How to Leverage AI in Math Modeling While Preserving Problem‑Solving Skills

In today’s AI‑pervasive environment, every aspect of life, including mathematics education and modeling, carries an "AI flavor" that brings both opportunities and challenges.

Many educators worry that if students use AI for coding, modeling, or writing, teachers may become redundant, risking unemployment. Another concern is the over‑reliance on AI, which could prevent students from acquiring truly essential abilities.

To address these worries, we first clarify the core problem: how to cultivate students' problem‑solving capability in the new AI‑driven context.

The essential problem‑solving ability is a comprehensive blend of thinking and practice, comprising:

Understanding the essence of the problem : probing beyond surface symptoms to the root causes.

Selecting appropriate tools and methods : choosing suitable models, strategies, and leveraging AI to broaden perspectives and improve efficiency.

Innovative and flexible thinking : adapting strategies and proposing creative solutions for complex or uncertain problems.

Continuous reflection and optimization : iteratively refining approaches based on results.

The article emphasizes the last point—continuous iteration—as the key to personal growth, arguing that both problem‑solving and modeling require repeated questioning, refinement, and integration of domain knowledge.

Five pedagogical options are discussed:

Persist with traditional teaching, ignoring AI.

Strictly prohibit AI use in modeling.

Guide students to use AI responsibly, improving efficiency while exposing AI’s limits.

Integrate AI with traditional methods for a comprehensive upgrade, boosting efficiency and fostering innovative practice.

Base education on AI to develop interdisciplinary collaboration and teamwork.

The author favors a combination of the third and fourth options, advocating for a balanced approach that embraces AI while maintaining solid mathematical foundations.

Teachers must transform from mere "instructors" to "collaborators" and "guides," helping students master basic modeling skills, critical thinking, and the ability to harness AI tools without losing independent thought.

Practical AI experiences are shared: using AI‑generated 3D Earth models with JavaScript, converting Excel tables to LaTeX, and employing large language models to draft code, generate formulas, and spark creative ideas for modeling problems.

I have used AI to write code—for example, downloading a 3D Earth model and drawing on it with JavaScript, a language I had never used before; AI taught me the syntax and saved me a lot of time.

Large language models excel at understanding natural language and linking it to mathematical symbols, helping modelers quickly build frameworks, translate text to LaTeX, and propose innovative ideas such as logistic growth equations for population modeling.

These examples illustrate how AI can expand students' creative space while reinforcing the need for continuous reflection, interdisciplinary collaboration, and a proactive teaching mindset.

Ultimately, embracing AI in education is not a marketing gimmick but a necessary evolution to cultivate future‑ready innovators.

In summary, AI tools should be integrated thoughtfully into mathematics education to enhance efficiency, foster interdisciplinary teamwork, and develop students' innovative and critical thinking abilities.