When I try to describe great teaching, I notice a certain phrase pops out of my mouth again and again.

*Productively stuck*.

As in, the goal of the teacher is to get her students *productively stuck* as soon as possible. As in, we want to hook the students with a compelling question and then leave them *productively stuck*. As in, when a student is *productively stuck*, we don’t want to tell them the answer, because that robs them of the educational experience.

You could say that being productively stuck is virtually the same thing as learning. Talk to any teacher worth their salt and they’ll tell you how they draw their students in, how they frustrate them, how they force them to grapple with big ideas. It’s a surprising idea because *learning* connotes something so positive and *frustration * and *stuckness* something so negative. And yet, they’re intertwined. Frustration just means you have a need that hasn’t yet been filled; learning is taking in (or creating) a new thing to fill the need.

Which means teachers need to be just the right kind of mean. They have to care enough not to be nice and relieve their students’ suffering (a relief that teaches a terrible lesson: that you can complain and the adult will solve your problems for you). No, the caring teacher lets their students suffer in just the right ways and struggle at just the right level: challenging, but not overwhelming.

I’ve noticed that a lot of folks who write about this topic have different descriptions for it.

- James Tanton: “Let students flail.”
- Dan Meyer: “Be less helpful.”
- Paul Lockhart:

“Give your students a good problem, let them struggle and get frustrated. See what they come up with. Wait until they are dying for an idea,*then*give them some technique. But not too much.”

Here’s another coinage from Emily, a teacher we worked with over the last few years: *good frustration. *I talked to her in the spring, and she shared this story of how starting with a question that her students didn’t have the tools for motivated them to want to learn multiplication and division (skills they would later master). What I love is that she goes seamlessly from talking about teaching math in a way that kids love, to starting your lesson with a question, to getting kids frustrated. She read me her student’s feedback on the class from surveys she had them take, and you know what they said, over and over. *They loved the challenge*.

Here’s the video.

I’ve been struck repeatedly over the last decade or so by how opposed to letting students struggle some educators are. It’s not easy to know in many cases why. Some, I suspect, just can’t let go of the notion that teaching = telling, and that if you’re not telling/showing/demonstrating/explaining for a class or individual then you’re not teaching, particularly in mathematics classrooms. Such teachers have rarely, if ever, seen effective teaching of mathematics done in any other way, and many who have simply dismiss what they’ve been shown as irrelevant to their own practices.

For other teachers, I believe it’s a matter of being battered, bullied, cajoled, and otherwise assailed by parents, students, administrators, and perhaps colleagues into never letting students have to “suffer” through any meaningful sort or amount of struggle. Those who stray are called cruel, arrogant, presumptuous, elitist, or worse. I know: I’ve been accused of all those things and worse. But it hasn’t changed my fundamental viewpoint on this issue: to be able to do meaningful math, you HAVE to know how to struggle, flail, etc., and you have to be willing to do so. Anything else is but the palest shadow of what it means to do mathematics.

I think you hit the nail on the head when you said “such teachers have rarely, if ever, seen effective teaching of mathematics done in any other way,” and I think that’s the real key to making a change. The people who teach math need to have had an experience of doing math—the real stuff—themselves. Until they’ve experienced the joy and challenge of doing math themselves, and had a chance to reflect on that experience, there’s no way to get buy in, and the idea that struggle is the best way to learn seems esoteric at best, cruel at worst.

The good news is, I think that when you do give teachers an opportunity to do real math, it is so compelling that they begin to ask themselves how they can give this kind of experience to their students as well. And then change can happen. It just needs to start with experience. To paraphrase Morpheus, I can’t tell you what it is; you have to experience it for yourself.

As for those who are bullied and battered by the system, sometimes they just need the inspiration to do what they want to do anyway. I’ve seen some teachers see what’s possible and choose to do it their own way, and it’s a pleasure. There’s so much potential waiting to be unleashed.

This is an important message for parents too. While its hard to watch your children fail without stepping in, and often publically frowned upon, it is so import at that we let them have that experience of failure. Only then will they gain true problem-solving skills, as well as deeply rooted confidence and resilience. When I am able to step back and watch my children flail, I am so often surprised by the speed and grace of of their learning, and their true happiness and pride in their newfound abilities.

I absolutely agree. I read a great piece about a family that moves to Russia for a year, and the kids have to flail their way through learning Russian and making friends from ground zero. And by the end of the year, they’ve overcome, and it’s an amazing experience.

Paul Zeitz tells me that a group of teachers he worked with this summer coined the term “funstration”. I think the fun component is one way to keep people struggling productively.

Cute! I agree on the fun. We’ve been talking about how there are two phases sometimes: first, where you build up confidence and momentum by playing and having early successes, and second, when you push into the difficulty. And the more momentum you have, the further you go.