高中生数学抽象能力发展水平划分与基于水平划分的调查研究

A Study on the Development Level Classification of Mathematics Abstraction Ability of High School Students and an Investigation Based on Level Classification

数学抽象能力作为数学关键能力之一,涵盖数量关系与空间图形两个横向维度,可以划分为归纳与释义、关联与构建、拓展与普适三个纵向水平。基于水平划分的调研结果表明:高中生数学抽象能力呈现进阶发展趋势;高中生数学抽象能力在数量关系与空间图形上发展不均衡;高三年级学生数学抽象能力的归纳与释义有待提升;高中生数学抽象能力的发展与学生所在年级有关。

As one of the key abilities in mathematics,mathematics abstraction ability covers two horizontal dimensions of quantitative relations and spatial figures.It can be divided into three vertical levels of induction and interpretation,association and construction,and extension and generalization.An investigation based on level classification reaches the following conclusions:the mathematics abstraction ability of high school students shows a development trend of progression;the mathematics abstraction ability of high school students is unevenly developed in quantitative relations and spatial figures;the induction and interpretation of mathematics abstraction ability of high school students in Grade 3 need to be improved;and the development of mathematics abstraction ability of high school students is related to the grade of students.