Long before students start to work on their solution report to submit for the High School Mathematical Contest in Modeling (HiMCM)® or the Middle Mathematical Contest in Modeling (MidMCM), they’re learning how to think differently. They’re experiencing problems that don’t come with instructions. And maybe most importantly, they’re learning how to work together when there isn’t one “right” answer.

When Nothing Feels Clear Yet

Most middle and high school students are used to traditional math class problems that generally look familiar. There’s a formula to use, a method to follow, and one answer at the end.

It’s the opposite with HiMCM and MidMCM. Teams are handed a problem that is messy, open-ended, and maybe even poorly defined. There’s no obvious starting point, and no step-by-step process.

Before students can start doing some math, they have to step back and figure out what the problem actually is. They do this by figuring out what matters, what doesn’t, and what trade-offs they’re willing to make.

That early stage, when nothing quite makes sense yet, is where things begin to click and students get an idea of how to bring some math into the situation.

Preparation Isn’t About Studying

Unlike other types of math contests, getting ready for HiMCM or MidMCM isn’t about working through math problem after problem and memorizing techniques. Instead, students should focus on building habits like asking better questions, making sense of complicated problems, communicating with their teammates, developing and working through ideas together, and staying with it even when things feel uncertain. Kind of like life…

In fact, many HiMCM/MidMCM advisors say the most effective preparation doesn’t feel like “test prep” at all. It ends up feeling more like exploration with mini modeling activities, conversations, and time for students to dig into real-world situations.

The Team Dynamic Matters 

HiMCM and MidMCM aren’t individual competitions. They’re collaborative by design. And that changes everything. A strong team isn’t just made up of the “best” students. It takes a combination of strengths such as:

• Someone who likes digging into data.
• Someone who can organize ideas for the paper and express them clearly.
• Someone who loves math.
• Someone who is creative and asks questions no one else is.

When students learn how to take on these roles (when they’re under time pressure!), they tend to get a lot more out of the experience. And it’s often where students grow the most.

Advisors Set the Tone, Not the Direction

Team advisor's aren’t there to coach students toward the right answer. They’re there to support the process by encouraging students to ask questions, test ideas, adjust, and persevere.

How do they do this? It can look different from team to team. Some advisors run structured practice sessions, while others take a step back and let students lead, offering guidance along the way. There’s no single “right” way to do it. But the most successful teams usually have students who are given ownership early on.

The Mathematical Modeling Mindset

One thing that often happens when students participate in math modeling contests is that by the time contest arrives, they’ve already developed a mindset… a mathematical modeling mindset.

They get comfortable with a little ambiguity. They’re more willing to test ideas, and more aware of how to communicate their thinking. And those are the skills that carry far beyond the contest itself.

A Different Way to Think About Preparing

Getting ready to participate in HiMCM or MidMCM isn’t about practicing a certain type of problem, over and over. It’s about helping students become the kind of thinkers who can deal with challenges, even when they don’t know how to move forward.

And if you want to learn even more about the benefits of contests like HiMCM or MidMCM, check out these reasons to participate.