A Study On The Level And Characteristics Of Pupils’ Mathematical Abstraction Ability

Abstraction is the fundamental idea on which the discipline of mathematics is developed,and it is also the core literacy that mathematics education should cultivate in students.Developing students’ mathematical abstraction ability is an important task in mathematics education in various countries.In China,since the core literacy of mathematical abstraction was first proposed in the 2017 edition of the “the General High School Mathematics Curriculum Standards”,the level and development issues of middle and high school students’ mathematical abstraction ability have received widespread attention,but there is not much understanding of primary school students’ mathematical abstraction ability.However,the thinking development of primary school students is undergoing a qualitative transformation from concrete to abstract,and the development of mathematical abstraction ability in primary school students can lay the foundation for the development of higher-order abstraction ability and play an important role in the acquisition of other key mathematical competencies.Therefore,it is necessary to investigate and analyze the mathematical abstraction ability of primary school students.According to the inherent rules of children’s cognitive development,the development of mathematical abstraction ability among students in different stages of learning has both consistency and continuity,as well as stage-specific characteristics.Through sorting out existing research,it is found that the current academic community still lacks a systematic and mature mathematical abstraction ability assessment model and tools for primary school students.Therefore,it is necessary to clarify the specific manifestations of primary school students’ mathematical abstraction ability and develop measurement tools based on this,which is the basis for understanding the development level and characteristics of primary school students’ mathematical abstraction ability.Based on the above considerations,this study conducts a series of researches using numbers and algebra as examples to explore the development of primary school students’ mathematical abstraction ability.The specific research questions are as follows:Question 1: What is the structure of the evaluation model for primary school students’ mathematical abstraction ability?Question 2: What test questions are included in the tool for measuring primary school students’ mathematical abstraction ability?Question 3: What is the current situation of primary school students’ mathematical abstraction ability?Question 4: What are the development characteristics of primary school students’ mathematical abstraction ability?Based on the above research questions,the whole research process was divided into three stages.The first stage is the model construction stage.Through empirical test,literature analysis,expert consultation and other methods,the basic connotation of primary school students’ mathematical abstraction ability and the specific performance of different stages of the development of abstraction ability were clarified,and on this basis.After three rounds of expert consultation,the evaluation model of primary school students’ mathematical abstraction ability was formed.The second stage is the measurement tool development stage,which is based on the multi-dimensional Rasch model to develop the measurement tool.Through the preparation,pretest,revision and posttest,a measurement tool for primary school students’ mathematical abstraction ability was finally formed.The third stage is the investigation stage of the level status and development characteristics.The quantitative and qualitative research methods were used to analyze the current situation and development characteristics of the level of mathematical abstraction ability of pupils in three different types of schools in C city.Through the research,the main conclusions are as follows:First,the evaluation model of primary school stuents’ mathematical abstraction ability was constructed,which includes three elements of single abstraction ability,associative abstraction ability and constructive abstraction ability,and three levels of perception level,internalization level and interiorization level.Secondly,taking the content of numbers and algebra in primary school as an example,a measuring tool for primary school students’ mathematical abstraction ability including 27 test items of three dimensions and three levels was developed,and the score of the level grade was determined according to the measured data.Third,by measuring the level of mathematical abstraction ability of students in grades 2 to 5,it was found that,the level of mathematical abstraction ability of the pupils tested mainly concentrated on the level of perception and internalization,and the proportion of students who can reach the interiorization level is not large;Grade and school type are important factors that affect the level of mathematical abstraction ability of pupils,but the degree of influence exists at different stages of development difference;The influence of gender on the level of mathematical abstraction ability of pupils is not significant.Fourth,by analyzing the development characteristics of the pupils’ mathematical abstraction ability,it was found that,the performance of pupils’ mathematical abstraction ability is different on different mathematical objects;The transition from perception level to internalization level may be the key link in the development of pupils’ mathematicalion abstract ability,and the difficulty of development is greater than the difficulty of transition from internalizaton level to interiorization level;The mathematical abstraction ability of the pupils tested has developed rapidly in the fourth grade(about 10-11 years old),and also shows the characteristics of active but not stable and mature thinking;The mathematical abstraction ability of the tested pupils has a significant positive effect on the mathematical academic performance.Finally,the process and results of the above research are reviewed and summarized.Some shortcomings of this study and some directions for further research are pointed out.