The Comprehension Of Vector Of Senior School Students In Shanghai

Vector is the important sections of senior high school mathematical curriculum. Vector has its operational method and system unique to number, and it is closely connected with algebra, geometry and so on.In this paper, the author takes a survey on students' comprehension and application of vector by using questionnaire and interview. 379 senior high school students in Shanghai are involved in this investigation which focuses on the following aspects such as students' comprehension of basic concepts, operation, expression and application.From the survey the author obtain the results:students don't hold the essence of vector, though they seem to be solving problems using vector. They rely on coordinates in nature. The findings show following aspects:1. Students can't comprehend the vector equality by combining direction and modulus of vector. Besides, students just regard the modulus of vector as a formula;2. There are serious confusion between directed line segment and vector. Students make proficiency in calculating coordinates of vector without comprehension of its signification;3. Students are inclined to apply formula mechanically without comprehension of minus, plus and dot product. Students have poor exhibition in picturing;4. Students don't exhibit high willing to solve geometry exercises using vector. Most of students who solve geometry exercises using vector rely on the coordinates of vector.Eight suggestions for teaching, textbooks and teacher education are proposed based on the analysis of students learning:(1) change the sequence; (2) increase the application of vector without using coordinate; (3) encourage students to make more reflection; (4) encourage students to acquire more mathematical thought from the vector teaching; (5) improve students'understanding from instrumental to relational; (6) improve students' memory method; (7) increase teachers' knowledge about vector and linear algebra through in-service training; (8) improve teachers' orientations from calculational to conceptual.