Research On The Development Of Early Algebraic Thinking Of Elementary School Students

Developing students' ability to abstract and generalize and form early algebraic thinking is an important prerequisite for further study of mathematics.With the continuous progress of algebra teaching and learning research,in the past two decades,mathematics education researchers have gradually reached a consensus: the development of algebraic thinking should start from elementary school and run through the entire mathematics education.This view is also reflected in our country's compulsory education curriculum reform.For example,the 2022 edition of "Mathematics Curriculum Standards in Compulsory Education " regards "symbolic awareness" as one of the mathematics core literacies in elementary school.Therefore,it is of great theoretical and practical significance to investigate and analyze the early algebraic thinking of elementary school students.Through literature review,it is found that the elementary school mathematics curriculum in our country has advantages in the cultivation of early algebra.However,the relevant research mainly focuses on teaching activity design,and pays less attention to the development of students' thinking.Based on this,this study mainly raises the following three research questions: 1.What is the current situation of early algebraic thinking of elementary school students? 2.What are the differences in the early algebraic thinking of elementary school students in different grades? 3.How does the early algebraic thinking of elementary school students develop?According to the research questions,this research is mainly divided into three research stages.The first stage is a pilot study.Through three rounds of revisions,including expert questionnaires,case interviews,and item-response theory analysis,an early algebraic thinking test paper covering generalized arithmetic,functional thinking,and quantitative relations was finally formed.The second stage of research is crosssectional research.Through a survey of 526 students in grades 3-5 in Shanghai,we understand the current situation of students' thinking,and analyze the differences of students in different grades,so as to answer the first and second questions of this research.The third stage is a panel study.This study selected 79 fourth-grade students and 63 fifth-grade students in a public primary school for a one-year follow-up survey.By analyzing the data of students' pre-and post-tests,interviews and classroom observations,the development path of students' early algebraic thinking is explored.It mainly responds to the third research question of this study.At the same time,qualitative research and quantitative data results are mutually verified.According to statistical analysis results,this study mainly draws the following five research conclusions.First,from the perspective of the current situation of students' thinking development,the overall development of early algebraic thinking is well.Students' performance in generalized arithmetic is relatively well,but functional thinking still needs to be improved.Second,through latent class analysis(LCA),students' early algebraic thinking can be divided into four categories,from low to high,"arithmetic thinking,specific algebraic thinking,generalized algebraic thinking and symbolic algebraic thinking".Third,with the increase of grades,students' early algebraic thinking has developed significantly,gradually changing from "specific algebraic thinking" to "symbolic algebraic thinking",but there are different trends in different mathematics tasks.Fourth,through the analysis of students' representation methods,it is concluded that multiple representations are beneficial to the development of students' early algebraic thinking and that letters represent numbers can help students to carry out effective reasoning and argumentation.Fifth,through classroom observation,it is found that the early algebraic thinking of primary school students can be developed in the classroom according to the teaching activity design principles of "create similar situations and explore relationships;find patterns and verify laws;generalize laws and expand patterns".Based on the above research conclusions,this paper puts forward the following teaching suggestions: First,teachers can try to introduce from the "graphic pattern" task,combined with the "function table" and other representation methods,to strengthen the cultivation of students' functional thinking.Secondly,enrich the function of letters to represent numbers,and strengthen its general reasoning function of representing "a class of numbers" and "variables" on the basis of representing "unknown numbers".Finally,teachers can follow the development path of students from "arithmetic thinking" to "symbolic algebraic thinking" to design teaching activities,and follow the teaching principles of " create similar situations and explore relationships;find patterns and verify laws;generalize laws and expand patterns " to explore the structural elements of arithmetic curriculum so as to promote the development of students' early algebraic thinking effectively.