Research On Plane Vector Teaching Based On Multivariate Representation Theory

Plane vectors are an important part of mathematics,with profound mathematical connotation and rich physical background,and with the dual property of "number and shape".However,due to the abstract nature of plane vectors,some students have difficulties in learning plane vectors,and often fail to achieve the desired learning effect.Multiple representations refer to the use of graphics,images,actions,situations,physical aids,words,language,symbols,and other forms to interpret the basic features of the same object.Applying multiple representations in mathematics teaching can better present diverse information to students and help them understand the nature and connotation of mathematical objects.The fact that plane vectors themselves have rich representations provides the possibility of using multiple representations theory to optimize plane vector teaching.Therefore,how to apply multiple representations in teaching plane vectors has certain research significance.The research methods used in this paper include literature research method,questionnaire survey method,and interview method.Firstly,we analyze the theory of multiple representations and its application in mathematics teaching,plane vector teaching,and the theoretical basis of multiple representations in an overview to form a scientific understanding of this study;then,the author explores the current situation of plane vector learning from students' perspective through the form of test papers,and understands the cognition,understanding and application of multiple representation theory by high school teachers through interviews,so as to provide a basis for the later paper on multiple representation teaching strategies.The test was administered to students to find out the students' knowledge,understanding,and application of multiple representation theory.Through the test on students,we found that: students' mastery of vector representations was not satisfactory;they could not achieve flexible conversion between algebraic,geometric and coordinate representations;their understanding of vector concepts and operations was weak;they could not integrate multiple representations of vectors on the basis of conversion,and their ability to use three representations of vectors to solve comprehensive application problems was weak.Through interviews with teachers,we found that: most teachers have not formed a scientific cognition of the theory of multiple representations,and their learning of the theory needs to be further strengthened;teachers generally recognize the value of the theory of multiple representations,but the application of multiple representations in the teaching of plane vectors is not satisfactory;teachers are not fully aware of the importance of tapping the representational forms of plane vectors;if the design of multiple representations is not appropriate in teaching,it will make teaching deviates,and certain teaching principles should be followed;teachers encounter both external and internal resistance when they try to use multiple representations theory in teaching plane vectors,and the sources of resistance mainly include: teachers' own insufficient understanding of the theory,students' poor cooperation and easy deviation from the classroom,so effective teaching strategies need to be applied.Finally,in response to the problems found in the survey and research,the teaching principles are analyzed in depth based on multiple representations theory;the teaching strategies are proposed: information attention strategy,representation information diversification strategy,multiple connection dynamization strategy,scaffolding teaching strategy,variation teaching strategy,and graphic organizer strategy.And under the guidance of the teaching principles of multiple representations and according to the teaching strategies,three teaching cases of plane vector content are designed.