A Studay Of Primary School “fraction” Concept Learning Progression

“Learning progression” originated in the field of science education in the United States,aiming to describe the development sequence of students' thinking in the process of knowledge learning through empirical research,in order to provide suggestions for the reform of curriculum,teaching and evaluation.Fraction is an important part of the field of “number and algebra” in primary school mathematics,which has great significance.The concept of fraction is very rich and abstract,which is one of the difficulties for primary school students to learn.This study took “fraction” as the core concept,and two tests were conducted in the form of test papers: 30 sixth-grade students from Kunming H Primary School were selected to complete the pretest,and 300 students from grade three to six were selected to complete the formal test.This study uses three research methods: literature literature research method,text analysis and test method.The research questions presented in this paper are follows:First,what is the primary school “fraction” concept learning progression?Second,how is primary school “fraction” concept learning progression applied to the teaching design of fraction concept?This paper draws on APOS theory will students get fraction concept of the concept of “concept understanding”,“concept formation”,“concept deepening” and“concept development” four stages,combined with the curriculum standards and elementary school textbook concept preset primary school “fraction” concept learning progression,SPSS was used to the performance of students in the fractional concept test,finally determine the primary school “fraction” concept learning progression includes five levels:The “concept understanding” stage includes the first level and the second level:The first level: understand the “average”,can read and write fraction,can add and subtract the simple fraction;The second level: the initial development of the fraction concept of “part-whole”,“quotient”and“ratio”;“Concept formation” stage ——the third level: understand the improper fraction,obtain the concept of “part-whole” and “quotient”,initially develop the concept of "measurement",can carry out simple different denominator fraction addition and subtraction calculation,and understand the fraction of the discrete situation;“Concept deepening” stage —— the fourth level: can use the concept of "part-whole" to solve the fraction problem,form the concept of equivalent fraction,can solve the fraction problem on the straight line;“Concept development” stage —— the fifth level: can distinguish between the“quantity” and “rate” in the discrete situation,and can solve the fractional multiplication and division calculation and mixed calculation.After establishing the primary school “fraction” concept learning progression,this study makes three teaching designs based on the primary school “fraction”concept learning progression: “Preliminary understanding of fraction”,which corresponds to the first level and the second level of the primary school “fraction”concept learning progression.“Meaning of fraction” is the third level teaching design,and the teaching design of“fraction division” " is the fourth level and the fifth level of the “fraction” concept learning progression.Each teaching design starts from the starting point,with a series of advanced activities to promote students to complete low level to high level advanced.According to the research results,get the following enlightenment:(1)Pay attention to students' level and optimize teaching;(2)pay attention to the learning process and reasonable evaluation;(3)pay attention to concept teaching and connect concepts.