“数理–金融–数据”融合的大学数学虚拟实践平台构建与教学改革研究

A Virtual Practice Platform for University Mathematics: Integrating Mathematical, Financial, and Data Elements

摘要: 在数字化转型与智能技术深度融合教育领域的时代背景下，大学数学教学仍面临内容抽象、实践薄弱、学科割裂等结构性困境。本文依托教育部产学合作协同育人项目，以“数理–金融–数据”三维融合为主线，构建了以知识图谱为组织骨架、以虚拟仿真与数据化实践任务为载体的大学数学虚拟实践教学平台。平台通过“概念可视化–模型构建–算法实现–现实问题求解”的闭环设计，贯通数学、金融与数据分析能力链条，形成“理论–案例–工具–实践”四阶递进教学模式。研究采用准实验思路与证据链评价框架，结合高等数学、金融数学、复变函数与积分变换等课程的试运行，系统分析平台在提升学生结构化理解、建模能力与学习投入方面的实施效能。平台试运行数据显示，实验组在概念理解、项目可复现性等关键能力指标上显著优于对照组，学习过程数据亦表明其学习路径更系统、实践投入更深入。最后，本文总结平台建设中的关键难点与治理策略，提出可复制的评价指标体系与未来研究方向，以期为高校数学教学改革提供系统性解决方案与实践参照。

Abstract: In the era of digital transformation and the deep integration of intelligent technologies into education, university mathematics teaching still faces structural challenges such as abstract content, weak practical application, and disciplinary fragmentation. Supported by the Ministry of Education’s Industry-University Cooperation Collaborative Education Project, this paper takes the tridimensional integration of “Mathematical-Financial-Data” as its core thread to construct a virtual practical teaching platform for university mathematics. The platform uses a knowledge graph as its organizational framework and incorporates virtual simulation and data-driven practical tasks. Featuring a closed-loop design of “Concept Visualization-Model Construction-Algorithm Implementation-Real-World Problem Solving”, it bridges the competency chains of mathematics, finance, and data analysis, forming a four-stage progressive teaching model: “Theory-Case Study-Tools-Practice”. Employing a quasi-experimental approach and an evidence-chain evaluation framework, combined with trial runs in courses like Advanced Mathematics, Financial Mathematics, Functions of Complex Variables and Integral Transforms, the study systematically analyzes the platform’s effectiveness in enhancing students’ structured understanding, modeling capabilities, and learning engagement. Trial data indicates that the experimental group significantly outperformed the control group on key competency indicators such as conceptual understanding and project reproducibility. Learning analytics also revealed more systematic learning paths and deeper practical engagement within the experimental group. Finally, the paper summarizes the key challenges and governance strategies encountered during platform development, proposes a replicable evaluation index system, and outlines future research directions, aiming to provide a systematic solution and practical reference for reforming mathematics teaching in higher education.