A Survey On Vector Comprehension Level Of High School Students

Vector is developed along with physics and mathematics,and is widely used in physics,medicine,network,information technology and other fields.The introduction of vector into high school mathematics as instrumental knowledge,on the one hand,highlights the important role of vector,on the other hand,makes teachers lay stress on problem solving and application in teaching,ignoring the importance of concept,which inevitably leads to the utilitarian learning of vector,which is not conducive to students’ understanding of the connotation of vector.The purpose of this study is to explore the specific situation of students’ vector understanding level under the condition of new curriculum reform.This paper attempts to investigate the change of mathematics understanding level and the development process of concept cognition of high school students in a middle school in Guangzhou when learning vector.At the same time,it analyzes the causes and influencing factors of the differences and tries to find ways to improve teaching.In this study,the investigation method is adopted to understand the actual status quo of students’ vector understanding level,and the "dynamic theory of mathematical understanding level" proposed by Pirie & Kieren’s mathematical model is used to describe the learning process and existing characteristics of vector concept.Through interviews with students and teachers after class,this paper further studies the obstacles in students’ understanding of the concept of learning vector and teachers’ strategies in the teaching process.Through the case analysis of students in answering the relevant questions with different levels of problems and response.At the vector understanding level of students in a middle school in Guangzhou,stratified sampling was used to randomly select students from two classes to issue test papers and retrieve them.According to the basic results of the survey,two students were interviewed as investigation supplement.Test papers and interviews are used to sort out the real process of students’ understanding.The main research tool is the test paper,and the scoring rules are written according to the mathematical understanding model.Finally,SPSSPRO was used for descriptive analysis,normal distribution test,differentiation analysis and correlation analysis.The main conclusions of this paper are as follows: In the teaching process,the characteristics of "global,nonlinear,dynamic and transcendent recursion" of students’ vector understanding level are unified with the Pirie-Kieren mathematical regression model;Chi-square test analysis found that there was no significant correlation between the gender of students and the vector understanding level.Based on the case analysis,it is found that the essence of students’ understanding vector is limited to the concept of the textbook and lacks of re-processing to form their own understanding.Therefore,in-depth teaching should be paid attention to to promote students’ understanding of the concept essence.From the descriptive statistical analysis of the test paper,it can be found that the mean value of students’ vector understanding at level 1 is the highest,while that at level 5 is the lowest,and the application degree of vectors is generally not high.Moreover,in level five,students have the largest gap in understanding vector.At the level one level,the students’ vector understanding level gap is the smallest.This shows that the difference of students’ preparatory knowledge is low and the influence of preparatory knowledge on understanding is not great in teaching.In the aspect of vector application,it is the focus of teachers to show the opposite sex among students.