Research On Senior High School Students’ Cognitive Level Of The Plane Vector

Vector is one of the most basic concepts in modern mathematics. It catches the attention of mathematics curriculum reform as a bridge of algebra and geometry, and is widely used. Many developed countries have added the vector content in middle school mathematics in the middle of the 20th century. Vector is also the important content of high school mathematics in the new round of reform of mathematics in China. "The mathematics curriculum standards for common senior high schools (trail)" has made detailed requirements of the plane vector content in required textbook 4, and adjusted the previous versions a lot. Under this background, getting to know the situation of students’plane vector learning may help to give suggestions on the content of the vector in the teaching material and teachers’teaching.This study focuses on the level and problems of the high school students’learning of the plane vector by using literature analysis and questionnaire survey. On the basis of "the Mathematics Curriculum Standards for Common Senior High Schools (trial)", the author worked out the test paper after collecting literature, analyzing curriculum standards and textbooks, and consulting high school teachers, and take 366 senior students(184 of grade 11,182 of grade 12) in Chongqing as survey respondents. Based on these answers, the author completed two following works:1. The author analyzes the students’answers based on the SOLO mold, and get the cognitive level of plane vector knowledge of high school students.(1) Cognitive level of plane vector concept:47.3% of the students get to level R-3, grade 11 (46.2%), grade 12 (48.4%).22.7% of students reach level 4, grade 11 (22.3%), grade 12 (23.1%). Cognitive level of the plane vector concept of students in different schools has a certain gap, but the gap is not obvious.(2) Cognitive level of Plane vector operationCognitive level of Geometry operation:52.7% of the students gets to level R-3, grade 11 (51.1%), grade 12 (54.4%).19.7% of students reach level 4, grade 11 (18.5%), grade 12 (20.9%). Cognitive level of Coordinate operation is better:58.5% of the students get to level R-3, grade 11 (57.1%), grade 12 (59.9%).28.4% of students reach level 4, grade 11 (26.6%), grade 12 (30.2%). Cognitive level of algebraic operation is poor:46.7% of the students get to level R-3, grade 11 (45.1%), grade 12 (48.4%). 17.5% of students reach level 4, grade 11 (16.3%), grade 12 (18.7%). On the three operations of E -4 levels, key middle school students are significantly better than the ordinary middle school students.(3) Cognitive level of the plane vector application is poor:42.6% of the students get to level R-3, grade 11 (39.2%), grade 12 (46.2%). Only 12.6% of the students, grade 11 (11.4%), grade 12 (13.7%), reach level E-4. On the application of R-3, E-4 levels, key middle school students are significantly better than the ordinary middle school students.On the whole, the students’awareness of plane vector operation level is higher than that of plane vector concept and plane vector application, and the cognitive level of vector application is significantly lower than others. Cognitive level of the coordinate operation is the highest among the three kinds operations of plane vector, and then followed by geometric operation and algebra operation. Students tend to attach great importance to the coordinate operation, despising algebraic operation, and attach great importance to the operation, despising application.Cognitive level of plane vector application of grade 12 is obviously higher than that of grade 11. And cognitive level of plane vector operation of grade 12 is slightly higher than that of grade 11. While of the plane vector concept, grade 12 is almost the same with grade 112. Finding out the main problems of high school students in plane vector learning, analyzing reasons and making corresponding teaching suggestions.