Investigation And Research On The Errors Of Plane Vector Problem Solving Of Senior One Students

It is inevitable for students to make mistakes in solving problems in the process of mathematics learning.In recent years,more and more people have begun to pay attention to the educational value of problem-solving errors.Teachers can make targeted corrections by understanding the types of errors that students make in problem-solving,and analyzing the reasons for students’ problem-solving errors.Vector is a basic tool for describing mathematical problems in straight lines,curves,planes,surfaces,and high-dimensional spaces.It is also the foundation for further learning and researching other mathematical fields.Vector is not only the research object of algebra,but also the research object of geometry.It is an important bridge between algebra and geometry;Vector is also of great significance in physics,as it is also a bridge between mathematics and physics.In addition,vectors also occupy an important position in the college entrance examination,which is the focus of the exam.Therefore,it is necessary to study the errors made by students in solving plane vector problems.This article is based on the related content of Plane Vector and Its Application in Chapter 2of "High School Mathematics Compulsory Volume 1" published by Beijing Normal University Press(2019 edition),and mainly based on the "High School Students’ Plane Vector Test Volume" and Investigation on the Causes of Plane Vector Problem Solving Errors among High School Students,and investigates the following three issues:(1)The types and manifestations of plane vector problem solving errors among high school students;(2)The causes of plane vector problem solving errors among senior high school students;(3)Strategies to address these problem solving errors.This study mainly uses the methods of literature analysis,questionnaire survey,interview,and test paper analysis to analyze the plane vector problem-solving errors of senior high school students from four aspects: intellectual errors,logical errors,strategic errors,and negligent errors,and combines surveys and interviews to explore the reasons why senior high school students are prone to errors.Through research,it is found that the main reasons are students’ own internal and external factors,including: weak basic knowledge,insufficient internal motivation and interest in learning planar vectors,weak mathematical computing skills,poor methods of dealing with incorrect questions,influenced by thinking patterns,and weak metacognitive abilities;External factors include: the impact of knowledge difficulty,the way teachers deal with incorrect questions,and the way teachers teach.Based on the analysis of the survey results and teaching practice,this article proposes corresponding teaching and learning strategies for plane vector knowledge errors,logical errors,strategic errors,and negligent errors.It is hoped that this study can provide effective reference for front-line teachers in plane vector teaching and students in learning plane vectors,thereby reducing the occurrence of students’ plane vector problem-solving errors and improving teaching effectiveness.