Development And Utilization Of Error-prone Problem Sets In High School Mathematics

Mathematics exercises play a very important role in helping students consolidate and deepen what they have learned,and help teachers understand students' mastery and application of mathematical knowledge,problem-solving skills and problem-solving methods.Under the influence of cognitive structure,cognitive level and problem solving ability,it is normal for students to make mistakes in solving problems.Therefore,how to pay attention to the students' mistakes in teaching,how to find the holes in the students' knowledge and how to help the students avoiding the recurrence of mistakes in problem-solving is a meaningful research topic.First of all,through the literature research,this thesis sorts out the classification methods of students'error-prone exercises.Then start study the classifications of error-prone exercises based the background of knowledge errors,logic errors,strategic errors and the psychological errors.Secondly,through interviews with students and questionnaires,we know that the current situation of students in the aspects of problem sorting,collection,error cause analysis,classification and utilization of error-prone exercises.The situation is that many students have their own error-prone questions,but they do not classified them reasonably.Their error-cause analysis has some deficiency,the utilization rate of the error-prone exercises is not high.Mathematics teachers were interviewed,and they were informed of the timely evaluation error-correcting,training of students' error-prone exercises in the teaching process.But guidance of teachers is relatively scattered in management of students for their own error-prone exercises,resulting in students' understanding of errors is scattered and superficial,and make mistakes again and again for the same problem.Based on the understanding of the present situation,this thesis collects some error-prone exercises of students and divides them into seven categories:(1)confusion of concept and properties;(2)neglecting of conditions of formula;(3)inequivalent transformations,(4)incomplete classifications;(5)neglecting constraints or implicit conditions;(6)improper "potential assumptions" for conditions;(7)other errors.In each category,some examples are selected for which the points of easy-errors are found,the error-causes are analyzed,and correct solutions are given.At the same time,according to the error rate of a problem,the classification is divided into three levels as level ?,level ? and level III from high to low rates.This sort of classification and grades can help teachers to effectively and pertinently choose error-prone exercises from the collection.Finally,we design a specific teaching case to show how to find the wrong points,analyze the causes of the mistake and how to use the collection developed of error-prone exercises.How to effective use the collection of error-prone problems is further discussed through interviews with teachers.There are six chapters in this thesis.Chapter I is an introduction,including research backgrounds,research contents,methods and significance.Chapter ? is theoretical basis of this study and a summary of relevant research results.Chapter III is a survey of current situation of dealing with mathematics error-prone exercises in high school,including questionnaires to students and interviews with teachers.Chapter IV is about the classification,grades,developing and utilization of mathematical error-prone problems.Chapter V is a case study on utilizing of error-prone questions and teacher interviews on the effective use of error-prone problem collection.Chapter VI is the siummary of research results and future research topics.