Investigation And Research On The Consciousness Of Mathematics Symbols Of High School Students

Symbols are the medium of communication and dissemination of ideas.In 2001,the mathematics curriculum standard of full-time compulsory education(experimental draft)proposed for the first time that "the sense of symbol" should be regarded as a kind of ability that students should develop in course learning.With the development and improvement of the curriculum system,the standard of mathematics curriculum in Compulsory Education(2011 Edition)clearly proposes to develop students' symbolic awareness.Entering the high school stage,students generally reflect that mathematics is difficult.Compared with junior high school mathematics,senior high school mathematics has many contents and high abstractness,and the abstractness of high-school mathematics is largely expressed as the "Symbolization" of mathematics knowledge.Mathematics symbol is the carrier of mathematics knowledge,method and thought.Mastering mathematics symbol is the precondition of learning mathematics knowledge.Therefore,it is very important to improve the mathematical symbol consciousness of high school students.Based on the Pisa evaluation framework,from the perspective of problem-solving,combined with the general laws of high-school students' cognitive level and psychological development,this study divides the mathematical symbol consciousness into four dimensions: symbol representation,symbol understanding,symbol conversion and symbol operation,each of which is subdivided into three levels,and then constructs a mathematical symbol consciousness evaluation framework suitable for high-school students.Based on the evaluation framework,the author randomly selects four classes of different classes in the first year of the internship school.By using the method of combining quantitative research and qualitative research,the author investigates the current situation of the development of high school students' mathematical symbol awareness,and further makes data statistics and correlation analysis with the help of software Excel and SPSS.The main conclusions are as follows:(1)High-school students perform well in the four dimensions of mathematical symbol consciousness.Most of the students can understand the mathematical problems and choose the appropriate mathematical symbols to express the problems,master the mathematical symbols clearly defined in the teaching materials,be able to carry out flexible conversion and deep association of mathematical symbols,and also can choose simple methods for operation.A small number of students have some problems,such as inaccurate logic,improper use of symbolic language,nonstandard writing process,weak understanding of derivative mathematical symbols,symbol conversion can only associate with the latest knowledge,cumbersome operation process and so on,.(2)There is a significant positive correlation between the four dimensions of symbolic consciousness.Among them,the correlation coefficients of symbol conversion and symbol understanding,symbol operation and symbol representation are smaller,showing a low degree positive correlation;the correlation coefficients of symbol understanding and symbol representation and symbol operation are larger,showing a high correlation.(3)The level of mathematical symbol consciousness of high-school students is significantly related to their academic level.Among them,the correlation between symbol conversion and academic level is relatively small,and the correlation between symbol representation and symbol understanding and academic level is relatively large.(4)There are significant differences in the four dimensions of mathematical symbol consciousness among students of different academic levels.The higher the academic level of students,the better the overall performance of mathematical symbol consciousness,and the smaller the difference of each dimension of symbol consciousness.In order to further explore the influencing factors of students' awareness of mathematical symbols,the author interviewed seven teachers.Furthermore,the paper puts forward the following strategies for cultivating symbol consciousness:(1)clarifying the origin of symbols,perceiving the interest of symbols;(2)Guide students to participate and understand the meaning of symbols;(3)teaching in various ways to deepen the connotation of symbols.