Productive Struggle in Mathematics: A Two-Part Series
Building the Foundations for Productive Struggle
What does it really mean to support productive struggle in a math classroom?
In this two-part series, Paul Battaglia reflects on both the mindset and the instructional moves that help students grow through challenge rather than shut down because of it. Drawing from his classroom experience, Paul explores how productive struggle shapes not only mathematical understanding, but also resilience and identity.
“Can We Have Another One?” Making Productive Struggle Work in Your Math Classroom
Stephanie is working at the whiteboard with two other students in my Algebra 2 Data Science class. She has been struggling to comprehend operations with polynomials for a few classes now. As I look on from across the room, I can see Stephanie and her group struggling to figure out where they have gone wrong. There is banter back and forth. There are moments where students correct each other. There are jokes and gentle ribbing when students present a somewhat outlandish idea or answer. Then I hear a sharp change in Stephanie’s tone. “Wait, wait!” she tells her peers. “I see it! We didn’t add these exponents when we multiplied the terms. Wait, let me see what happens when…”
Next thing I know, Stephanie isn’t just fixing her group’s mistake. She’s explaining to her peers where they went wrong, how to correct it, and then turns to me to ask the question every teacher loves to hear: “Can we have another one?”
While that question is certainly music to a math teacher’s ears, it is helpful to explore a deeper, overarching question: How do we honor student struggles without letting the struggle turn into frustration, despair, or even despondency?
Productive Struggle (ish)
Personally, I do not care too much for the term “productive struggle.” I fear it has become a rope that gets tugged on by factions of educators, allowing the term itself to be stigmatized. For this post, I will often use the term productive struggle, but what I am really referring to is a diverse set of data points in the way of perseverance, flexibility, failure, resilience, and much more that provide meaningful feedback to a learner about where they are in their comprehension and mastery of a given topic. In short, productive struggle is a process, and like anything worth mastering, that process is not linear, yielding many missteps and flaws in understanding along the way. What it is not is a bona fide pathway to comprehension. In fact, a common misconception among educators is that “struggling or grappling with challenging math tasks causes students to gain a deeper understanding than would be achieved if they learned the same skill without a struggle” (Advocates for the Science of Math, 2021). The reality is that when executed poorly, moments that call for productive struggle can devolve into incredible frustration and the feeling that one is constantly taking “one step forward, two steps back.” Needless to say, this gives way to that defeated feeling any of us have likely experienced when the support we needed in a crucial moment was nowhere to be found.
Then, why? Why does productive struggle matter? One word captures it all—feedback—about students’ thinking, their strategies, and most importantly, their growth. For students whose brains are still developing, any challenge that yields failures is invaluable for developing perseverance. As students build their capacity for mathematical fluency, they simultaneously build resilience. Understanding why struggle matters is one thing; creating the conditions for it is another. Let’s explore how.
Creating a Classroom Culture That Embraces Struggle
The elegance of mathematics is magnified when one perseveres through the struggle that accompanies multiple failures, only to satisfactorily arrive at a place where one is wiser than before the struggle began. Not unlike the value in learning how to ride a bike, change a flat tire, or master a difficult yoga pose, success can be found only as a byproduct of failure. Yet somehow, when students struggle with quadratic equations, we reach for the rescue rope.
My students were fully immersed in an activity called “Marbleslides” which asked them to manipulate the equations of various functions so that, when launched, a marble would travel along the resulting curve, hitting all the stars in its path. The activity was appropriately sequenced (given after students received direct instruction, guided practice, and checked their understanding). It was designed beautifully, starting with “easy wins” and progressing to various challenges. Yet in a class of 14 students, rather than allow each student to struggle as needed, I found myself violating nearly every widely accepted teacher behavior that productive struggle requires. On one hand, I was celebrating “beautiful mistakes,” but two students over, I was jumping in too soon, saying “wait don’t do that” or “let me show you what to do here.” While it is beneficial for students to hear how I think about my own mistakes or how I might revise my thinking, how can they have that same experience if I step in to rescue them? In this situation, it would have been more helpful to rely on my experience as a baseball player and coach. After a peculiar decision in a game, my baseball coach would pull a player aside and ask, “What did you see?” At that moment, players could let down their guard and fully explain their thought process. Similarly, I should have asked the student, “What have you tried?”
So what does healthy struggle from a student look like? I refer to it as relaxed determination. When I see a student thinking about what to do and then begin trying something, I know they are engaging with the material. They go as far as they can go, and then it is up to me to prove to them that their work, risk-taking, or questions are all helpful in one way or another. After directing student attention to a misstep or a flaw in their thinking, look for repeated attempts that move closer to success. Watch for frustration and remind students to self-assess. Are they frustrated because they feel lost? Is there a prerequisite skill they did not realize they needed to use within this scenario? How are they expressing their emotions? For instance, is the student using phrases like “I can’t….” In these situations, it is helpful to teach students how to reprogram their thinking with phrases such as “I’m confused why” or “I can do this up to a point, but then I get lost.” Ideally, students who begin using more forgiving language can turn frustration into determination. Be sure to celebrate student progress in this regard. Progress does not just come from completing a math problem. It also lies within the way students view themselves. The goal is for students to see themselves as capable thinkers.
This is more likely to happen if students feel that their classroom provides a safe environment for risk-taking. If I had chosen the Marbleslide activity as the entry point to teaching about a topic, the activity would have been a disaster, and the lesson plan would have deteriorated quickly. This is why I am a strong proponent of establishing deep relationships with students from the first day of school. As we begin the year, I take care to celebrate student thinking, regardless of how right or wrong a response might be. This can be done almost anytime and in many ways. Whether it is students working at whiteboards, choral response during explicit instruction, or gallery walks, there is always an opportunity to show students a safe environment to think without judgment. Do we acknowledge the difference between correct and incorrect? Of course! But students come to understand and value the importance of thought over rote answers.
In the next blog, Paul explores what this looks like in practice and how teachers can navigate the moment when students are stuck.
References
Advocates for the Science of Math (2021). “Common misconceptions: Productive struggle causes more robust understanding and learning.”
https://www.thescienceofmath.com/misconceptions-productive-struggle-causes-more-robust-understanding-and-learning
