基于反直觉案例的概率统计趣味教学模式研究

Research on the Interesting Teaching Mode of Probability and Statistics Based on Counter-Intuitive Cases

摘要: 针对当前概率统计教学中“公式抽象枯燥”与“学生直觉认知误区”的双重矛盾，本文设计了一套基于三大经典反直觉案例的一体化教学模式。该模式依托生日悖论、蒙提霍尔问题、辛普森悖论，构建了直觉预判、认知冲突、逻辑拆解、公式验证、思维升华、知识迁移的教学闭环模式。实践结果表明，此模式成功实现了从“被动灌输”到“主动探究”的教学转变，有效纠正了学生在概率判断中的习惯性谬误，促进了严谨统计思维的养成，为新时代概率统计课程的创新教学提供了有力支撑。

Abstract: To address the dual challenges of abstract and dry formulas and students’ cognitive biases from intuition in the teaching of probability and mathematical statistics, this paper designs an integrated teaching model based on three classic counter-intuitive cases. Using the Birthday Paradox, Monty Hall Problem, and Simpson’s Paradox as carriers, the study constructs a six-step closed-loop teaching procedure: intuition prediction, cognitive conflict, logical analysis, formula verification, thinking sublimation, and knowledge transfer. Empirical results show that the model successfully transforms teaching from passive instruction to active inquiry, effectively corrects students’ habitual fallacies in probability judgment, and fosters rigorous statistical thinking. It provides strong support for innovative teaching of probability and statistics courses in the new era.