Research On Typical Mistakes And Attribution Of High School Students' Space Vector And Three-Dimensional Geometry

With the advance of the new curriculum reform, space vector has gradually blended in with the three-dimensional geometry courses and received unprecedented attentions,but students'learning and application still have many problems. This research tries to find out some typical mistakes and the attribution in students'space vector learning to show the current situation of high school space vector teaching, with a view to provide some references for teachers'teaching.The focus of this study is on some typical mistakes and the attribution of the science students form senior 2, who have finished their high-school space vector learning. Based on the documents analysis, classroom observation and students'homework, the author finds out the mistakes and then works out the test with relevant data. The test is carried out through 310 students from three different levels of schools in Chongqing, Sichuan, Shanxi. Then the author makes the attributive analysis according to the test results and students'interview.Investigation results show typical mistakes in students'learning which are as follows:1. Most students can not understand the geometric meaning of scalar multiplication very good, and are easily to confuse the concept with some other related ones.2.Though students say that they have no problems in understanding the linear operations which coordinates with the comprehensive strong and the graphic elements relationship in more complex tasks in the more clear titles, they are prone to make vector coordinate mistakes or space cartesian coordinate system errors.3.Student's drawing ability and the analysis and problem solving ability are not strong; they tend to ignore subJective operating question; most students have the wrong idea that "they do not have to practice the type of titles if the university entrance exam does not test". 4.When using vector to prove the position relations of line and plane, students are easily to imagine false arguments subJectively, or will not prove the conclusion as conditions.5.By using vector method to solve problems related to space angle, the author finds that students do not often overall examine the title, or only examine the topic with a "blind eye", not aware the amount that is asked. When using vector method in line and plane angle, they are not clear about the ideas and apply the formula mechanically; they can not adopt the right method and appreciate the vector method improperly.Most of these mistakes belong to the knowledge type and strategical one. The former is due to concept confusion or vague concept; the latter is attributed to the one-sided understanding of the title, which leads to the ignorance of the right mathematical model. Certainly, there are still some other types of errors that belong to logical one and psychology one.Besides, the change of textbooks makes students'mappig capacity obviously improved; the average student is more inclined to use vector method solving three-dimensional geometry problems than the good student.Based on the above research conclusion, the author puts forward some related proposals for space vector teaching.