| As a common thread through the whole process of mathematics study,function plays a very important role in everyone’s life.However,it’s abstract and difficult to understand for juniors who just learn function formally,therefore,the mistake about function part isn’t accidental,but the detours repeated by successive students.In the usual teaching process,teachers can’t care each student considerately because of limited energy,so this paper wants to summary the fallible questions of the whole students by researching some medium level students’ fallible questions.Firstly,found the fallible questions by testing some students at medium level,then analyzed the reasons for mistake by interview.This article mainly divided the reasons for four aspects,not enough the cognitive level for function concept,habitual associations leading to errors,not completed discussing the function questions and strategic errors solving comprehensive questions.Nextly,tested the whole students through the picked fallible questions according to the above research and finally drew a conclusion by analyzing the whole’s testing paper.It can be concluded that the error rate of the partial students in Grade 8 presents N-type that the thinking set problem highest,the comprehensive strategic faulty secondly and the error of function concept lowest.However,the error rate of the whole students in Grade 8 presents V-type that the error rate of function concept higher than thinking set and the error rate of classified discussion lower than thinking set and comprehensive strategic faulty.The error rate for the partial students and the whole students in Grade 8 is similar,but the error rate of thinking set for the partial students in Grade 8 can’t represent the whole students,and the error rate at the other 3 aspects can still represents the whole’s faulty.The error rate for partial students in Grade 9 presents N-type that the thinking set highest,the comprehensive strategic faulty secondly,and the incompleted classified discussion lowest.The error rate for the whole students in Grade 9 presents N-type,so it can be seen that the error rate for the partial students in Grade 9 can represent the whole.Overall,due to the increase of the function types,the errors leading by thinking set increase,and there’s little difference between the students in Grade 8 and Grade 9 for classified discussion problems.The students in Grade 8 have a more profound understanding of the function concept,so their error rate is much lower than the students in Grade 9.Because the quadratic function is introduced to the students in Grade 9,and the comprehensive questions they faced which usually link with geometric thought,the most value problem and the method of changing element that requirehigher comprehensive ability,so the solving ability for comprehensive questions of students in Grade 9 is poorer than the students in Grade 8. |
