| It is common for students to make mistakes in mathematics learning and solving problems.In other words,error will exist in students’ learning process.Rational use of students’ error resources is conductive to improving the effectiveness and pertinence of teachers’ teaching.At the same time,many errors are stubborn and will eventually evolve into “second error”.It is of great theoretical significance and practical value to deeply study mathematical “second error”,to make reasonable attribution and analysis,and to put forward effective coping strategies.Therefore,this study takes “trigonometric function” learning as an example to study the phenomenon of “second error”.First of all,this research adopts literature analysis and assignments(paper)analysis,and combing the relevant literature about mathematical error and trigonometric function,identifying and classifying substitute class assignments to wrong(papers),thinks the types of error in trigonometric function learning mainly have intellectual error,strategic error and psychological error.Also,this research analyses the main causes of trigonometric function errors from the following five aspects: students’ mastery of trigonometric function concepts and properties,their memorization and application of trigonometric formula,their mastery of mathematical thinking and methods,their operation ability and their psychology in learning trigonometric function.Secondly,on the basis of the study of trigonometric learning errors,teachers’ interviews and students’ questionnaires were conducted to explore the types and causes of“second error” in trigonometric learning.It was found that “second error” includes cognitive “second error” and non-cognitive “second error”.More specifically,cognitive“second error” includes knowledge " second error",ability "second error" and strategy“second error” and non-cognitive "second error" includes habit “second error” and psychology “second error”.On this basis,this study puts forward the correction and prevention strategies of “second error”,prevention strategies include solid knowledge foundation,the construction of mathematical network,attaches great importance to the error resources,seriously paper correction and prelection,strengthen the variant training,timely consolidated and the other three aspects.Improving correction strategy includes playing a role of main body,finding out the error source,conducting or an effective error correction to the tutorial,cultivating the habit of error correction and the consciousness of error correction and the other three aspects.Finally,it can obtain a good results to take “trigonometric function” as the carrier,the recognition results of "secondary error" in test as the basis,the correct strategy as the guide for the five students in individual coaching,error correction of different level students,which proves that high student mathematics “second error” corrective strategies have certain feasibility and validity. |
