数学问题提出能力的类别特征:基于潜剖面的分析

The Category Characteristics of Mathematical Problem Posing Ability:Analysis Based on Submersible Profile

在已有测评框架的基础上,建构了测评指标的评分标准,通过应用多元概化理论验证了评分标准的可信度,进一步将其应用于小学生数学问题提出能力的实践调查中,通过潜剖面分析考察了小学生数学问题提出能力的现状及类别特征.研究结果表明:1)小学生在数学问题提出能力测评指标的3个子维度上的协方差分量较大,这说明用问题3个特征的得分来确定学生的数学问题提出能力的水平结果比较一致;2)测评工具全域总分的合成概化系数为0.9904,相对误差比较小,这说明评分者一致性程度较高,评分标准设置合理;3)潜剖面分析的拟合指数与分类验证结果表明,小学生数学问题提出能力可划分为差异明显的3类;4)问题提出能力不同类型的小学生在数学成绩上的差异明显.

Aiming at multiple nested and complex data structures,the theory of multivariate generalization is used to roughly retain the original information of the data,and the graders′consistency reliability of the evaluation indexes of the students′mathematical problem solving ability is verified.In addition,the problem raising ability of primary school students is classified through latent profile analysis to verify whether there are differences in math scores among students with different problem raising ability levels.The results show that the covariance component of the three sub-dimensions of the evaluation index of the students′mathematical problem posing ability is large,which indicates that the results of determining the level of the students′mathematical problem posing ability by using the scores of the three characteristics of the problems are consistent.The synthetic generalization coefficient of the overall score of the evaluation tool in this study is 0.9904,with a relatively small error,indicating a high degree of consistency among the raters in this test.The results of fitting index and classification verification show that it is reasonable to divide students′mathematical problem putting ability into three categories.Students with different problem-solving abilities have different performance in mathematics.