Designing Modular Math Modeling Courses: From Problem Posing to Paper Writing

1. Math Modeling Is More Than Modeling

Mathematical modeling ability is a comprehensive skill whose core is translating real‑world situations into mathematical models, but effective teaching also requires attention to problem formulation and result presentation to complete the learning cycle.

2. Modeling Learning Modules

Commonly, modules are organized by model type—evaluation, optimization, prediction—each covering theory, case studies, implementation, and writing. Instructors may prefer classification by method (e.g., differential equations) or by problem type; the author favors the latter for its alignment with problem discovery.

3. Modular Teaching Process

Step 1: Introduce module knowledge with illustrative cases (e.g., ranking student scores, city safety rankings) to show the scope of evaluation models.

Step 2: Guide students to propose similar cases from their own experiences, encouraging extension rather than immediate rejection of their ideas.

Step 3: Have students pose a specific problem they wish to solve, emphasizing that at this stage only the problem statement is required, not a solution.

Step 4: Assign homework where students restate their problem, decompose it into sub‑problems, and reference competition requirements such as those from the Shanghai Math Modeling joint‑school activity.

Step 5: Teach paper‑writing skills alongside module content, continuously integrating students’ evolving ideas and addressing obstacles.

Step 6: Refine the modeling paper, providing iterative feedback to improve structure, streamline sections, and add essential content.

4. Teaching Case

When studying evaluation models, students examined how to assess city responses to a pandemic, iteratively updating their papers with background, methods, and tools. Their final solution combined TOPSIS and entropy methods into a hybrid evaluation model, producing a 7‑page modeling report.

5. Course Design Reflection

Three aspects need extra attention:

Problem‑posing stage: maximize student autonomy to enhance motivation and preserve the originality of their questions.

Process feedback: regularly monitor student progress, address conceptual doubts (e.g., assumptions, variable selection, model validation) and technical issues (e.g., coding bugs) to keep learning momentum.

Paper iteration: provide multiple rounds of constructive feedback rather than a single exhaustive review, allowing gradual improvement without discouraging students.

Reference

Shanghai Math Modeling Joint‑School Activity – https://mp.weixin.qq.com/s/WXmqAc-F2iBxQIvyOIGMVA