Design and Practical Exploration of Visualized Teaching Cases in Mathematical Analysis Based on Multimodal Representation and Cognitive Load Theories

文章基于多模态表征理论、认知负荷理论和建构主义学习理论，构建了数学分析可视化教学的理论框架，并设计了两个典型教学案例，分别针对函数极限的ε-δ定义和定积分概念。通过整合GeoGebra等动态可视化技术，探讨如何在保持数学严谨性的同时提升教学直观性，帮助学生完成从直观认知到形式化理解的思维过渡。可视化教学能够显著降低抽象概念的认知负荷，促进学生对数学概念的深度理解。本研究为数学分析教学改革提供了创新路径，对推动数学教育创新发展具有参考价值。Based on multimodal representation theory, cognitive load theory, and constructivist learning theory, a theoretical framework for visualized instruction in mathematical analysis was constructed. Two representative teaching cases were designed, focusing on the ε-δ definition of function limits and the concept of definite integrals. By integrating dynamic visualization technologies such as GeoGebra, this study explores how to enhance instructional intuitiveness while preserving mathematical rigor, thereby facilitating students’ cognitive transition from intuitive understanding to formalized comprehension. Visualized instruction significantly reduces the cognitive load of abstract concepts and promotes students’ deep understanding of mathematical ideas. This research provides an innovative pathway for reforming mathematical analysis education, offering valuable insights for advancing the creative development of mathematics education.