Investigation And Analysis Of The Cognitive Level Of High School Students' Flat Vectors

Vector,as one of the most basic concepts in mathematics,has the dual identities of "number" and "shape",and has its unique value in the content of middle school mathematics.The plane vector is closely combined with other mathematics content in middle school,and it has the function of "common method" in solving many mathematical problems.The knowledge of plane vector itself has the characteristics of easy to apply and difficult to understand.Under the new curriculum and key competency concept,it is necessary to understand deeply the level of plane vector cognition of high school students today,and the factors that affect plane vector learning of high school students.For current mathematics,For teaching and learning,it has not only practical significance and application value,but also theoretical research value.With the help of the SOLO classification evaluation theory,this paper uses literature analysis and survey analysis to start from the three dimensions of the basic concept of plane vector,the calculation of plane vector,and the comprehensive application of plane vector.Prepare test papers and questionnaires under the guidance of front-line teachers.In addition,319 students from Harbin No.9 Middle School were selected as the survey objects,and the following work was done based on the students' answers:1.A statistical analysis of the distribution of the level of cognition of plane vector in high school students,the following conclusions are obtained:On the whole,students' cognitive level of plane vector operations is higher than the basic concepts of plane vector and the application of plane vectors.Among them,in the dimension of plane vector operations,the cognitive level of plane vector coordinate operations is higher than that of geometric operations and Cognitive level of algebraic operations;plane vector applies this dimension.The level of cognition of plane vector in physics is higher than that of plane vector and plane geometry.Different grades have different perceptions of plane vectors.It shows that the overall cognitive level of Senior Three is higher than the overall cognitive level of Senior One.The dimension of plane vector application is obviously different.There was no significant difference in the level of planar vector cognition between boys and girls.2.The comprehensive survey results analyze the factors affecting students' planar vector learning as follows:Insufficient understanding of concepts;obfuscation of formula memory;deeper notion of "heavy calculations but light application";insufficient attention to core mathematical literacy;poor learning habits;improper teacher teaching methods3.Propose corresponding suggestions from the perspective of teaching and learning:Suggestions for students to learn flat vectors: focus on the essence of the concept;avoid mechanical memory;pay attention to vector applications;develop learning habits.Suggestions for teachers on flat vector teaching: abstract mathematical concepts from the physical background,attach importance to the process of acquiring knowledge;strengthen the construction of logical thinking processes;strengthen the teaching of vectors in mathematical applications;strengthen the memory of formulas,attach importance to the improvement of computing capabilities;Fusion;strengthen the mastery of ideological methods,focus on the cultivation of core literacy.