面向材料专业的概率统计课程案例教学设计——以陶瓷材料强度数据的两个教学实例为例

Case Teaching Design of Probability and Statistics for Materials Majors—Taking Two Teaching Examples of Ceramic Material Strength Data as Examples

摘要: 概率论与数理统计作为公共数学课程面向不同专业授课时，通用例题虽便于说明定义和计算方法，却难以充分呈现课程内容与后续专业学习的联系。本文以材料专业学生为对象，选取美国国家标准与技术研究院公开的陶瓷强度数据，设计两个连续教学实例。实例一将单件陶瓷强度视为连续型随机变量，在正态模型下完成事件表达、标准化和质量阈值概率计算；实例二继续使用同一数据中的两个材料批次，通过两独立正态总体均值检验和置信区间分析批次平均强度差异。两个实例把正态分布、参数估计和假设检验依次置于同一材料质量问题中，形成由个体概率到总体推断的递进关系。教学借鉴基于问题的学习理念，先由小组讨论提出分析思路，再结合案例学习与Excel数据分析，形成对材料强度表现的综合判断。该设计重在保持数据情境连续，使学生理解概率模型与统计推断的不同作用，并明确模型假设与结论边界。

Abstract: When probability and statistics is taught as a public mathematics course across different majors, generic examples can explain definitions and calculations but often fail to show how the methods connect with subsequent disciplinary study. Focusing on materials majors, this paper develops two linked teaching examples using an open ceramic-strength data set from the National Institute of Standards and Technology. The first models the strength of an individual specimen as a continuous random variable and uses a normal model, event notation, and standardization to calculate the probability of meeting a quality threshold. The second continues with two material batches from the same data set and uses a two-sample t test and a confidence interval to analyze their mean-strength difference. Placing the normal distribution, parameter estimation, and hypothesis testing in one materials-quality context creates a progression from individual probability to population inference. Drawing on problem-based learning, students first discuss possible approaches in groups, then use case-based learning and Excel analysis to assess the strength performance of the two batches. The design emphasizes continuity of context, the distinct roles of probability modeling and statistical inference, and the limits imposed by model assumptions.