数学专业学生AI素养评价——基于组合赋权云模型

Assessment of AI Literacy among Mathematics Majors—Based on a Combined Weighting Cloud Model

摘要: 针对数学专业AI素养评价学科适配性不足、评价存在模糊性与随机性的问题，构建基于最小相对熵组合赋权–云模型的AI素养评价体系。以KSAVE模型为基础，面向数学专业优化指标内涵，建立AI素养评价体系；采用层次分析法与熵权法分别确定主、客观权重，基于最小相对熵原理求解组合权重；引入云模型刻画评价不确定性，实现等级判定。以南昌航空大学202名数学专业学生为样本实证分析，结果表明：学生AI素养整体处于良好偏下水平，AI技能是核心短板；AI方案设计能力与模型数学原理认知权重最高；数学建模竞赛对AI素养提升显著，但作用限于知识与技能层面。该方法兼顾专家经验与数据规律，可为数学专业AI教育改革与分类培养提供科学支撑。

Abstract: To address the issues of insufficient disciplinary alignment and the ambiguity and randomness in the evaluation of AI literacy for mathematics majors, this study constructs an AI literacy evaluation system based on the Minimum Relative Entropy Combined Weighting-Cloud Model. Building upon the KSAVE model, we optimized the indicator definitions for mathematics majors to establish the AI literacy evaluation system; we used the Analytic Hierarchy Process and the entropy weighting method to determine subjective and objective weights, respectively, and calculated the combined weights based on the principle of minimum relative entropy; we introduced the cloud model to characterize evaluation uncertainty and implement grade classification. An empirical analysis was conducted using a sample of 202 mathematics majors at Nanchang University of Aeronautics. The results indicate that students’ overall AI literacy is at a slightly below-average level, with AI skills being the core weakness; AI solution design ability and understanding of the mathematical principles underlying models received the highest weightings; and while mathematics modeling competitions significantly enhance AI literacy, their impact is limited to the knowledge and skills levels. This method integrates expert experience with data patterns and can provide scientific support for AI education reform and differentiated training in mathematics programs.