AI交互式动态模拟器在《概率论与数理统计》中心极限教学中的思政案例

A Case Study on Ideological and Political Education in Teaching the Central Limit Theorem of Probability and Mathematical Statistics Using an AI Interactive Dynamic Simulator

摘要: 本教学案例面向《概率论与数理统计》课程中“中心极限定理”这一教学难点，针对学生普遍存在的“概念抽象、理解片面”问题，设计并实施了一项融合AI技术与课程思政的教学方案案例以交互式中心极限定理动态模拟器为核心AI工具，通过可视化、可操作的仿真实验，将抽象定理具象化。在教学过程中，自然融入了透过现象看本质的辩证思维、严谨求实的科学精神以及从局部推断整体的方法论等思政元素。初步实施表明，该模式显著提升了学生的概念理解深度与学习投入度，使用模拟器的班级在“定理条件判断”和“结论正确解释”两类概念性题目上的平均分达到90，较往届未使用模拟器的传统教学班级有显著提升。

Abstract: This teaching case study addresses the instructional challenge of the “Central Limit Theorem” in the Probability and Mathematical Statistics course, targeting students’ common difficulties with abstract concepts and partial understanding. It designs and implements a teaching approach that integrates AI technology with curriculum-based ideological and political education. The case uses an interactive dynamic simulator of the Central Limit Theorem as the core AI tool, transforming the abstract theorem into tangible, operable simulations through visual and hands-on experiments. The teaching process naturally incorporates elements such as dialectical thinking (revealing the essence behind phenomena), rigorous and realistic scientific spirit, and the methodology of inferring the whole from the parts. Preliminary implementation shows that this model significantly enhances students’ conceptual understanding and learning engagement. Students who used the simulator achieved an average score of 90 on conceptual questions related to “judging the conditions of the theorem” and “correctly interpreting the conclusion”, marking a significant improvement compared to previous cohorts taught without the simulator.