EM (Expectation Maximization)算法是统计学中的核心算法,也是本校近代数理统计课程教学过程中的一个重难点。论文采用案例式、启发式、研讨式教学方法,以基于高斯混合模型(GMM)的轴承退化阶段划分问题为例,引导学生发现隐变量模型极...
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EM (Expectation Maximization)算法是统计学中的核心算法,也是本校近代数理统计课程教学过程中的一个重难点。论文采用案例式、启发式、研讨式教学方法,以基于高斯混合模型(GMM)的轴承退化阶段划分问题为例,引导学生发现隐变量模型极大似然估计(MLE)存在的困难,设计问题链启发学生探寻参数估计的数值方法,并总结出EM算法的一般过程。基于matlab编程可视化EM算法下的GMM模型参数更新过程,对比MLE目标函数和EM迭代目标函数,分析EM算法的内涵思想并结合图形进行直观展示,并且挖掘其中蕴含的思政元素,在知识传授的同时实现价值塑造。Expectation maximization (EM) algorithm is a core algorithm in statistics and also a key and difficult point in the teaching process of modern mathematical statistics courses in our school. The paper adopts a case-based and heuristic teaching method, taking the Gaussian Mixture Model (GMM) based bearing degradation stage division problem as an example, guiding students to discover the difficulties of maximum likelihood estimation (MLE) in the latent variable model, designing a problem chain to inspire students to explore numerical methods for parameter estimation, and summarizing the general process of EM algorithm. Based on Matlab programming, the parameter update process of GMM based on EM algorithm is visualized. Comparing the MLE objective function and EM iteration objective function, the intrinsic thought of EM algorithm is analyzed and visually displayed with graphics. The ideological and political elements are also explored, so as to achieve value shaping while knowledge transmission.
本文旨在探讨和实践以“学为中心”的轻混合式教学模式在军校物理类课程中的应用。通过分析当前军校物理教学的现状,本文提出了一系列创新的教学方法和策略,旨在提高教学质量和学员的学习效果。研究结果表明,轻混合式教学模式能够有效地解决传统教学中存在的问题,并为军校物理教学提供一种新的教学模式。This paper explores and practices the application of a “student-centered” blended learning model in military physics courses. By analyzing the current situation of physics teaching in military academies, this article proposes a series of innovative teaching methods and strategies aimed at improving teaching quality and learning outcomes for students. The research results indicate that the blended learning model can effectively address issues in traditional teaching and offers a new teaching model for military physics courses.
工程例证式教学法(EETM)是一种以工程案例进行组织教学的教学方法,也是一种更侧重工程实践的过程式教学,以侧重问题牵引和思维启发为基本原则组织教学。与传统的“以理论支撑理论”的教学模式相比,工程例证式教学是一种“以实例支撑理论”的教学模式,贴近工程实际,更符合工程类数学课程“以数学为工具并且学以致用”的根本目的。The Engineering Example-based Teaching Method (EETM) is an instructional approach that organizes teaching through engineering case studies. It is a process-oriented teaching method that emphasizes engineering practice, with a fundamental principle of problem-driven and thought-provoking instruction. Compared to the traditional “theory-supported-by-theory” teaching model, EETM adopts a “theory-supported-by-examples” approach, which is closer to real-world engineering scenarios and better aligns with the fundamental purpose of engineering mathematics courses: to use mathematics as a tool and apply it in practical contexts.
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