Productive struggle is probably one of the leading buzzwords in education. (I have seen multiple “The Productive Struggle is Real” conference sessions at NCTM.) Growth mindset! Grit! I’ll keep trying! Mistakes help me learn! While I support all of these messages, they start to sound empty after a while. These are things that need to be fleshed out and embodied, not just written on posters. So how do we do that?
We have to start by becoming crystal clear about what we mean by productive struggle, how it differs from unproductive struggle, and why productive struggle is critical for helping students understand mathematics on a deep level. Let’s get started.
What is productive struggle?
The verb struggle is defined as “to contend resolutely with a task or problem”. The noun form means “the process, or an act or instance of struggling”. Thank you dictionary.com. Very helpful.
Digging further, the word “contend” includes an aspect of opposition or rivalry. “Resolutely” implies determination. Since math is not a war to be fought, I was at a bit of a dead end (no pun intended). But maybe the opposition isn’t with math itself. Perhaps the opposition, the thing we have to grapple with when things get hard, is the uncertainty about how to move forward. The discomfort that comes from unfamiliarity. Not having the information or knowledge we need to advance. Maybe struggle occurs whenever the path is unclear. Productive struggle, then, is when the path is unclear but the destination is clear. This is in contrast to unproductive struggle, when the path and the destination are unclear.
And because everyone loves a 2x2 matrix, we can also consider the kinds of activities that occur in our classrooms when the path is clear.
It is important to note that when I say “destination unclear” I mean that the destination is unclear to the student. A teacher might be crystal clear about where they’re trying to get their students to go, what skill they’re trying to teach, but the student has no real sense of why they’re doing what they’re doing. They might be able to read off the board that the goal is to “solve a system of equations using elimination” but they have no idea why that might be worthwhile, or how it relates to other destinations they’ve visited in the past.
Our goal is not to help students avoid struggle or even cope with struggle. Our goal is to help students value struggle and persevere through struggle in a way that fosters their self-efficacy as a learner. Only when students are entrusted with the cognitive load of having to search the databanks of their current understanding, identify helpful information, and compose that information to solve an unfamiliar problem, do they learn in a meaningful way. By this I mean that they “own” the new learning and it sticks, disrupting the constant cycle of reviewing and reteaching. This works best of course when students have multiple data banks to draw from and can leverage the help of others to organize and synthesize ideas (i.e. group work).
Struggle, if it is productive, is the means by which students come to understand mathematics.
Productive struggle and learning
I find Vygotsky’s idea of a zone of proximal development (ZPD) helpful here. This is the potential for new learning that exists just outside of a student’s current [individual] set of skills, knowledge, and capabilities.
In his theory, this potential is only realized through social interactions with others, what he describes as “assistance from adults or more capable peers”. Two things of note here:
There is a transfer of responsibility. Things that used to be in the ZPD move to the inner circle, or what a student can do individually and without assistance. Permanent scaffolding is not the goal here!
The word “assistance” may not mean what you think it does. As teachers who care deeply about the success of our students, we often run the risk of helping our students too much. We take over too much of the thinking and funnel them toward the right answer. Assisting is not laying out the path for the student and breadcrumbing them to an answer. Assisting looks like asking focusing questions, offering students opportunities for collaboration and proper scaffolds so that collaboration is effective, and skillfully leading a debrief in a way that organizes, structures, and formalizes ideas that are still in-process.
When students engage in productive struggle, they are working in their ZPD, that sweet spot of wrestling with ideas just beyond their current comfort and skill level, but not so out of reach that it becomes frustrating. We wouldn't try to teach integrals to a third grader! The good news is that working within the ZPD is inherently motivating. Responsibility is transferred from the helpful peer or adult to the learner which leads to that sense of pride we get when we master something we’ve been working hard at, and increases the learner’s sense of self-efficacy. Students are more willing to engage in future challenges because they have seen the fruit of their persistence.
Why should we build students' capacity for struggle?
When we teach with tasks that engage and challenge students, when we use peer-to-peer dialogue as a primary method for helping students make sense of ideas, and when we communicate through our words and actions authentic views of what it means to do and learn mathematics, we build students’ capacity for struggle. We widen the student’s ZPD. We take things that used to be beyond reach and make them accessible to students, because the idea of wrestling, making sense, and persevering are no longer foreign to them.
My closest airport in Grand Rapids, Michigan is teeny tiny. Twelve gates, that’s it. Although flying out of GRR is really convenient, I’m often quite limited in my options. There are only so many destinations that you can get to directly, and oftentimes the price for such ease is horrendous. But if I’m willing to drive 3 hours to Chicago O’Hare, the world is my oyster! I can travel virtually anywhere and if my flight gets canceled, no problem– there are plenty of other flights on which they can rebook me. Committing to a classroom centered around productive struggle is like choosing to make the drive to ORD. It might not feel like the most convenient or efficient choice in the short run, it might take time that you don’t think you have, it certainly adds complexity to the journey, but when you get there, when you truly have a classroom where all students are empowered to think and make sense of mathematics for themselves, the possibilities are endless!