A Study On The Correlation Between High School Students' Multiple Representation Level And Their Ability To Solve Math Application Problems

Multiple representation of mathematics refers to representing the same mathematical object in different ways.It is of great significance for students to understand mathematical knowledge and develop diversified thinking from different directions and angles.Math application questions are an inspection of students'mathematical application consciousness and comprehensive ability,and are an important manifestation of one of the core qualities of mathematics,namely,mathematical modeling quality.In the past,the research on the influencing factors of the ability to solve mathematical application problems mainly focused on reading comprehension and operation skills.In order to explore whether it has correlation with students' multiple representation level,thus providing high school teachers with new teaching ideas to improve students' ability to solve mathematical application problems,this research topic was proposed.This research is mainly carried out from two aspects:literature research and empirical research.In the aspect of literature research,it mainly defines the core concepts of mathematical multiple representations,mathematical application problems,etc.In the aspect of empirical research,taking senior three students as the research object,I designed two sets of examination papers,namely,the multiple representation questionnaire and the mathematics application test paper.Among them,the multiple representation questionnaire takes three main contents of high school mathematics:function,algebra and geometry,probability and statistics as dimensions,and designs six concepts:monotone function,trigonometric function,vector,parabola,probability and expectation.There are four questions in the math application test paper,which are related to six concepts in the multiple representation questionnaire.The problems that this study attempts to explore include:(1)The present situation of high school students'multiple representation level;(2)The differences between the multiple representation levels of different types of students mainly involve gender,class and school;(3)The current situation of high school students' ability to solve mathematics application problems;(4)The differences between different types of students' ability to solve math application problems mainly involve three types:gender,class and school;(5)The relationship between high school students' multiple representation level and their ability to solve mathematical application problems.Through statistical analysis,the following conclusions are drawn:(1)The overall level of high school students' multiple representation is low and lacks richness;(2)There are significant differences in the level of multiple representations between students in ordinary classes and key classes,there are no significant differences between boys and girls,and there are significant differences between students in superior schools and secondary schools;(3)The ability of high school students to solve math application problems is generally biased and needs to be improved;(4)There are significant differences in the ability of students to solve math application problems between ordinary classes and key classes,there are no significant differences in the ability of boys and girls to solve math application problems,and there are significant differences in the ability of students from superior schools and secondary schools to solve math application problems;(5)There is a moderate correlation between high school students' multiple representation level and their ability to solve mathematical application problems,that is,the higher the multiple representation level,the stronger the ability to solve mathematical application problems,and vice yersa.Finally,this study puts forward suggestions to improve the ability of high school students to solve math application problems and teachers to carry out multiple representation teaching,as well as the shortcomings of this study and its future prospects.