Designing an Engaging Intro to Mathematical Modeling for High Schoolers

The special course on mathematical modeling has already held two classes, four teaching periods in total. The first class was merely an introduction, covering basic concepts of mathematical modeling and sharing some of my own modeling experiences. The second class presented several elementary model cases (equations, functions) and added methods of proportional modeling.

This course is offered to the second‑year mathematics class, and similar special courses include a calculus preparatory class, bridge, and a course on reading and writing mathematical papers. My biggest difficulty with this course is that I am unsure how to organically select and organize teaching materials.

Previously I always performed modeling based on advanced mathematics knowledge; switching to a more basic level revealed that much of that content is not applicable, and the methods remain somewhat difficult for students to grasp. Many of my modeling experiences have become personal anecdotes that are hard to articulate, and I also feel insecure about some models that I find challenging to understand.

However, after teaching the two sessions, I have a clearer idea of how to teach the course. Initially the students did not know what mathematical modeling was or how to do it, but after I presented several cases and introduced steps such as “defining objectives,” “stating assumptions,” “building the model,” and “validating the model,” they quickly understood. By the second class they were already questioning the assumptions of the models, which met my expectations for the course.

Regarding material selection, I aim to follow a progressive approach, first elevating mathematical knowledge that students are already familiar with—such as elementary equations, functions, geometry, sequences, probability, and statistics—to the level of modeling. Using a “example + pattern summary” method, students become acquainted with various models. Next, I will introduce difference‑equation models, graph‑theory models, and other more advanced models that may involve calculus and linear algebra. While delivering theory, I also emphasize practice; both are equally important. Without hands‑on experience, it is hard to foster genuine enthusiasm and motivation to learn. I need to improve assignment design, ensuring ample practice opportunities, selecting appropriate problems, and supporting self‑learning.

The next step is to provide students with abundant resources, including my own insights on mathematical modeling, students’ modeling projects, and additional learning materials. Distributing these via tablets is also very convenient.

This course also challenges my own abilities, requiring me to deepen my understanding of various models and master the modeling process. I need to practice as much as possible outside class. Perhaps this is the true meaning of teaching and learning mutually enhancing each other.