When students participate in math modeling, they often expect to walk away with a solution. What they might not realize at first is that they’re also developing something much more powerful: a mindset.

In his editorial on the mathematical modeling mindset, COMAP Executive Director Ben Galluzzo shares what he’s learned from educators and students around the world. Whether he’s visiting teams in Hong Kong or reconnecting with former students, the theme remains the same: math modeling changes how students think, collaborate, and solve problems. As Galluzzo states, “Mathematical modeling is not just a process, it is a mindset.” 

What Is the Mathematical Modeling Mindset?

COMAP defines mathematical modeling as more than a technique. It’s a way of seeing the world through a mathematical lens. Students who model learn how to simplify complex problems, test assumptions, form mathematical representations, perform calculations, evaluate their results, collaborate across disciplines, and communicate their reasoning. They become comfortable with ambiguity and learn to iterate rather than search for a single right answer.

This mindset includes habits like:

• Curiosity and thoughtful questioning
• Assumption-making and simplification
• Pattern recognition and systems thinking
• Communication, collaboration, and reflection
• A tolerance for imperfection and a willingness to revise

Through contests like HiMCM®/MidMCM or MCM®/ICM®, students engage with real-world problems that require far more than textbook skills. They’re asked to think deeply, make decisions as a team, and write about their process. A challenge that fundamentally improves how students understand and communicate complex ideas (and helps them grow from productive struggle in math!).

From Classroom to Real Life

Galluzzo shares examples of students who carried their modeling experience into science labs, university courses, and personal growth. One former contestant later recognized a mistake in her contest paper while studying advanced statistics. Instead of seeing it as a failure, she saw it as a learning moment, connecting what she was learning back to the modeling process.

At a recent NCTM conference, educators echoed these insights. Participants noted how math modeling:

• Sparks critical thinking by removing rigid constraints
• Gives students voice, agency, and relevance
• Builds identity and confidence
• Encourages exploration and meaning-making

These are exactly the skills that will help students thrive in today’s complex world and they’re at the heart of COMAP’s mission.

Supporting the Math Modeling Mindset

To help teachers foster this mindset, COMAP shares resources such as: 

• GAIMME (Guidelines for Assessment and Instruction in Mathematical Modeling Education) 
• A practical introduction to getting started with math modeling
• A guide for how teachers can incorporate math modeling for different grade levels
• And a lot more math modeling resources and insights on COMAP’s math modeling blog

These tools are designed to make modeling more approachable in everyday classrooms, while still holding onto its real-world complexity.

COMAP is also rolling out new digital badges for contest participants, making it easier for students to showcase their achievements on platforms like LinkedIn and resumes. It’s another way to recognize not just what students accomplish, but how they think.

As Galluzzo concludes: “Modeling is not just about producing solutions; it’s about negotiating ideas, testing assumptions, and refining understanding.”

Download the full editorial here to explore how COMAP is working to support this mindset in students and educators alike.