The Influence Of Senior High School Students' Mathematical Multiple Representation On Problem Solving

Mathematical multiple representation is to represent mathematical knowledge and mathematical problems from different angles and ways.In recent years,multiple representation of mathematics is a hot topic in mathematics education.There are many articles about the influence of multiple representation of problems on problem-solving.The main purpose of their research is to cultivate students' awareness of multiple representation through multiple representation of mathematical problems,so as to improve students' ability to solve problems.In fact,most of the mathematical problems come from the deformation of mathematical knowledge If students can make multiple representations of mathematical knowledge,they will consciously make multiple representations when solving problems.However,there are few researches on the influence of multiple representations of mathematical knowledge on problem solving.In this study,students are required to have multiple representations of knowledge,so their cognitive structure is relatively complete and their problem-solving ability is relatively mature.This paper mainly studies the effect of multiple representation of mathematical knowledge on problem solving.How about high school students' multiple representation of mathematical knowledge?How does the mastery of the levels,richness and connections of multiple representations of students' knowledge affect the accuracy of students' problem-solving,the richness of problem-solving methods and the selection of problem-solving methods?In this paper,through the questionnaire test method,we will get the situation of high school students' multiple representation and problem-solving of mathematical knowledge.With the help of Excel and SPSS software,we will make qualitative and qualitative analysis on the richness of students' knowledge representation and the level of representation content,the relationship of multiple representation of problems,the accuracy in the process of problem-solving,the diversity of solution methods and the correlation between them Quantitative analysis.The following conclusions can be drawn from the data:1.Most of the senior high school students tend to have multiple representations of knowledge,and a few of them have a single representation;2.The influence of multiple representation richness on problem solving:the richness of multiple representation is positively related to the accuracy of problem solving to a certain extent;and the richness of multiple representation is positively related to the diversity of problem solving methods to a certain extent.3.The influence of multiple representation level on problem solving:the higher the level of multiple representation of knowledge,the higher the accuracy of problem solving.Especially for the students of knowledge unit representation is more obvious,but some students' knowledge multiple representation types are rich but the level is low,and the accuracy of such students' problem analysis and solution is not as high as the students of low richness but high level.Different representations of knowledge will affect students' choice of problem-solving methods.4.If students have multiple representations of knowledge and understand the relationship between them,then it is easier and more diverse for them to transform the various conditions of the problem when solving the problem.The higher the accuracy of solving the problem,the more diverse the methods.However,if students can't understand the relationship between the elements,there may be cognitive load problem.At this time,the accuracy of students'problem-solving is not as good as that of students with low abundance.Therefore,multiple representation of knowledge has a positive impact on problem-solving to a certain extent.