability of function will also become the training direction of high school mathematics core literacy.However,for high school students,the abstraction of function concepts,the diversity of image properties,and the flexibility of thinking methods are all the difficulties for students to learn functions.Under this background,the research content of this paper is determined as follows:(1)Through the questionnaire survey,we can understand the students’ attitude towards the problem solving errors in the process of function learning;(2)Through the analysis of the students’ test and the actual problem-solving cases,combined with the teaching cases collected in my six-year teaching practice,this paper classifies the common error types of the senior one students when learning functions,mainly from the three levels of function concept,image property and practical application;(3)Combined with the students’ errors in solving function problems,the internal causes of the errors are analyzed in depth,and the sources of the errors are found from the perspectives of attitude,calculation,methods,habits,so that teachers can apply the right medicine to the case in teaching;(4)In view of the causes of errors in students’ function learning,relevant teaching suggestions are put forward: take students as the core,grasp the essence of function definition,take gradual steps as the means,cultivate the ability of comprehensive application,use "problem string" guiding teaching,and strengthen the teaching guidance of function content.Finally,the following conclusions are drawn:(1)The high school students’ overall understanding of the concept of function is low,especially in the aspects of image properties and comprehensive applications;(2)In practical teaching activities,many teachers also have different degrees of irrationality and lack of correct understanding in dealing with students’ mistakes;(3)Students need a lot of time and repeated training to gradually digest and master several major difficulties of functions,such as abstract functions,constantly-established problems with solutions,and problems with parameters.This process of digestion is also the process of gradually forming their thinking methods such as the combination of numbers and shapes,transformation,classification and discussion.The purpose of this paper is to explore and study the root causes of the problems that teachers and students have in the process of function teaching,help teachers and students to understand the internal causes of function errors,and give reference suggestions and targeted teaching strategies on the teaching of function courses,function thinking and the cultivation of core literacy. |
