Research Of Conic Curve Solving Errors Among High School Students ——Ellipse As An Example

With the further understanding of the laws of psychology and pedagogy,teachers are increasingly aware that it is normal for students to make mistakes in mathematics,and that mistakes are a valuable resource for deeper learning.As an important part of plane analytic geometry,conic curves have been the focus of college entrance examinations,and are also an important point of study for students.Therefore,the thesis takes ellipses as an example to study the solving errors of sophomore students in the process of learning conic curves,aiming to investigate the common types of errors and the causes of errors in students' problem solving,and to propose improvements in teaching and learning.This paper takes the ellipse knowledge point as the carrier,"sophomore students'mathematics learning questionnaire" and "sophomore students' ellipse test paper" as the basis,combined with teacher and student interviews,there are three main areas of investigation and research:(1)What errors do students make in solving problems related to ellipses?(2)What are the types of these errors?What are the reasons for these solution errors?(3)How can we correct the errors that students make when solving ellipse-related problems?The thesis mainly used questionnaire,test analysis and interview method.The main flow of the study is as follows:The first step was to review the relevant literature,and to develop questionnaires and tests by communicating with instructors and front-line teachers;Secondly,a sample of three classes of sophomore students in a high school was surveyed;Interviews were again conducted with teachers and some students in this grade;finally,the collected information was counted,summarized and analyzed,and the error types were categorized to obtain the corresponding research results.Through the survey and analysis of sophomore students,it was found that sophomore students mainly made intellectual and negligent errors in solving ellipse-related problems,but there were also strategic and negligent errors.The main reasons for the error are:defects in elliptical knowledge,lack of corresponding mathematical knowledge,poor understanding of the meaning of the topic;students solve problems with confusing logic;deviation of solution direction or improper choice of method;students have poor study habits,etc.Finally,the author proposes appropriate strategies according to the type of error questions.Suggestions for teachers to teach ellipses:strengthen knowledge construction,focus on the generation of concepts such as ellipse;focus on the development of question review strategies to improve students' ability to extract information;variation teaching,infiltration of mathematical thinking;selecting good questions,exploring multiple solutions,and reflecting practically;make a "mistake paper" to reduce students' mistakes.Suggestions for students studying ellipses:maintain a sense of traceability of knowledge and methods by proactively organizing a collection of errors;establish study groups to help each other study and strengthen the foundation;organize math notes,build a knowledge network,and review in a timely manner;develop good arithmetic and checking habits,and improve mathematical ability;review the process of solving problems,and develop good mathematical learning habits such as reflection.