Investigation And Research On CPFS Structure Of Planar Vector For Junior High School Students

Vector is one of the important and basic mathematical concepts in modern mathematics,it is a tool for communicating algebra and geometry,and it is also the meeting point of mathematical knowledge such as "triangulation function" and "analytical geometry" in middle school mathematics.However,in the actual teaching,students do not understand the concept of vector,and they lack of a complete concept system in their mind.In the conceptual application,there is a general phenomenon that they don't know how to start if it is a different way or angle.The same as the proposition.The process of mathematics learning is essentially the process of the formation,development and perfection of the mathematical cognitive structure,and the CPFS structure,an excellent and perfect mathematical cognitive structure,is an important way to solve the above-mentioned phenomenon.Most of the existing plane vector surveys are conducted from the perspectives of SOLO Theory,APOS theory and representation theory,while the plane vector surveys conducted from the perspective of CPFS structure is vacant.Therefore,this paper combines CPFS structure theory to investigate the learning of plane vector by the students of grade two in senior high school.The study is based on the requirements of Senior High School Mathematics Curriculum Standard and the four compulsory textbooks of Senior High School Mathematics People's education edition,combining the concept field,concept system,proposition field and proposition system of plane vector,using the CPFS structure detection method of goal recall,node connection and recognition reasoning,to develop a plane vector CPFS structure test to test the CPFS structure of plane vector of 366 high school students in grade two.It will have a quantitative analysis of the CPFS structure by using SPSS17.0 software and Excel 2013 and have a the qualitative analysis based on the students' act the CPFS structure present situation ual answers.Through these analysis to has a quite objective assurance to present situation of the CPFS structure.In this paper,we will analyze the reasons of the current situation of the CPFS structure by means of the questionnaire survey of students' plane vector learning and teacher interviews,And finally it will put forward some suggestions on how to optimize and perfect the CPFS structure by combining the relevant theories of the CPFS structure.According to the investigation,the current situation of the plane vector CPFS structure of senior high school students in grade 2 is as follows:(1)The construction of the plane vector CPFS structure is not ideal on the whole,Only 16.12% of the students' plane vector CPFS structure is good,and 63.93% of the students are medium,19.95% of the students are poor.(2)87.70% of the students know the definition of vector,but only 33.61% of the students really understand it.And only 8.74% of the students know all the expressions of vector,most of them can only master one of the expressions of vector,and they can't form a good concept field of plane vector.In terms of the number of concept reserves,63.66% of the students are in the middle level of CPFS structure,while the number of concept reserves is large,only 18.31% of the students are in the excellent level,most students do not form a good concept system of plane vector.86.88% of the students can transform the vector vertically to form a good proposition field,but most of them can not form a good proposition field of the common line theorem and the basic theorem of plane vector.Students have a serious mind-set in the application of concepts and propositions.Their thinking is not divergent enough.And they have not been able to extract the relevant knowledge from different angles,channels and efficiently to analyze and solve the problems.They have not formed a good propositional system and perfect thinking system.(3)There is no significant difference between male and female students in the construction of CPFS,and gender is not an influential factor in constructing CPFS.In terms of subjects,the construction of plane vector CPFS.of science students is better than that of arts students.subject has a significant effect on the construction of Planar Vector CPFS.From the analysis of different grades,it is found that grades have a significant effect on the construction of plane vector CPFS.The better the students' scores in peacetime,the better the construction of plane vector CPFS.Analyzing the reasons for the formation of the CPFS structure of students' plane vector from the aspects of students and teachers: Students are not interested in plane vector learning,they lack the construction of plane vector cognitive structure,and do not take seriously of the study of concept and the application of knowledge.They are used to remembering knowledge by the way of doing exercises.Their learning methods are old and lack of integration of knowledge.However,teachers take the college entrance examination as a baton too much.They do not pay attention to concept teaching and knowledge sorting,and fail to use teaching resources reasonably and effectively to promote the construction of students' CPFS structure.Based on this,the suggestions for plane vector teaching are as follows:(1)Attaching importance to the teaching of vector concept and enriching students' vector concept domain;(2)Strengthening the connection of concepts.;(3)Skillfully setting problem clusters and building bridges between propositions;(4)Attaching importance to variant training and highlighting the connection between concepts and propositions;(5)Using various teaching methods and appropriating use of modern information technology;(6)Strengthening the application of vector;(7)Paying attention to students' self-exploration and promote students' self-construction of knowledge network;(8)Playing the role of concept map and constructing an ordered cognitive structure.