基于因子分析的中考数学测验结构研究

Examine the Structure for Mathematics Examination in Junior High School Graduation Test Based on Factor Analysis Model

通过对东部和西部地区两市普通初中学业水平考试中的数学科目测验进行数据分析,结合课程标准和考试大纲,对比学生在测验中表现出的能力结构是否与课标及考试大纲中规定的结构相一致。结果发现,运用探索性因子分析构建的模型包含"数学基本能力"、"数学综合能力"、"非数学能力"三个潜变量因子,模型整体拟合度明显优于依据考试大纲规定构建的模型。说明通过中考测验反映的数学素养结构与规定的"数与代数"、"图形与几何"、"统计与概率"三部分结构存在一定差距。基于此,建议应进一步提升测验命题技术,并思考课标及考试大纲中对于数学能力维度的界定如何与核心素养结构相契合,通过编制科学、合理的学业水平测验完善数学核心素养的测量与评价体系。

In this study, by use of two administrations of mathematics examinations in junior high school graduation test from a certain city in east of China in 2011 and a certain city in west of China in 2012, we did a factor analysis to explore whether the students＇ key competencies behave as intended which was stipulated by the curriculum standards and examination syllabus. As the result we found that, there were three factors included in the model by the method of exploratory factor analysis, which we named as ＂mathematical basic ability＂, ＂mathematical integrative ability＂ and ＂non -mathematical ability＂. By focusing on the model fit indices, the model explored was much better than the model constructed by the curriculum standards and examination syllabus. These results meant that observed structure of the math exam in junior high school was different from the intended structure, which was ruled as Number and Algebra, Measurement and Geometry, and Statistics and Probability. Based on this research, we suggested to make further improvement on items development, and consider how to make the definition of the mathematics abilities stipulated in curriculum standards and examination syllabus agreed with the construction of mathematical key competencies, which would help us to achieve the goal of consummating the assessment system of key competeneies by use of rational examinations.