Every year, students around the world take part in the High School Mathematical Contest in Modeling (HiMCM)®. They’re given a real problem and several days to figure out what to do with it. By the end, each team has developed a mathematical model and written a technical paper explaining its work.

For many students, it's unlike anything they've experienced in a traditional mathematics classroom.

But what does that experience look like from the advisor's perspective?

We asked four HiMCM advisors from different schools and countries what they've learned from working with student teams. They each approach HiMCM a little differently, but they agree on a lot. Mathematical modeling for high school students is about more than getting the math right. Students have to decide what matters, explain the choices they make, and work with their teammates when there isn't an obvious path forward.

Students Begin Thinking Like Mathematicians

Several advisors talked about how modeling changes the way students approach a problem.

For Patrick Honner, that transformation begins when students realize there isn't a single correct path waiting for them to discover.

"I think it can be hard for students to accept that they are in charge when it comes to modeling. Math is so often given to them. Models are something they create,” he said. “They decide what’s important, they design how to measure it, they determine its effectiveness. They are in charge. It can feel like a big jump! But once they make that leap, it changes them. They are more willing to take that jump again and again."

That shift from solving someone else's problem to defining their own is exactly what makes mathematical modeling so powerful.

Roger Zhan has seen that confidence extend well beyond the competition itself.

"You can see the shift as they approach hard problems” he explains. “They are not afraid to try solving hard problems. One of my students participated in a stock portfolio investment competition. The structural thinking serves the student well."

Nathan Warkentin believes HiMCM often fills a gap that many traditional curricula simply can't.

"I would go as far as to say that HiMCM is the decisive modeling experience for our students. Our HS math curriculum does a lot of things well, but - as with many curricula - the pseudocontexts in which problems and content are placed do not do justice to the rich data necessary for actual modeling of authentic phenomena."

Warkentin wanted to take modeling further at his school and proposed a dedicated course, but there wasn't enough staffing to make it work. "So, as it stands, HiMCM is easily the most rigorous modeling component of our students' experience," he explains.

Success Depends on More Than Mathematics

Strong mathematical ability certainly helps, but each advisor emphasized that successful teams depend just as much on communication and collaboration.

Over the years, Warkentin has learned that who is on a team matters. He considers how students communicate and work together when putting teams together.

He’s also moved away from formal team-building activities. Instead, he builds in time on the first evening for students to take a break, order dinner, and spend some time together.

"Now, I just carve out a period of time during the evening of the first day and tell students that they all have to take a break and can order delivery food for dinner,” Warkentin said. “The students don't always come together as a large group, but the relative informality has definitely made that evening a much better social experience."

He also believes student leaders often understand social dynamics better than adults do. "Much of the time, our student leaders have a much better sense of these dynamics... when they draft a team roster, they have avoided a number of scenarios that could cripple a team's efficacy and ability to enjoy the experience."

That ability to work together matters during HiMCM, when students have just a few days to make decisions, work through disagreements, and finish their paper as a team.

Great Models Still Need Great Writing

Perhaps the biggest surprise came from first-year advisor Nader Aziz Mansour.

Looking back, the mathematics wasn't what he wished his students had spent more time practicing. It was technical writing. "They wrote the report really quickly, and should have spent more time editing it to make it easier to follow," he said.

If he could start over, he says he would spend considerably more time helping students develop their technical communication skills before the competition even begins.

"Work with students on effective technical writing before the start of the contest, as their report was quite awkward and cliché-ridden,” he advises. I would probably have them write smaller samples of technical English to make sure they understood the different voices when explaining the procedure and the results."

His experience also showed just how much the writing matters. A team can build a strong model, but they still have to explain what they did and why they did it in a way the judges can follow.

Building Toward Modeling Makes a Difference

Several advisors also reflected on how they've changed their own preparation over time.

Rather than immediately handing students previous HiMCM problems, Honner redesigned the beginning of his program.

"In the past my approach has been to just jump right into existing tasks and previous competition prompts with students, which can be a little overwhelming for those new to modeling,” he explains. “This year I designed a multi-session activity that develops the key ideas, questions, and methods of modeling over a few meetings."

The result was noticeable. "It really helped bring new students into modeling while giving experienced students space to both explore and to mentor," Honnor said.

Zhan offers reassurance for new advisors who may feel intimidated by the competition: "It is quite easy to get started." He suggests looking at a few past competitions as one way to become familiar with what HiMCM involves.

Sometimes building a successful modeling program doesn't require an entirely new curriculum. It simply starts with giving students opportunities to wrestle with authentic, open-ended problems, a large part of the mathematical modeling process.

More Than a Competition

All four advisors have seen HiMCM change the way their students think about mathematics.

Instead of memorizing procedures, they define problems. Instead of searching for one correct answer, they justify decisions. Instead of working individually, they collaborate, communicate, revise, and defend their ideas.

As Honner puts it, "I think the most powerful part of these mathematical modeling challenges is that students get to experience math as mathematicians do: as a creative, collaborative, purposeful endeavor. Students are doing math, not just learning math."

For students, HiMCM is a chance to experience mathematics differently and see what they can do with it.

Interested in bringing HiMCM to your students? Learn more about the contest and how to participate.