A Study On The Teaching And Practice Of High School Mathematics Based On The Theory Of Multiple Representations

As pointed out in China’s General High School Mathematics Curriculum Standards(revised in 2017 and 2020),plane vectors are an important part of the four main lines of the high school mathematics curriculum,namely "geometry and algebra",and are a bridge between geometry and algebra.It is also a good vehicle for enhancing students’ core mathematical literacy.A large body of research has shown that the theory of multiple representations has a rich educational value,and that teachers can help students grasp the essence of mathematics by choosing the right form of representation for mathematical objects.Through the investigation of the current situation of plane vector teaching,it is found that students’ learning of plane vectors is related to teachers’ representations,but few teachers can give full play to the educational value of multiple representations theory in teaching.Based on this,it is necessary to study in depth and systematically how to organically combine multiple representations theory with plane vector teaching in order to improve the quality of teaching.In this study,a plane vector teaching model based on multiple representation theory was built by combining theory with practice."Basic theorem of plane vector" and "dot product of vector",which showed the biggest problems in the investigation of teaching status,were taken as examples to carry out relevant teaching experiments in practical teaching.Through the comparative analysis of the reference class and the experimental class,the following conclusions are drawn:(1)Based on the "dual identity" of plane vector algebra and geometry,it contains abundant multiple representation forms,which can be innovatively integrated into the theory of multiple representation in the classroom teaching of plane vector;(2)Finding the right entry point of knowledge in practical teaching for multiple representation,enrich the form of presentation of knowledge,can promote students to in-depth processing of knowledge from multiple perspectives,and then establish a complete and solid knowledge system;(3)Mathematics teaching based on multiple representation theory can well stimulate students’ interest in learning,effectively solve students’ learning difficulties,reduce ineffective cognitive load,and improve students’ understanding of mathematics knowledge.Finally,based on theoretical and practical research,the following countermeasures for teaching mathematics based on the theory of multiple representations are summarized:(1)pay attention to the value of educating people under multiple representations,and implement the fundamental task of establishing moral education;(2)pay attention to the effective representation of situations and problems,and improve students’ core literacy in mathematics;(3)strengthen the translation and integration between multiple representations,and promote the development of students’ innovative thinking;(4)pay attention to the multiple representations of concepts,and promote students to grasp the essence of mathematics;(5)pay attention to the choice of the form of representation and follow the law of students’ cognitive development;(6)attach importance to the deep integration of information technology and mathematics classrooms to improve the effectiveness of multiple representations;(7)pay attention to the connection between mathematics and life and find the right entry point for multiple representations.