A Study On The Levels Of Students' Mathematical Symbol Sense In Compulsory Education

The education significance of mathematical symbols is that it transcends symbolic things that it expresses,which releases maths from the shackles of cumbersome expression of words and language,and thus mathematics in the real sense,has become the “Language” of conveying thoughts.At the stage of compulsory education,the children' thinking begins to gradually shift from image thinking to abstract thinking,and the transformation process of thinking is the epitome of the formation and development of mathematical symbols.The mathematical symbols and its meaning students learn at this stage will become the sign of Understanding of mathematics essence and the important foundation of mathematics study later,it is the premise of learning mathematics better.Only through mastering the most basic and simplest mathematical symbols can they reason,think and express better.1990,Hilbert said in his mathematical problems: “the math symbols are text graphics,and the geometry is a graphical formula;Any mathematician can not lack these graphical formulas,just as they have to apply the operation of adding or removing brackets or other analytical symbols in the mathematics operation.” Since the 20 th century,Hilbert formalism mathematical philosophy is popular around the world,and mathematical formalization has become the mainstream in mathematics research now.Today,all the rigorous mathematics,are represented by the formal mathematical symbols.Most of the ancient mathematics were written in natural languages,then gradually letters,graphics and equations were used.This is because the mathematical symbols are unlike natural languages with no obvious ambiguity,and it is an important way to improve mathematical certainty,providing guarantee to grasp the essence of math from the perspective of the universality and profundity for scientific thinking.In mathematics learning,therefore,mathematical symbols impress people with the sense of icy charm,we should feel more about hot connotation behind formalized symbols.Symbol sense was written into our mathematics curriculum standard in compulsory education in 2011,so the research on the cultivation of mathematical symbol sense is lagging behind.Because education philosophy from knowledge-based to people-oriented and developing the students' consciousness of symbols has become a primary and secondary school mathematics curriculum goals.It is the core mathematical competencies during stage of compulsory education in China,and it also reflects the logic of mathematics and students' cognitive level.On former researches,there are not many researches about the level of development ofstudents' mathematical symbol sense within the entire stage of compulsory education.In mathematics education,systematic empirical research on the mathematical symbol sense is still insufficient.Therefore,from the perspective of development of the mathematical symbol sense,this research explores the connotation of students' mathematical symbol sense during the stage of compulsory education and analyzes hierarchy construction and its development level,in order to provide the theory reference for developing students' mathematical symbol sense.With the mathematical thought and the core of mathematical conpetencies as an entry point,this research is discussed mainly with quantitative method,supplemented by qualitative method,the research is analysed by clarifying the meaning of mathematical symbol sense,constructing the analysis level of the mathematical symbol sense,and finally dividing the development level of the students' mathematics symbol sense.First of all,through the mathematical symbol sense on keywords frequency statistics,after two experts consultation,the analysis of the levels of student' mathematical symbol sense comes out.Next,on the basis of the analysis hierarchy and the related theory,according to the basic principle of item design and basic principles of selecting,assessment questionnaire of consciousness of mathematical symbols in stage of compulsory education is prepared,to evaluate students' consciousness of mathematical symbols for the stage of compulsory education from grade 1 to 9.Finally,the researcher makes statistical analysis of the students' answers,and interview some individual students.The following conclusions are made from this study:Firstly,students' mathematical symbol sense in the stage of compulsory education can be analyzed from four levels,which is the perception and recognition of mathematical symbols,understanding and operation of mathematical symbols,association and reasoning of the mathematical symbols,and the abstract and expression of mathematical symbols.These four levels of analysis are improved from low to high,and mathematical symbols of perception and recognition is the lowest level of the consciousness,while the abstract and expression of mathematical symbols is the highest level.Secondly,students' mathematical symbol sense in compulsory education exists three demarcation,namely grade two and grade three,grade four and grade five,grade seven and grade eight.Compulsory education is divided into four set by the demarcation,which explains that there exits “a key age” in the development of mathematical symbol sense in compulsory education.The “age” is what we need to pay special attention to in the process of developing students' symbol sense,and it is also the division basis of developing level of students' mathematical symbol sense in compulsory education.Thirdly,students' mathematical symbol sense in compulsory education can be divided into four developing levels,the development of which has distinct gradation from simplicity to complexity,from low level to high level,from the concrete to the abstract,and the symbolsense develops as the growth of their grades.Symbol sense in grade 1 and grade 2 is characterized by perception and and embodiment,thus we call this experience observation level.Symbol sense in grade 3 and grade 4 is characterized by profundity and specialization,thus we can this nature internalization level.Symbol sense in grade 4,grade 5 and grade 6 is characterized by logicality and formalization,thus we call it rational dialectical level.Symbol sense in grade 8 and grade 9 is characterized by integrity and pattern,thus we call this structure universal level,which is quite different from the division of Curriculum Standard of High school Mathematics.In this sense,although teaching form in primary school and junior high school mathematics is separated,and curriculum standard is segmented,there is a certain continuity in the development of students' mathematical symbol sense.