Fostering Productive Struggle in Math Will Transform Your Instruction

Recently, our Vice President of Instructional Design, Amy Jones Lewis, shared a mistake she used to make as a math teacher.

“During my first couple of years of teaching, I’d be walking around the room, helping students with math problems, and all of a sudden, I’d realize I had somebody’s pencil in my hand,” Ms. Lewis recalled. “And that was because I had taken their pencil, fixed the problem, and walked off.” 

“I didn't like to see kids struggle,” she continued. “I wanted to help them. But instead, I was robbing them of that opportunity to work through that productive struggle.”

For the past two decades, education researchers have explored the impact of productive struggle on K-12 students, particularly in mathematics instruction. But only recently has the term broken into the mainstream—its inclusion in the new California math framework indicates its rising popularity.

So, what is productive struggle?

What is productive struggle?

Productive struggle is the deliberate, low-stakes grappling with an unclear concept, skill, or task that leads to deeper learning and long-term retention.

Some signs of productive struggle include:

• Asking on-task or related questions

• Using manipulatives, graphic organizers, calculators, or other tools

• Collaborating with classmates

• Walking around the classroom to read posters or access other reference materials

Struggle itself is not inherently productive. It must land on the threshold between boredom and frustration, also known as the zone of proximal discomfort. Beyond that zone, struggle can become unproductive–or even destructive.

Students who experience destructive struggle not only throw up their hands and disengage, but they do so believing that they are fundamentally incapable.

The research behind productive struggle

When struggle is productive, the knowledge gained is unique in that it is—and feels—earned. Math students who learn via productive struggle significantly outperform students in traditional direct instruction pedagogy. 

A study observed that 9th-grade students who learned about standard deviation through productive struggle outperformed their peers who received direct instruction. While the productive struggle cohort indicated their lesson took much more mental effort, their post-test results indicated they had much better conceptual understanding and skill transfer than their direct instruction peers. Interestingly, the direct instruction group did not significantly outscore the productive struggle group in procedural knowledge. 

How to foster productive struggle in your school or district

If you’re a building or district leader, you can foster productive struggle in these ways:

• Craft a school or district-wide initiative so that all teachers and support staff work to nurture productive struggle.

• Create a culture of making—and celebrating—mistakes. At Carnegie Learning, our CEO Barry Malkin puts this concept into practice by regularly bestowing a “First Pancake” award to employees who strive to innovate, even if their efforts fall short (like the first pancake of the batch!) 

• Provide curricular coherence by adopting the same standards-driven, high-quality instructional materials for all grade levels.

• Implement de-tracking policies to place students in regular math classes with appropriate supports that scaffold up, not down.

• Invest in quality professional development to assist math teachers in continually honing their craft through the lens of productive struggle.

• Collaborate with and support instructional coaches and teachers to think of alternatives to traditional grading schemas that systematically penalize mistakes.

Fostering productive struggle in your classroom

If you’re a classroom teacher, consider these approaches to fostering productive struggle in your students:

• Focus your lesson on understanding the math instead of finding the right answer.

• Choose high-quality tasks that will engage students.

• Have resources—manipulatives, calculators, posters, etc.—available for students to use or refer to independently.

• Monitor student thinking, progress, and struggle by moving around the room while students work.

• Discuss strategies and questions as they come up with the whole class.

• Debrief the task with a meaningful class discussion that explores the challenges students encountered and offers time for student reflection.

• Validate students' thinking process with responses like:

  • "It's okay if you can't solve it yet—that's why we're here."

  • "I understand your logic. Let's explore your thinking.”

  • "Never apologize for making a mistake. Rather than thinking about right or wrong, tell yourself, 'I'm figuring it out.'" 

• See your students as whole people with strengths, needs, interests, and fears. Teachers must recognize that all students are capable of succeeding in math.

• Embrace a growth mindset.

• Be transparent about your own learning journeys and show students that mistakes are stepping stones, not stumbling blocks. This requires an unlocked door to that level of heart.

• Build trust with students. We mustn't be adversaries to our students; we must be their partners. This partnership means making mutual commitments, encouraging feedback, and building trust.

• Reward collaboration among students.

• Avoid rows and group desks together instead.

• Build thinking classrooms.

• Rethink how you grade, since mistakes should not be reflected in a grade.

• Scaffold up, not down. In other words, avoid watering down the cognitive demands of a task, and instead provide students with the tools they need to succeed on grade-level tasks.

For productive struggle to truly be effective, all classroom stakeholders should be clear-eyed about the fundamental paradigm shift it requires.

Moving forward 

As Amy Jones Lewis discovered, sometimes the most powerful teaching moments come when we step back and let students work through challenges.

"I had to become the teacher who would stand behind students and let them make mistakes," she reflects. And instead of coming home with extra pencils, she started coming home with stories about the magic that happens when students persevere through struggle.

Ultimately, mathematics education should be about not just finding the right answers but building the confidence and resilience to tackle increasingly complex challenges. When we foster productive struggle in our classrooms, we're not just teaching math—we're teaching students how to think, persist, and grow.

Ready to put these principles into practice? Check out our K-12 ClearMath solutions for high-quality instructional materials that guide students through struggling productively.