The Relationship Between The Understanding Of Function Concept And The Mathematical Symbol Sense And Teaching Research

Mathematical symbols are the medium and tools of mathematical expression.A good mathematical symbol sense is conducive to promoting students’ communication of mathematical information,abstracting mathematical knowledge,reflecting mathematical ideas,and developing mathematical thinking,so as to use mathematical symbols to solve mathematical problems.An efficient understanding of the concept of function helps students to establish the connection between functions and equations and other parts of knowledge,to build a mathematical knowledge network,to master mathematical thinking and to promote the development of students’ dialectical thinking in mathematics.However,few studies have been conducted on the specific relationship between conceptual understanding of functions and mathematical symbol sense.Therefore,this paper chooses a ninth grade student in a junior secondary school as the research object,and conducts a detailed study on them with the help of literature analysis,questionnaire survey,statistical analysis and qualitative analysis methods.This study will help to improve the theoretical system of mathematical research;at the same time,it will help teachers to grasp the actual situation regarding the conceptual understanding of functions and the mathematical symbol sense,and provide teachers with a new starting point for classroom teaching.This paper first uses literature research to review the existing theoretical foundations and research findings on conceptual understanding of functions,mathematical symbol sense,and the relationship between the two.Secondly,a theoretical framework is developed in conjunction with the content of the literature review to construct a structural framework of conceptual understanding of functions and mathematical symbol sense and to classify the dimensions.Then,the questionnaire method is used to complete the preliminary work of determining the purpose of the study,selecting the research subjects,developing the research questionnaire and implementing the research programme.Next,the data collected were quantitatively processed and qualitatively analysed using statistical analysis and qualitative analysis: SPSS software was used to analyse the current status of students’ conceptual understanding of functions and their mathematical symbol sense,and statistical analyses such as correlations and regressions were conducted on the two;to make the study more rigorous,the paper selected six students to think out loud,transcribed and coded their solutions and strategies to portray,from a qualitative perspective,the The relationship between conceptual understanding and mathematical symbol sense.Finally,based on the findings of the data analysis,the findings are explained with the help of teaching cases,teaching suggestions are made to strengthen the understanding of function concepts and enhance the awareness of mathematical symbols,and teaching designs are written.Based on the above research process,the conclusions of this study are as follows:(1)Students’ overall mathematical symbol sense is good,but their understanding of function concepts is unsatisfactory,relatively weak and varies greatly between individuals.(2)Correlation analysis showed that there was a positive relationship between students’ conceptual understanding of functions and their mathematical symbol sense,and this relationship was relatively significant;regression analysis shows that the specific correlation between the two is approximately linear,and a multiple linear regression model can be developed,based on which mutual predictions can be made.(3)Mathematical symbol sense positively influenced the conceptual understanding of functions to a greater extent.Based on the above research findings,the following suggestions are made for teaching: on the conceptual understanding of functions,based on APOS theory,take understanding as the core throughout the classroom;combine different forms of representation of functions for conceptual penetration;pay attention to the connection with other knowledge and build a knowledge network;pay attention to classroom interaction and improve students’ communication and expression skills.In mathematical symbol sense,theoretical knowledge of the history,function and value of mathematical symbols is strengthened;the symbolisation process is reflected;practice of newly defined symbols is increased,variation is taught and holistic thinking is cultivated;transformation between different languages and representations is strengthened;symbolic connections are established and knowledge networks are constructed.Finally,the conceptual understanding of functions is improved with the help of mathematical symbol sense.