As an important component of students’ core competencies in mathematics,mathematical representation and transformation skills have received much attention in the world’s mathematics curriculum teaching research,and numerous researchers have confirmed the pedagogical function and value of multiple representations in mathematics through teaching experiments and other methods.Mathematical multiple representations means that for the same mathematical learning object,several different forms of representation can be used to represent.In high school mathematics,the highly formalized mathematical symbols of trigonometric functions and the diversity of their expressions are closely related to multiple representation.Based on this,trying to re-examine the teaching content of trigonometric functions with the relevant theory of mathematical multiple representations as a guide,and explore the instructional design of trigonometric functions in high school mathematics based on the theory of multiple representations,in order to provide some new ideas and experiences for the teaching of trigonometric functions.The research method adopts four methods: literature analysis,interview survey,test method and case analysis.First,we combed through a large amount of literature related to the theory of multiple representations in mathematics and its teaching,and the teaching of trigonometric functions in high school to understand the current status of domestic and international research and analyze the feasibility of the theory of multiple representations to guide the research on the teaching of trigonometric functions.Secondly,in order to grasp the current situation of teaching and learning of trigonometric functions in high school and teachers’ awareness of multiple representation theory,we designed and implemented teacher interview questionnaires and student test papers,and analyzed the results of the survey,and found that the following problems existed in teachers:(1)it is difficult to motivate students to learn by emphasizing the process over the conclusion.(2)focusing on knowledge explanation but neglecting the penetration of mathematical thinking and methods.(3)limited understanding of mathematical multiple representation theory itself,but generally positive attitude toward teaching mathematical multiple representations.The following problems exist on the students’ side:(1)some students have barriers to mathematical operations and lack rigorous logical thinking.(2)single and inflexible problem solving ideas,prone to strategic errors.(3)there are barriers to understanding relevant concepts,poor knowledge understanding,and students’ ability of multiple representations of knowledge is lacking.The innovation lies in the comparative analysis of teaching cases based on multiple representations theory immediately after,combining the principles of multiple representations theory to guide mathematics teaching,and further proposing strategies to improve the teaching of trigonometric functions in high school based on multiple representations theory:(1)focus on the connection and transformation between abstract and concrete representations,and enrich the multiple representations of trigonometric functions knowledge.(2)teaching in the order of contextual representation-operational representation-conceptual representation.(3)combining symbolic and pictorial representations to reduce the cognitive load,and using visual representation techniques reasonably.At the same time,based on the proposed teaching strategy,the teaching design of trigonometric function content is guided by the theory of multiple representations to achieve a deep integration of the two. |