Problem-solving is at the heart of so much of what we do, whether we’re designing a sustainable city, optimizing public health strategies, or finding new ways to run a business. But how do you train your brain to think like a problem solver? One powerful approach is to develop a math modeling mindset.

At its core, math modeling is the process of taking a real-world problem and using math to better understand it and find solutions. It’s about more than just numbers—it’s about asking good questions, recognizing patterns, making sense of variables, thinking creatively, and reflecting on how good your model is. Participating in math modeling challenges, like COMAP’s HiMCM®/MidMCM and MCM®/ICM® contests, is an opportunity to flex these mental muscles in ways that can apply to almost any field.

How Math Modeling Pushes You to Think Differently

In a typical math class, you’re often given a problem with a clear solution at the end of a formula or equation. Math modeling flips that on its head. Here, you’re faced with open-ended problems—there’s no “right” answer, no single path to follow. Instead, you’re challenged to break down complex issues, identify key factors, and make decisions about how to model a situation.

For example, imagine being tasked with developing a plan for sustainable water distribution in a growing city. You’d need to think like a city planner, considering population growth, environmental impacts, and infrastructure limitations. Through math modeling, you’re able to simulate different scenarios, evaluate possible outcomes, and make recommendations based on your findings. This process mirrors how problems are tackled in the real world: messy, uncertain, and full of trade-offs.

From the Classroom to Real-Life Problem Solving

Math modeling doesn’t just make you a better student—it prepares you for real-world problem solving. In life, especially in fields like economics, engineering, or environmental science, issues are rarely straightforward. Math modeling challenges you to think critically and holistically, just like professionals who are tasked with solving some of today’s biggest challenges.

When you’re faced with an open-ended problem, like those found in COMAP’s contests, you learn to approach it from all angles. You might start by gathering data and identifying assumptions, but then you’ll dive deeper into apparent patterns, exploring potential solutions, testing hypotheses, and revising your model as needed. This type of thinking helps build resilience and creativity—skills that are essential in both professional and everyday problem-solving.

Skills That Go Beyond Math

While math modeling sharpens your math and problem-solving skills, it also hones other important abilities like communication, teamwork, and critical thinking. It forces you to explain your reasoning clearly and work with others to find the best solution. These are skills that carry over into almost any career, whether you end up in science or engineering, business, social science, or the arts.

What’s more, math modeling teaches you perseverance. Real-world problems aren’t solved in a single attempt. It takes multiple tries, revisions, and sometimes failures before you land on a workable solution. By engaging in math modeling, you learn the value of iteration and persistence—qualities that are invaluable in life and work.

Ready to Get Started?

If you’re interested in solving real-world problems and developing a math modeling mindset, getting involved in COMAP contests is a good place to begin. COMAP’s math modeling contests, like HiMCM/MidMCM and MCM/ICM, are designed to push you to think deeply, collaborate with others, and explore innovative solutions to some of today’s most pressing challenges.

Whether you’re a student looking to stretch your problem-solving abilities or an educator wanting to introduce your students to a hands-on learning experience, math modeling offers a unique, rewarding way to build essential skills for the future. 

Learn more about COMAP’s math modeling contests here. And explore these math modeling resources:

• 12 Ways Math Modeling Contests Can Boost Your Career
• 15 Careers That Rely on Mathematical Modeling
• A Student Guide for Getting Started with Math Modeling
• 10 More Reasons to Participate in a Math Modeling Contest