数学学科核心素养要素析取的实证研究

数学核心素养是学生应具备的适应终身发展和社会发展需要的必备数学品格和数学关键能力。在理论分析基础上，初步析出数学核心素养要素，采用大样本问卷，对数据进行因素分析和不同的聚类分析标准，得到数学核心素养的两种结构。第一种由8种基本成分组成：数学抽象、运算能力、推理能力、数学建模、数据处理、空间能力、问题解决能力、数学文化品格。第二种由7种成分组成：数学抽象、运算能力、推理能力、建模与数据处理、空间能力、问题解决能力、数学文化品格。

Empirical Study on Elemental Extraction of Key Competencies of Mathematics

The key competencies of mathematics is the essential mathematics character and key mathematics ability students should have, which can meet the need of both long-life and social developments. On the basis of theoretical analysis, the writer preliminarily dissolves out the elements of key competencies of mathematics. Then the writer makes a factor analysis and different standard of cluster analysis by using large simple questionnaire, which produces two types of structures of the key competencies of mathematics. The first type consists of 8 kinds of basic components, which are mathematics abstraction, operational capacity, inferential capacity, mathematical modeling and data processing capacity, spatial capacity, problem-solving capacity and mathematical culture character. The second type consists of 7 kinds of basic components, which are mathematical abstraction, operational capacity, inferential capacity, mathematical modeling and data processing capacity.