新工科背景下人工智能驱动的离散数学课程教学模式探索

Exploring an AI-Driven Teaching Model for Discrete Mathematics Courses in the Context of Emerging Engineering Education

摘要: 在新工科“智能+”战略背景下，离散数学作为衔接数学理论与计算思维的核心基础课程，面临“内容抽象、场景缺位、智能缺位”的三重困境。本文深入剖析其根源：1) 概念高度抽象，脱离真实工程语境，导致学生难以建立认知锚点；2) 教学场景单一，缺少跨学科项目驱动，致使知识迁移受阻；3) 智能化手段流于表层，未能与课程知识图谱、学习数据深度融合。针对上述痛点，提出“一体两翼三融”教学模式：以“课堂教学”为体，承载课程目标与能力指标；以“人工智能相关竞赛”和“企业项目实践”为两翼，分别提供智能交互环境与工程实践场域；通过“专业教师与思政教师–思政教育和岗课赛证–线下与线上育人”三融，实现专业教师与思政教师协同、思政元素与岗课赛证融通、线下与线上育人联动，形成“价值塑造–知识传授–能力培养”一体化的离散数学课堂新生态。教学实践表明，该模式使学生的复杂问题解决能力显著提升，为新工科基础课程智能化转型提供了一种有益的探索和参考。

Abstract: Against the backdrop of the “Intelligent+” strategy for emerging engineering education, discrete mathematics—as a core foundational course bridging mathematical theory and computational thinking—faces a triple dilemma of “abstract content, absent scenarios, and absent intelligence.” This paper dissects the root causes: 1) highly abstract concepts detached from authentic engineering contexts, making it difficult for students to establish cognitive anchors; 2) monotonous instructional scenarios lacking interdisciplinary project drivers, impeding knowledge transfer; and 3) superficial application of intelligent technologies that fail to integrate deeply with course knowledge graphs and learning data. To address these pain points, we propose the “One-Body, Two-Wings, Three-Fusion” teaching model: classroom teaching serves as the “body,” carrying course objectives and competency indicators; AI-related competitions and enterprise project practices constitute the “two wings,” providing intelligent interactive environments and authentic engineering arenas, respectively. The “three fusions” integrate subject and ideological-education teachers, ideological elements with “post-course-competition-certificate,” and offline and online education, creating a new discrete-mathematics classroom ecosystem that unifies “value cultivation, knowledge delivery, and competency development”. Empirical results show that this model significantly enhances students’ complex problem-solving abilities and offers a valuable reference for the intelligent transformation of foundational courses in emerging engineering education.