An Investigation On The Vector Understanding Level Of Senior High School Students

“Mathematical understanding” is the core of international mathematical education.With the development of cognitive psychology research,researchers cast further light on individual mathematical learning process.After China has developed a new outline of high school mathematical outline since 2000,the vector has become an independent chapter,and has been extensively studied for its dual nature in algebra and geometric in the practice of mathematics.More and more mathematical educators began to study the vector and put forward teaching suggestions on applications of vector problem solving through textbooks and curriculums.However,these studies lack the survey of the level of Chinese high school students' comprehension of the vector,and fail to provide the status quo of vector comprehension of high school students in China.This study attempts to classify the level of vector comprehension from the perspective of the three-dimensional goals of the new curriculum,and combine the APOS theory to examine the status of high school students in the vector to understand the level of the level,while putting forward valuable suggestions for the teaching of senior high school teachers.This paper first divides the four levels of vector comprehension through the study of existing literature and related theories,as well as the requirement of vector knowledge of three dimensions of new curriculum: knowledge level,skill level,application level,ideological level.The four levels of vector comprehension include action level,process level,object level,scheme level.And then a test paper is designed to examine the level of high school students' vector comprehension.Secondly,we selected six different levels of high school nearly 550 senior one high school students as a research sample.We conducted a test and interviewed the representative students.Through the statistical analysis of the test results,we obtained the current situation of the high school students' vector comprehension and summarize its deficiencies.The main conclusions are:From the general trend point of view,the level of vector comprehension of high school students showed a decreasing level,in which the ideological level of vector comprehension decreased most significantly.At all levels,the knowledge level and application level performed best.Compared with the different levels of schools,the vector understanding at all levels in key senior high school are higher than ordinary schools,especially in skills level and the ideological level.From the analysis of some students' papers and the contents of the interview,students are mechanized towards memorize the definition of theorems and formulas;Students lack the initiative to use vector methods to solve other problems;Students lack reflection after the solution and lack the ability on constructing vector knowledge framework and incorporating new knowledge into the existing knowledge system.Based on the above conclusions,we put forward suggestions for high school teachers' teaching: The appropriate additional vector teaching section,mainly about the application in other areas and part of vector history content;Using the geometric drawing board and other electronic software properly in teaching,strengthen the students' consciousness of vectors in different symbols;Teachers should sum up the knowledge points in time after the vector teaching and lead students to construct knowledge structure.In this paper,we provide the theoretical and practical support for the teaching of teachers by the investigation on the high school students' status understanding on vector in our country.And this paper also have some reference value for the development of curriculum standards in our country.