Research On A Learning Progression Of Vector Operation Based On Mathematical Operation Literacy

Vector is the bridge between geometry and algebra,and operation is the soul of vector,constructing the learning progression of vector operation is a good strategy to enhance the accomplishment of mathematical operation.Through literature research,observation and written material analysis,based on the standard of ordinary high school mathematics curriculum,we constructed a hypothetical learning progression of vector operation based on mathematical operation literacy.Based on vector operation of a hypothetical learning progression,we used the questionnaire survey method,selected test contents,compiled test questionnaire,selected the class to proceed test pretest,the test questionnaire has good reliability and effective,then we randomly selected two science classes in the second year of senior high school in No.12 Middle School of Wuhu as the research objects,used SPSS24.0 software for statistical analysis of questionnaire data,and find that there is a significant positive correlation between dimensions and levels of learning progression of vector operation.The lower level of vector operation affects the higher level of vector operation.On the basis of statistical analysis,we revised the learning progression of vector operation,adjust the order of the two stages,from the longitudinal view,our learning progression included two dimensions which are "static operation view of vector" and "dynamic operation view of vector",and divided into "knowledge preparation","knowledge understanding","knowledge fusion","knowledge transfer" and "knowledge innovation" five levels.It contained ten steps: " perceptive vector operation","preliminary linear operation","initial dot product operation","primary coordinate operation","concatenate coordinate operation","joint vector operation","comprehensive coordinate operation","flexible vector operation","procedural coordinate operation" and "ingenious vector operation";horizontally,this learning progression includes four aspects: learning performance,learning blind spot,task type and teaching strategy.Accordingly,we put forward the following suggestions for senior high school students,senior high school math teachers,teaching and learning about vector operation: we hope that senior high school students understand vector operation rules,master vector coordinate operation and form the static operation view of vector;besides,students should construct coordinate operation procedure,synthesize vector operation methods and transform the dynamic operation view of vector.We propose that the high school mathematics teachers locate the dimension of students,point to the level,analyze the mystery,answer the questions and solve the doubts;in addition to this,teachers can help whole students reach from the static operation view to dynamic operation view of vector,and guide each student to operate well step by step.We suggest that the teaching and learning of vector operation should build on the physical background,consider the collinear situation,to move from "knowledge preparation" to "knowledge understanding";clarify algebraic representation,clear geometric meaning,to move from "knowledge understanding" to "knowledge fusion";identify the types of operation,sort out the ideas of transformation,to move from "knowledge fusion" to "knowledge transfer";analyze the characteristics of problems,choose appropriate methods,to move from "knowledge transfer" to "knowledge innovation";add vector dimension,synthesize operation program,to step from low order to high order at the "knowledge innovation" level.