How Can Math Teachers Turn Modeling Lessons into Real-World Solutions?

Dear mathematics teachers,

In the journey of teaching mathematical modeling, we are both learners and guides. While modeling blends theory and practice, many of us find its teaching challenging.

One challenge is the tendency to continuously collect and rely on others' modeling materials instead of solving problems ourselves. Borrowing is valuable, but over‑reliance can limit our perspective.

Here are several concrete suggestions for improving how we learn and teach mathematical modeling:

Practice‑oriented. Actively participate in real modeling projects, experiencing the full cycle from problem definition to model construction, solution, and validation, either individually or with colleagues and students.

Continuous learning. Regularly update your knowledge base with the latest modeling theories and tools; many MOOCs, B‑station, NetEase Open Courses, and public accounts offer systematic courses.

Reflective practice. After each teaching activity, analyze what worked and what needs improvement, record experiences, and consider guiding competitions or elective courses to teach through practice.

Student‑centered. Encourage students to propose topics of interest and guide them in building and solving models, boosting engagement and problem‑solving ability.

Team collaboration. Form modeling study groups with colleagues to share experiences, discuss cases, and grow together, sparking new teaching ideas.

Many teachers hesitate to tackle real problems due to fear of leaving their comfort zone. Without personal experience, it is hard to empathize with students struggling with problem solving.

Mathematical modeling is dynamic; it requires applying abstract tools to messy real‑world issues. Even experienced teachers may encounter new knowledge, and learning by doing remains the most effective strategy.

Problems abound in daily life—traffic optimization, pollution control, economic forecasting, public health strategies—offering ample opportunities for modeling. We must teach not only model construction but also problem identification, analysis, and solution.

Therefore, let us set aside collected lesson plans, bravely engage with authentic problems, experience both failure and success, and become better educators who cultivate true mathematical modelers.

Wishing all of us growth as both learners and mentors.

Best regards,

A fellow colleague dedicated to mathematical modeling education