The Study Of The Present Situation Of High School Students' Understanding And Application Of Symbolic-graphic Combination

Symbolic-graphic combination is one of the common thought methods in mathematics.It has been widely used in mathematics teaching and plays an important role in the formation and development of students' mathematical literacy.The Visual Imagination Literacy proposed in the Mathematics Curriculum Standards for Senior High Schools(2017 edition)has different level requirements for the combination of symbolic-graphic combination in thinking and expression.However,in recent years,the research on symbolic-graphic combination has mostly focused on problem solving and teaching.However,there are few studies on students' thought level of symbolic-graphic combination.This study will be based on the Chinese mathematics curriculum standards since the 20 th century,representation theory and related literatures to give a concrete analysis framework,and analyze high school students' understanding and application of symbolic-graphic combination from three dimensions: connotation,type and level.From Representation Theory,symbolic-graphic combination embodies the communication and transformation between algebraic representation and geometric representation.There are two levels of transformation mode: representation correspondence type and representation construction type.Through the content analysis method,the requirements for symbolic-graphic combination in each academic period are explicit,draw on the experience of the division of representation ability level in German Mathematics Curriculum Standard,the level performance of high school students' symbolic-graphic combination is given.Through questionnaires,interviews and content analysis,the following aspects are studied: senior high school students' understanding of symbolic-graphic combination;senior high school students' application of symbolic-graphic combination;Compare the comprehension and application of symbolic-graphic combination among students of different grades.Through the research,it is found that senior high school students have a one-sided understanding of the ideological meaning of symbolic-graphic combination,and more than 60% of them regard it as "from symbol to graph",lacking the consciousness of "from graph to symbol".Most of the students' understanding of the ideological role of symbolic-graphic combination is from the perspective of problem solving,and very few mention its role in the development of thinking.High school students' ideological level of symbolic-graphic combination is concentrated in level 1 and level 2,and the number of people in level 1 who reach the two-way communication between symbol and graph is higher than that in level 2.High school students are weak in the "from symbol to graph" problem of constructing geometric representation,and better in the problem of "from graph to symbol".Senior two students have a more comprehensive understanding of symbolic-graphic combination than senior three students.Nearly 80% of senior three students regard symbolic-graphic combination as a tool to help solve problems,and use the intuition of graphics to help understand problems.However,in Level 2,the ratio of symbol and graph two-way communication among Senior Three students is higher than that of Senior Two students,which shows that with the increase of grade,students' ability to use symbolic-graphic combination is also gradually improved.