Research On The Concept Of Plane Vector Misconceptions

Plane vector is one of the important and basic concepts in modern mathematics.It has a profound geometric background and is also a must for the college entrance examination in recent years.It occupies an important position in the high school mathematics curriculum.Because of its size and orientation,the combination of numbers and shapes like a semiconductor,the role of the combination of numbers and shapes is self-evident.Therefore,we use it as one of the important tools for studying the content of high school mathematics knowledge.However,due to the abstract nature of the learning of high-level mathematics plane vector knowledge points,many students have deviations and misunderstandings in cognitive and comprehension when learning plane vector concepts.Researchers define the concept of planar vector myth as: students have These concepts are deviated from the scientific concept.This concept has a great impact on the learning of students' mathematical concepts.Therefore,teachers should fully understand the concept of plane vector myths that hinder students' learning before conducting subject teaching,and use reasonable teaching strategies to transform students' myths.Therefore,teachers must adopt some strategies to explore the hidden myths in the minds of students.The two-stage diagnostic test,which is widely used by scholars at home and abroad in the fields of physics and chemistry,is the mainstream method of mythological concept diagnosis,but it is extremely rare in the field of mathematics.To this end,this paper attempts to explore the mythological concept of students in the process of plane vector content learning by using two-stage diagnostic tools,and analyzes the reasons for its formation.Based on this,it explores the teaching strategy of effectively transforming the concept of plane vector myth.It provides inspiration for teachers to carry out effective teaching of plane vectors.On this basis,the author determined that the research topic of this paper is "the investigation and study of the concept of plane vector myth",and carried out several aspects of work.First,collect a large number of research literatures that are closely related to this concept,and clarify the research direction according to the current research status in China.The following two theories are used as the theoretical basis of this study: cognitive development theory and APOS theory.Second,based on the design process of the two-stage questionnaire in Chergst,a two-stage questionnaire for this concept was prepared.The mythical concept formed by students in the process of plane vector learning is examined.With the help of the data analysis system spss19.0,the results of the questionnaire survey are analyzed.It is concluded that the high school and high school students hold the following myths in the study of plane vector:(1)If the two vectors are equal,their starting point and ending point are the same;(2)The vector is a directed line segment,and the directed line segment is a vector;(3)The collinear vectors are the lines where the vectors are aligned.(4)If a//b,b//c,then a//c;(5)Parallel vectors refer to two vectors that are parallel to each other.(6)Zero multiplies any vector is zero.(7)From a·b=a·c(a?0)to b=c;(8)(a·b)·c=a(b·c);(9)Any two nonzero vectors can be used as a set of bases of plane vectors.(10)The projection of a vector on another one is non-negative number.(11)The projection of a vector on another one is still a vector.(12)The angle between two vectors in a straight line is the angle between two vectors.(13)If nonzero vector a·b<0,then the angle between a and b is an obtuse.(14)A quantity with a positive or negative difference is a vector.(15)The direction of a unit vector is uncertain.(16)The coefficient of the base is the coordinate of the vector.(17)Only two vectors that are connected to the first and the end can be added.Thirdly,combined with the results of the two-stage questionnaire,the author summarizes the reasons for the existence of the concept of plane vector myth instudents: the abstraction of the concept itself,the student's thinking mode,the lack of students' active construction of knowledge and the pre-student concept.Impact.Fourthly,according to the formation of the concept of student plane vector myth,three teaching strategies,such as concept map strategy,contrast teaching strategy and APOS theory,are proposed to transform the concept of student plane vectormyth.