Investigation And Research On The Present Situation Of Mathematical Abstraction Ability Of Junior Three Students

The ability to abstract is one of the main manifestations of the core literacy of mathematics for junior secondary school students.It is the ability of students to abstract quantitative relationships and spatial forms in the real world to obtain the objects of mathematical study and to form mathematical concepts,properties,laws and methods,and is the most important ability of students to observe the world through the eyes of mathematics.Therefore,in the process of developing students’ core literacy in mathematics,it is particularly important for them to develop their abstraction skills.Based on the above considerations,this study poses the following three research questions:(1)What is the current status of junior secondary students’ mathematical abstraction ability?(2)What are the factors influencing the abstraction ability of junior secondary students in mathematics?(3)What are the suggestions for improving the abstraction ability of junior secondary students in mathematics?The study selected junior high school students from three different schools in Q city as the subjects of the study.Using the literature analysis method,a test framework for junior high school students’ mathematical abstraction ability was derived,and the test questions for junior high school students’ mathematical abstraction ability were compiled according to the test framework.The current situation of junior high school students’ mathematical abstraction ability was analysed through the test results,and then the factors affecting junior high school students’ mathematical abstraction ability were analysed in conjunction with questionnaires and interviews.The results of the study show that the current status of the mathematical abstraction ability of junior secondary students is at an intermediate level overall,and that there are significant differences in the mathematical abstraction ability of students in different schools,with students in urban schools performing significantly better than those in rural schools.In terms of the different types of abstraction,relational abstraction was the best,conceptual abstraction was the second best,and methodological abstraction was the worst.For both conceptual and relational abstraction,the number and algebra question types scored higher than the graphical and geometric question types,while the opposite was true for methodological abstraction.There was a significant correlation between students’ performance in mathematics and their ability to abstract mathematics,while there was no significant correlation between reading comprehension and their ability to abstract mathematics.There was a significant correlation between students’ mathematical abstraction ability and students’ perceptions of mathematical abstraction,their affective attitudes,self-perceptions and the importance of teachers.There was no significant difference in the performance of male and female students in mathematical abstraction ability,but girls scored slightly higher than boys.The factors influencing students’ mathematical abstraction ability are divided into two aspects: students themselves and teachers.The factors affecting students are: lack of awareness of mathematical abstraction skills;lack of positive attitude towards learning about mathematical abstraction skills;lack of solid basic knowledge of mathematics;lack of observation and identification skills;and poor ability to compare and classify key information.Teachers’ influences include: insufficient awareness of mathematical abstraction skills;a single approach to developing students’ mathematical abstraction skills;and failure to make full use of teaching materials.Based on the survey of the current situation and the analysis of the influencing factors,recommendations are made in terms of both students themselves and teachers.Recommendations for students: change their attitudes towards learning mathematics,overcome their fears and correctly understand the abstract nature of mathematics;summarise and generalise frequently to master basic knowledge and methods;understand the history of mathematics and discover mathematics from realistic situations.Recommendations for teachers: gain a comprehensive understanding of mathematical abstraction as well as the ability to abstract mathematics;seek a variety of teaching methods to suit the characteristics of different students;strengthen the integration of information technology and mathematics teaching to reduce the abstraction of mathematics;emphasise the teaching of the process of concept generation and understand the origins of mathematical concepts;emphasise the infiltration of ideas and methods so that students can understand the universality of ideas and methods;focus on the connections between knowledge and summarise and generalise the commonalities;emphasise the process of synthesis and practice and mathematical modelling to enhance the teaching of practical problems.