An Empirical Study On The Errors Of Solving The Problem With Binary Linear Equation Group For Seven-grade Students

Application questions have been the key points and difficult points for middle school students for a long time.The seven-grade students,at a turning point from primary to middle school,would inevitably meet some typical application questions during the studying of math,but the count method and mathematical equation modals in primary school can’t satisfy the need of the students to solve this kind of questions.Therefore,it is time to need a binary linear equation group which is an effective way of solving problems,and it is challengeable for students to master and apply this method.So this essay aims to study the typical mistakes which students make by using this equation group and to find specific mistake types.Besides,this essay would let people know the thoughts of students about the method as well as some problems teachers encounters in this lesson type,which provides some basic facts used to reduce the mistakes in applying the binary linear equation group.This essay would conduct the study by using the method of document analysis,questionnaire survey and interview.The questionnaire survey includes one test questionnaire about how to solve application questions by using the binary linear equation group and another survey focusing on the situation of students learning application questions.At first,document analysis,based on researches of plenty of experts and scholars,is adopted to summarize the main types of application questions solved by the binary equation groups,such as problems of travelling,different multiples,geometry,growth rate and profit,and to make test papers according to these problems.387 students from three public middle schools and a private school are selected as a testing sample.To show the distinctiveness,the selected students come from normal classes and intensive training class.The analysis method,based on the theory of Dai Zaiping and Luo Zengru,is used to analyze three kinds of errors——intellectual errors,strategic errors and negligence errors.After a testing questionnaire survey,the students receives another questionnaire and interviews.The studies shows based on some common types of application questions solved by binary linear equation groups,it can be concluded the following ideas by analyzing the errors students easily make and horizontally comparing the data of the testing questionnaire:(1)Most of the errors the students make belong to intellectual errors which are showed as theincorrectly using of formulas of opposite direction meeting and same direction pursuing in the travelling questions as well as equilateral triangle theorems in geometry questions and,the confusion of relations among the adding,subtracting,multiplying and dividing and of growth rate and reduction rate formulas in growth rate questions.(2)There is a lower rate of strategic errors,which are demonstrated that students can’t transfer their literal understandings into math language and that they cannot find effective equivalent relations because of one-sided understanding of questions.Besides,the lack of life experience leads to the errors students make in profit questions.(3)Careless errors has a lowest rate.This kind of errors is demonstrated that students do not read the questions carefully and leave out effective information and that they do not write the answers normatively without units.What’s more,the students copy the formula data incorrectly and give irrelevant answers without units because of carelessness.Finally,the essay gives the following suggestions according to the teaching of binary linear equation groups as following:(1)Strengthen the understanding of math knowledge for students.It is not enough to dictate the concepts,be sure to give examples to students so that they can get a visual understanding of concepts.Besides,teachers can also give some incorrect examples to let students have a comparison in order to change the concepts into their knowledge.(2)Expand the thinking pattern of students to solve application questions.Enhance the auxiliary analyzing ability such as using diagrams,tables,line segments and so on.(3)Improve the good habits of studying math for students,for example,develop the good habits of labeling effective information and putting in the original answers to check.