Research On Solving The Problem Of Junior High School Function Based On Multi-representation

The knowledge of functions shows its importance in mathematics subject in both junior and senior high school studies.It is regarded as the spine of mathematics in high school period.In other words,the methodology and ideology of functions exist and play significant roles throughout the high school mathematics education.Therefore,it is of certain value and meaning that the knowledge of functions is studied in the teaching activities.In the recent years,studies on multi-representation have gradually brought increasing discussions.This study will focus on the identification of relationships between the multi-presentation of knowledge of functions and problem solving.To begin with,in this study,the existing research outcomes on multi-representation and problem solving by other researchers is reorganized and reviewed,based on which multi-representation are classified as tabular representation,econic representation,literal representation,and symbolic representation in this study.Secondly,questionnaires and tests by students on the current situation of multi-representation and problem solving were conducted.The results show that students are relatively good at converting tabular representation into other representations,while students show weakness on conversion between literal representation and symbolic representation.The students in different schools show extreme differences on multi-representation of knowledge of functions.On the contrary,no significant distinction is observed between students of different genders.In regard to problem solving,half of the students can solve function problems by more than one way.Also,evident differences between schools and genders are both observed on problem solving of functions.In details,the difference between genders is that male students are better than female students on problem solving of functions.It is recognized that there exist connections between the level of student representation ability and the level of students' ability for problem solving of functions.Next,according to the question answering process of students,based on the angle of multi-representation,the influence of multi-representation on problem solving is discussed.Firstly,the ability for representation significantly affects the problem solving of students,a proper representation can facilitate problem solving,and the flexible manipulation of different kinds of representation may contribute to the accuracy of problem solving,thus facilitate problem solving process.In a word,the understanding level of representation in a question will directly impact the realization of successful solution.At last,some recommendations on the aspect of representation preference,multi-representation cultivation,and the teaching and learning of effects of flexible utilization on problem solving are provided in this study.