The Investigation Of The High School Students Vector Understanding Level

Since the20th century, the mathematical understanding has become another hot topic of today’s mathematics education research. With the continuous progress of curriculum reform, the vector has been become teaching content of the high school mathematics in many countries.The full-time ordinary senior high school mathematics curriculum issued by China in1996provided "plane vector" as a compulsory and space vector as a way to deal with spatial geomety problem, since then,the vector officially entered our high school mathematics curriculum."Ordinary High School Mathematics Curriculum Standards (Experimental)" promulgated by the Ministry of Education in2003set the plane vector in the compulsory module4and space vector in elective series2-1. Now the vector has become an important part of the high school mathematics, but how do the high school students understand it? It became a concern of high school teachers that how to design and implement teaching and to select teaching strategies according to the students’understanding.In this paper, the APOS theory as the base, the concept of vector as the carrier, the author surveyed289high school students and three mathematics teachers in Yangzhou city. Specific research questions include:(1)To survey high school students understanding of the vector;(2)To explore the reasons for students to achieve a certain level of understanding;(3)To base on the students’ level of understanding,what is the effective teaching and learning strategies.The author analyzes the survey data,found that:(1)Understanding of the operational phase on the vector, the survey find that67.53%of grade one students is excellent, the students surveyed are more than qualified;38.21%of grade three is excellent,45.75%of students is good. The two-year students have basically reached the conventional level of the operational phase of the vector. The students basically are able to judge the vector, can understand the essential difference between the physical vector and scalar.(2)Students’ understanding of the various types of vector are difference. In the inspection process, students are easy to overlook the consideration of the zero vector, and lack the classification discuss in the habit of thinking.(3)Students’ understanding of the transformation between the vector form is some one-way. The form of images into symbols or in the form of coordinates and symbols and the coordinate transformation between are easy, but more difficult to solve the problem for the image format conversion from symbolic form.(4)Grade three students are more flexibility in the use of vector kownledge to solve problems than grade one students. But from the kownledge network,the contents of the two grades are not enough rich, and don’t show the linear growth of the grades; The main link is under the concept,lack of link about parallel concept.Combined with the results of this study, the author proposes some teaching requirements:(1)To enrich emotional experience,intuitively understand the concept;(2)To understand the concept of multiple representations;(3) To pay attention to strengthening the link between knowledge points.And to put forward two suggestions for normal students education:(1) With the accumulation of expertise, be attention to the understanding of concepts in elementary mathematics;(2)To guide the normal school students to carry out the reseach study,and consciously improve the level of understanding of elementary mathematical kownledge.