看见统计学：AI赋能概率论核心概念的动态可视化教学研究

Seeing Statistics: AI-Enabled Dynamic Visualization Teaching Research on Core Concepts of Probability Theory

摘要: 概率论与数理统计是高校数学与统计学核心课程，概念抽象、逻辑严谨、公式复杂。传统课堂教学难以实现教学过程的直观化、过程化，缺乏与学生的有效互动。本文以生成式AI工具豆包为技术支撑，依托HTML、JavaScript、Canvas构建跨平台动态可视化网页应用，选取概率论中依概率收敛与数列收敛、泊松分布与指数分布、二维正态分布及其边缘、条件分布三大教学难点，设计可交互、可调控、可模拟的动态演示系统，实现抽象概念“看得见、摸得着、可探究”的教学革新。实践表明，这种模式可以有效降低认知难度、强化概念辨析、提升学生学习兴趣与思维深度，为新时代概率论课程的数字化、智能化教改提供可复制的实践路径。

Abstract: Probability Theory and Mathematical Statistics serves as a core compulsory course for mathematics and statistics majors in institutions of higher education. Nevertheless, its highly abstract concepts, rigorous logical reasoning and intricate mathematical formulas pose major challenges to conventional teaching, which struggles to visualize and contextualize the teaching process and lacks effective interaction with students. Supported by the generative AI platform Doubao, this study develops cross-platform dynamic visual web applications via HTML, JavaScript and Canvas. Targeting three key difficult teaching contents—convergence in probability and sequence convergence, the linkage between Poisson distribution and exponential distribution, and two-dimensional normal distribution along with its marginal and conditional distributions. We construct an adjustable, interactive and simulation-based dynamic demonstration system. This innovative approach enables abstract probabilistic concepts to be visualized, operable and exploitative. Practice shows that this teaching mode can effectively reduce cognitive difficulty, strengthen conceptual discrimination, and enhance students’ learning interest and thinking depth. It provides a replicable practical path for the digital and intelligent teaching reform of Probability Theory courses in the new era.