A Teaching Case Study On The Concept Of High School Function From The Perspective Of Multivariate Representation

With the continuous development and perfection of the theory of multiple representations in cognitive psychology,the theory of multivariate representation has attracted the attention and attention of international mathematics Education Psychology,and in recent years,it has been classified as the main content of the curriculum standard in many countries that the teaching of multiple representations and the cultivation of students ' pluralistic representation ability.function is one of the core concepts in middle school mathematics,and the function thought runs through high school mathematics.The rich pluralism of function concept representation and the theory of multivariate representation have a natural connection,which is a powerful material for the application of multivariate representation theory in teaching practice,and the theory of multiple representations provides new ideas and methods for the teaching and learning of function concept.In this study,the method of literature through the study of mathematical multivariate representation theory and function concept and relevant literature of teaching,it is concluded that the teaching of function concept in the view of multivariate representation should grasp the following four key aspects;(1)Paying full attention to the necessary cohesion and integration of the new concept and the students 'knowledge experience.(2)To help students establish the plural representation form of function concept by enriching examples.(3)The "connection" between different representation forms should be embodied in teaching.(4)Teaching should help students identify and familiar with different forms of representation,and can be transformed according to needs to achieve the same concept of different representations of the integration of the form.Combined with the above theoretical research,the comprehensive use of classroom observation method,questionnaire and interview method,this paper analyzes the present situation and existing problems of the students 'understanding of the pluralistic representation of function concept,analyses the status quo of senior middle school mathematics teachers about function concept and teaching,and establishes the cognitive model of multivariate representation learning of function concept(see figure 4);According to the cognitive model,from the learning stage of function concept,the representation level of function concept,in the course of classroom teaching,three dimensions are implemented,the teaching of function concept is analyzed,and the basic frame of the teaching case is established(see Figure 5),combining the teaching material,the analysis of the study situation,the goal of the education and the difficulty,the specific teaching case is formulated.This paper illustrates the case from the theoretical basis and the concrete operation,and uses the classroom experiment method combined with the result of the investigation to analyze and study the effect of the case,to reflect and improve the problems and deficiencies in the case.Studies have found that using the theory of multivariate representation to guide the teaching of function concept,using various representation forms to carry out function examples can effectively connect students ' existing cognition,and make full use of the differences between different representations to create cognitive conflict,which can impel students to realize the active transformation of cognition,so that the development of students ' thinking will be implemented.