| One of the major characteristics of the mathematics subject is abstraction,and students’ learning in the mathematics subject cannot be separated from the process of mathematical abstraction.“The Curriculum Standards for Compulsory Mathematics Education(2022 Edition)”(hereafter referred to as " The Curriculum Standards(2022 Edition)")presents abstraction skills as a separate core quality,fully reflecting the importance of abstraction skills in mathematics learning and students’ future personal development.Eighth graders are at a critical stage of cognitive development and a critical period for developing abstraction skills in mathematics.Therefore,it is necessary to analyze the current situation of eighth grade students’ mathematical abstraction ability from the perspective of mathematical core literacy and pay attention to the development of students’ mathematical abstraction ability.In this study,the dimensions and levels of mathematical abstraction ability of eighth grade students are classified in relation to " The Curriculum Standards(2022 Edition)" and the relevant theories of Yu Ping,Shao Guanghua,and Huang Youchu.First,the mathematical abstraction ability was divided into two content dimensions,namely,number and algebra and graph and geometry,and then each content dimension was further divided into representational abstraction ability and principle-based abstraction ability,and finally,representational abstraction ability and principle-based abstraction ability were each divided into three levels.The specific performance of each dimensional level was elaborated according to " The Curriculum Standards(2022 Edition)" and the learning progress of the study subjects,based on which the "Mathematics Abstraction Ability Test Paper for Grade 8 Students" and "Mathematics Abstraction Ability Post-test Test Paper for Grade 8 Students" were prepared.By issuing the test papers to explore the current situation of the development of mathematical abstraction ability of eighth grade students,the following main conclusions can be obtained:(1)The overall level of students’ mathematical abstraction ability is high,but there are large differences among individuals.(2)The overall differences in students’ mathematical abstraction ability in the content dimensions of number and algebra and graph and geometry were not significant,and students’ representational abstraction ability was stronger than their principlebased abstraction ability in the ability dimension.(3)Students’ mathematical abstraction ability was highly positively correlated with mathematics achievement both overall and in all dimensions,and there was a significant correlation between mathematical abstraction ability and mathematics achievement in all levels except representational abstraction ability level 1.(4)The differences between students of different genders in mathematical abstraction ability overall,in each content dimension,and in each level did not reach the significance level.From the analysis of students’ answers in the test papers,it was found that the main problems of students were as follows: in the dimension of representational abstraction ability,firstly,they did not understand mathematical concepts accurately or had omissions;secondly,they had difficulties in describing the common properties of abstracted mathematical objects in mathematical language accurately.In the dimension of principle-based abstraction ability,firstly,they do not understand the nature of properties,methods and formulas thoroughly;secondly,they have difficulty in establishing quantitative relationships in real situations accurately.Combining the findings of the above status quo and relevant theoretical foundations,corresponding cultivation strategies are proposed to address the problems of students in each dimension:(1)Focus on teaching concepts to help students build up mathematical abstraction ability.(2)Make good use of induction and summarization to help students develop mathematical abstraction ability.(3)Emphasize flexible application to help students improve their abstraction skills.The case training program was designed based on the above development strategies,and the students were trained for seven weeks.At the end of the training,the effectiveness of the case training was tested by issuing post-test papers to analyze the effectiveness of the development strategies.The following conclusions were obtained:(1)The mean values of all dimensions of mathematical abstraction ability and the overall post-test of the students were greater than the mean values of the pre-test,and the overall differences between their pre-test and post-test data reached the significance level.(2)The overall improvement was more pronounced for struggling students than for intermediate students,and the improvement in principle-based abstraction ability was more pronounced than in representational abstraction ability;the smallest improvement in representational abstraction ability was found in the graph and geometry dimension,and the largest improvement in principle-based abstraction ability was found in the number and algebra dimension.(3)The students’ ability to grasp and apply common properties and relationships among mathematical objects was improved,and they were gradually able to consider mathematical problems in a comprehensive and rigorous manner in the process of development.(4)The improvement of mathematical abstraction ability has a positive impact on students’ mathematical performance. |
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