Research On Teaching Practice Of Junior High School Function Based On Multivariate Representation

Function is an important concept of modern mathematics and one of the important contents of junior high school mathematics.Also it's the basis of learning high school mathematics and even higher mathematics.However,due to the high degree of abstraction and comprehensiveness,the function content has always been the difficulty of the students in study.How to improve the students' understanding and applying of the function has always been the thinking problem of mathematics education researchers and first-line mathematics teachers.Through the literature review,the author finds that the researchers have studied the function teaching from different angles,and provided many teaching strategies for improving the function teaching.This research through literature review,test questionnaire programming,and then analyzing it,so as to put forward the teaching strategies of function multi-representations,based on this,it carries on teaching design and teaching experiment.Specifically,this paper covers the research of both investigation and practice two aspects.Firstly,taking an ordinary junior middle school in Changzhou as an example,this paper chooses all the Junior students as the research object,and investigates the students from the two dimensions of function basic knowledge and function representation.The results of the survey show that:(1)Junior students have no good overall mastery of the function,especially that students' understanding of the function concept is in low level;(2)Junior students have biases in the choices of the three representations of the function.Whether the top students,the middle students or the poor students,they all are biased towards symbolic characterization,followed by figure representation,and finally table representation in problem solving;(3)Junior students have some difficulty in transformations among the the function representations,especially,in transformation from image representation to symbolic representation,not know how to deal with the image information,the conversion capacity between representations needs to be strengthened.Secondly,the function itself has a rich form of representation,which is closely related to the multivariate representation theory.Therefore,based on multiple representation,this paper puts forward teaching strategies of the junior school function:(1)Set up the circumstances of multi-representations,including:situational representation include "analytic expression,figure and table";strategy of combining" listening,speaking,looking,and writing";(2)Promote students to transform the multi-representations of the function,including:strategy of representation of sequence design;strategy of combining numbers and images;strategy of variant teaching;strategy of scaffolding.Based on the above teaching strategies,this paper carries on the teaching design of quadratic function,and selects two classes of Grade Three to carry on teaching experimental research.Discussing students' leaning effect of quadratic function from the teaching design,classroom observation,after-school test three aspects,the experiment results show that:compared with usual teaching strategies,the implementation of the function multiple representations teaching strategy can significantly improve the student's learning effect in the teaching of quadratic function.On the basis of investigating the status quo of junior high school function teaching,this paper puts forward the function teaching strategies based on multivariate representation and the strategies are validated by teaching experiment,which provides some reference for improving the function teaching of junior high school.