There are a few different kinds of struggles that students may experience in school. There’s the frustrating kind that occurs when instructions are unclear, the material feels completely out of reach, or students are stuck without support. And then there’s the kind of struggle that leads somewhere, the kind that challenges students just enough to keep them engaged, thinking, and problem-solving on their own. This sweet spot is called productive struggle: not too easy and not too hard.

Productive struggle is critical for deeper learning, especially in math. Math modeling gives students an ideal space in which to develop their capacity for and understanding of productive struggle. Let’s take a look at what a productive struggle in math and modeling means, how it can benefit students, and how educators can take this approach.

What Is Productive Struggle in Math?

Productive struggle happens when students are given the chance to work through tough problems on their own, without being handed the answer right away. They might feel a little stuck at first, but that’s part of the process. It gives them room to try different ideas, make mistakes, and think through what actually makes sense. Instead of focusing on speed or just getting it right, they’re encouraged to slow down and understand why the math works the way it does.

A blog post from AAAS talks about how productive struggle is most effective when students:

“delv[e] more deeply into understanding the mathematical structure of problems and relationships among mathematical ideas, instead of simply seeking correct solutions.”

(National Council of Teachers of Mathematics, 2014, p. 48)

Students who work through problems like this have an opportunity to test their ideas, ask questions, and start to form an understanding of the process. 

And this isn’t just a good idea; it’s backed by research. An International Journal of Education in Mathematics, Science and Technology 2024 review of studies on productive struggle found that learning this way is incredibly valuable:

“The productive struggle is considered essential for deepening understanding, fostering problem-solving skills, and promoting long-term learning.”

(Young, Bevan, & Sanders, 2024, p. 471)

In the end, productive struggle helps students become better thinkers. And math modeling gives them a great way to practice that kind of thinking.

Math Modeling + Productive Struggle = Big Wins for Students

Math modeling gives students the chance to experiment and figure things out for themselves. Since there’s usually no single “correct” answer, they can make their own decisions, test their thinking, and adjust as needed along the way.

This helps students build confidence. It encourages them to keep working through tough challenges. And they essentially begin to think more deeply, especially when they get a good solution and then want to do better.  Productive struggle can be provide intrinsic motivation.They start to see math as a tool for solving real-world problems, not just something to get done.

This is why math modeling and productive struggle go hand in hand. COMAP’s modeling contests are built around open-ended problems that don’t have a single right answer (and that’s by design!). These challenges ask students to apply math to real-world situations that are often complex and full of unknowns.

There’s no single way to approach the problem. Students have to figure out what matters, come up with a plan, create a model, evaluate how well it works, and adjust if needed. It might feel a little uncomfortable at first, but that’s exactly what pushes them to grow as problem solvers and critical thinkers.

Because math modeling is often done in teams, students learn to collaborate and communicate more effectively. They learn how to explain their thought processes and listen to different perspectives. And they figure out how work together to make the best decision they can.

What Educators Can Do

Educators can help students work through productive struggle by incorporating math modeling into their curriculum and, if needed, adapting it for different grade levels. One of the most impactful things they can do is encourage students to stay with a tough problem, even when it gets uncomfortable. This builds confidence over time. But it only happens when teachers resist the urge simply to tell students the answer or give them hints. The best pedagogical advice is to ask students questions that lead them to reflect on their own thinking — constructing their own understandings, evaluating, and improving them.

Modeling tasks, like those from COMAP’s contests and a wide range of in-class math modeling modules, and many more resources in our library, are a great way to support this math modeling mindset. These kinds of problems encourage students to move away from just trying to “get the right answer” and toward figuring things out for themselves.

Productive struggle helps students become better problem solvers, critical thinkers, and collaborators. And math modeling is the perfect way to support that kind of learning. With the open-ended nature of real-world problems, we’re not just teaching students math; we’re teaching them how to think.