数学问题提出能力的测评模型及指标赋权

数学问题提出能力的测量与评估成为数学教学研究的热点议题,其测评模型及指标赋权的合理性与科学性是研究者关注的首要问题.该文在梳理数学问题的定义、已有的测评内容和方式的基础上,从问题的本质特征、数学特征和语言特征这3个维度构建数学问题提出的测评模型,并对该模型中的指标进行了2级赋权.研究结果表明:(i)验证性因素分析的各项指标均较好,所提测评模型具有较好的结构效度,并且各维度的内部信度也较高;(ii)最大特征根计算的一致性指标C_I和一致性比例C_R表明,基于矩阵判别表的专家赋权具有较高的一致性,赋权具有较好的合理性和科学性.测评模型和指标权重的确定,为如何测量及评估学生的问题提出能力提供了较为合理的思路.

The Evaluation Model and Index Weighting of Ability to Propose Mathematical Problems

The measurement and evaluation of the ability to propose mathematical problems has become a hot topic in mathematical teaching research,among which the rationality and scientificity of the evaluation model and index weight have become the primary concern of researchers.On the basis of sorting out the definition of mathematical problems,the existing evaluation contents and methods,the evaluation model proposed by mathematical problems is constructed from the three dimensions of the essential characteristics of the problems,the mathematical characteristics of the problems and the linguistic characteristics of the problems,and two levels of weights are assigned to the indexes in the model.The results show that the indicators of confirmatory factor analysis are good,the evaluation model has good structural validity,and the internal reliability of each dimension is high.The consistency index C_I and the consistency ratio C_R calculated based on the maximum characteristic root show that the expert weighting based on the matrix discriminant table has a high consistency,and the weighting is reasonable and scientific.The determination of evaluation model and index weight provides a scientific and reasonable way of thinking on how to measure and evaluate students’ ability to propose problems.