数学类大学生创新训练项目的分阶指导与过程评价——以时滞SEIR流感传播建模为例

Staged Mentoring and Process-Based Assessment in Innovation Training Projects for Mathematics Undergraduates —A Case Study of Time Delayed SEIR Modeling of Influenza Transmission

摘要: 针对低年级数学类学生在大学生创新训练项目中先修知识不足、理论与计算容易脱节、个体贡献难评价等问题，本文以“时滞SEIR流感传播建模”为载体，设计分阶指导与过程评价方案，并在中国矿业大学(北京)理学院2024级11名学生组成的两个项目组中开展1年试点。项目设置机制辨析、模型比较、稳定性分析、数值验证和干预表达五个阶段，以理论与计算相互核验、角色轮换、阶段审查和修订记录组织学习。试点累计形成62次版本提交，周志完成率98%；学生后测较前测明显改善，最终报告总体完成较好，代码复现通过率80%。11份有效问卷和6人访谈显示，学生普遍感受到理论与计算联系较紧密、团队分工较公平，并较完整地经历了从前期调查、逐步研究到汇总形成报告的过程。结果表明，该方案具有较好的可实施性，但周志反思深度和代码复现规范仍需加强。受样本规模和单一院校限制，本文不作普遍因果推断。

Abstract: This study addresses three common difficulties faced by lower-year mathematics students in undergraduate innovation projects: insufficient prerequisite knowledge, separation between theoretical analysis and computation, and difficulty in evaluating individual contributions. A staged mentoring and process-based assessment scheme was developed around a time-delayed SEIR influenza modeling project and piloted for one year with 11 students from the 2024 cohort of the School of Science, China University of Mining and Technology-Beijing, divided into two teams. The project comprised five stages: mechanism analysis, model comparison, stability analysis, numerical verification, and intervention modeling. Theory-computation cross-checking, role rotation, milestone review, and revision records were used throughout the project. The two teams made 62 version-control submissions, and the weekly-log completion rate was 98%. Post-assessment performance improved clearly from a relatively weak baseline; final reports were generally completed well, and the code reproduction pass rate was 80%. Eleven valid questionnaires and six interviews indicated that students perceived a close connection between theory and computation, relatively fair teamwork, and a comparatively complete research process from initial investigation to final reporting. The pilot supports the feasibility of the scheme, while also indicating the need to improve the depth of reflection and code-reproduction standards. Because the sample was small and drawn from a single institution, no broad causal claim is made.