The Investigate Of The Vector Knowledge Cognition Of High School Students Based On Representation

Vector is an object which has both size and direction,and it is an important bridge in algebra,geometry and trigonometric function.It is significant to understand the cognitive situation of high school students' plane vector knowledge for improving teaching.The knowledge of plane vector can be divided into three parts: vector concept,vector operation and vector application in high school.From the perspective of representation,we focus on three representations of vector which are geometrical,coordinate and algebraic symbol.Based the perspective of representation,this article surveyed the cognition of high school students' knowledge of plane vector by the method of quantitative analysis.Subjects in the study are 270 students of grade 2 from provincial key high school,the city priority high school and the key county high school.Specific research results are as follows:1.The cognitive level of high school students on vector knowledgeIn this part,the author established individually evaluation standard from level1 to level 5 according to the SOLO theory.(1)The cognitive level of vector concept: under the geometric representation,the quantity of students who get the level 4 is largest,the understanding of vector concept is limited by the special points for these students.Under the coordinate representation,the quantity of students who get the level 3 is largest,students can understand the concept of vector by size and direction,but they can't use coordinate to represent it.Students' cognition under geometric representation is better than the cognition under coordinate representation.(2)The cognitive level of vector operation: under the coordinate representation,the quantity of students who get the level 2 is largest.Under the geometric representation,the quantity of students who get the level 3 is largest.Under the algebraic symbol representation,the quantity of students who get the level 2 is largest.Under the three representations,students can't operate flexibly;the understanding of the vector operation is not enough thorough;ability is required to solve the more abstract vector operation.Students' cognition under the coordinate representation is better than the cognition under geometric representation,students' cognition under the geometric representation is better than the cognition under algebraic symbol representation.(3)The cognitive level of vector application: the quantity of students who get the level 2 is largest under algebraic symbol and coordinate representation.Under the two representations,students have the consciousness of solving the problem of plane geometry by vector,but it is difficult to set up corresponding relations between the geometric elements and vector.Students' cognition under algebraic symbol representation is better than the cognition under coordinate representation.In study of cognitive level of students' vector knowledge,the students' cognition in provincial key high school is higher than those in city priority high school,the students' cognition in city priority high school is higher than those in key county high school.2.The transformation among representationsStudents aren't flexible in transformation of representation.The situation of transforming from algebraic symbol representation to coordinate representation is better than the situation from coordinate to algebraic symbol for students;the situation of transforming from algebraic symbol representation to geometric representation is better than the situation from geometric to algebraic symbol for students;the situation of transforming from geometric representation to coordinate representation is better than the situation from coordinate to geometric for students.3.The answer situation of vector's representation typesMost students can only answer one or two of the three representations whichever school they are in.The innovation of this article: From representation,the author surveyed cognitive level of vector,transformation of representation,and types of vector representation,so we can learn students' cognition from these.And author maked some teaching suggestions,according to the results of the study.