An Investigation And Research On Mathematical Abstract Ability Of Junior Two Students In Different Contextual Problems

Since the 1990s,"key competence" has become a hot topic in the field of education.In the newly issued "Curriculum Standards for Compulsory Education(2022 Edition)" last year,a major focus is on designing integrated key competence.The curriculum standard uses "three skills" to highly summarize mathematics key competence,among which the main expression of mathematical vision is abstract ability in junior high school.At the same time,many scholars believe that contexts and the development of key competence are closely related,so the author chose to investigate and study students’ mathematical abstract ability from the perspective of contexts.In this study,the author defined mathematical abstract ability and contextual problems based on the literature,and then developed a framework for evaluating mathematical abstract ability that includes three kinds of context,three cognitive dimensions,and three horizontal dimensions.Based on the framework,the author developed test questions about number and expression,equation and inequality,and function content under number and algebra content.The survey was conducted with junior school students in Shanghai X School as the research object.The survey found that(1)the junior school students in Shanghai X School generally performed well in mathematical abstract ability,and the students’ mathematical abstract ability performed well in realistic contexts,while the students’ mathematical abstract ability performance in interdisciplinary contexts was relatively poor;(2)In the horizontal dimension,students’ performance in Level 1,Level 2,and Level 3 shows a downward trend,and most students are in the Level 1 and Level 2 stages of mathematical abstraction.In both Level 2 and Level 3,students’ performance of mathematical abstraction ability in purely mathematical contextual problems is superior to that in realistic and interdisciplinary contexts;(3)In the cognitive dimension,students perform best in mathematical concepts and rules in the cognitive dimension,with mathematical expression and transformation ranking second,and students perform worst in mathematical methods and rules.From contextual perspective,different contextual problems have no significant and regular impact on students’ mathematical conceptual rules,mathematical methods,and laws.However,contexts do have an impact on students’ mathematical expression and transformation,especially interdisciplinary contexts that increase the difficulty of students’ mathematical expression and transformation;(4)In terms of content dimensions,students’ performance in mathematical abstraction of numbers and expressions is relatively good,significantly superior to equation and inequality and function content dimensions.In pure mathematical contextual problems,students perform best in terms of mathematical abstract ability reflected in the content of numbers and expressions;The performance of mathematical abstract ability embodied in the content of equations and inequalities in realistic contextual problems is significantly superior to the other two contextual problems;In interdisciplinary contextual problems,students perform relatively well in responding to the content dimension of functions,while their performance in mathematical abstraction is not ideal in terms of equation and inequality content;(5)There are significant differences in mathematical abstract ability among junior school students with different grades.In response to the current situation of mathematical abstract ability among junior school students,this paper proposes feasible suggestions for teachers’ teaching,students’ learning,and the preparation of textbooks and test questions,and reflects and prospects the research.