Delight in the Risk of Not Knowing

Lessons From the Whiteboard

A Note About the Essay:

Lately, I've been thinking about mistakes and how mistakes in math get intertwined with fear. The way so many students learn to treat being wrong like evidence they are incapable, unintelligent, or somehow not meant for mathematics at all.

The more time I spend teaching, tutoring, and studying mathematics, the more I realize that learning has never been linear. It bends, loops, stalls, collapses, and rebuilds. Sometimes understanding arrives quickly. Other times it arrives only after confusion, frustration, and trying again.

This reflection grew out of a moment while teaching Algebra 2 when I got a problem wrong in front of an entire class.

The Moment at the Board

There's this moment, standing in front of the smartboard, pencils scratching paper, calculators clicking softly against desks, when I realize I've made a mistake.

It was more than just a tiny arithmetic slip that I could erase quickly and keep going.

It was a mistake where the logic stops making sense halfway through the problem. The kind where your own work suddenly looks unfamiliar to you. The kind where you can feel the answer pulling away from correctness in real time.

The terrifying part is that I realized my mistake while thirty Algebra 2 students are watching my every squiggle on the board.

For a split second, instinct kicks in. The old reflex so many of us develop in school: just keep moving. Pretend confidence long enough that maybe nobody notices. Smooth over the uncertainty. Protect the image of competence at all costs.

But standing there with the marker still in my hand, I can feel the problem unraveling in real time. The answer doesn’t fit. The reasoning doesn’t follow. I have confidently walked myself into mathematical nonsense.

So instead of pretending, I stop:

"I don't know. I'll have to think about it."

The words land heavier than expected, but somehow lighter too.

To add even more weight to the moment, the principal is in the room watching me teach. I can feel her presence beside me like a shadow of authority, polite but watchful.

Then something surprising happens. A laugh catches in my throat and tumbles out, because really, what else can you do?

And somehow, the room exhales with me. A couple students smile. Someone quietly says, "I was wondering about that too."

The tension softens and the room becomes human again.

Revising in Real Time

I promise the students I'll come back to the problem later, and I do.

I sit down with a scrap piece of paper and begin revising and repairing my thinking. Rebuilding the logic line by line until the math settles back into place again.

Then, later that class period, I walk back up to the board. This time, slower and quieter.

I walk back up more certain, not because I got lost but because I found my way back.

I explain what went wrong. I show them where my thinking drifted off course. I walk them through how I noticed the mistake and how I fixed it.

Strangely, the mistake makes the lesson better.

The room feels more engaged afterward, not less. Students ask more questions. They seem more willing to think out loud, more willing to risk uncertainty themselves.

It's funny how the moment that could have become humiliation turns into connection.

The Fear of Being Wrong

For a moment, while standing at the board, I remembered what it felt like to be a student.

Staring at numbers on a worksheet. Feeling my stomach knot whenever the teacher asked:

"Does everyone understand?"

Usually I didn't. I just didn't want anyone to know.

I think a lot of students live inside that fear every day: the fear that being wrong will expose something about them. That confusion is proof they are behind. That asking questions will reveal they don’t belong in the room at all.

I know that fear because I carried it for years.

When I was younger, being wrong in math didn’t feel like a normal part of learning. It felt like evidence. Evidence that everyone else understood something I didn’t. Evidence that maybe I just wasn’t “a math person.” Evidence that there was something defective about the way my brain worked.

I used to think that if I just learned enough mathematics, eventually I would stop making mistakes altogether.

After completing a math degree, I can confidently say that I still make mistakes all of the time.

I'm grateful for mistakes now. They've slowly taught me something much more important than correctness ever could: they taught me how to stay.

How to sit with confusion long enough to work through it instead of running from it.

How to separate not knowing something from being incapable.

How to try again without collapsing into shame.

The Human Part of Mathematics

I think students spend years absorbing the idea that being good at math means being certain quickly, publicly, and without hesitation.

We praise speed so often that students begin confusing fast answers with understanding. We celebrate correctness in ways that quietly teach students to hide confusion instead of exploring it.

And eventually, many students stop seeing mathematics as something creative or exploratory at all. Instead, it becomes performance. A performance of competence, confidence, and always knowing.

Real mathematics has never looked like that. Real mathematics is messy.

It is forgetting things you once understood.

It is staring at a problem for twenty minutes before realizing the mistake was in line two.

It is trying one approach, abandoning it, and trying another.

It's full of uncertainty, revision, and persistence.

The longer I study mathematics, the more I realize that confusion is not the opposite of learning, it is often the doorway into it.

What a strange, lovely risk it is to admit uncertainty in the land of right answers.

To let the neatness of mathematics blur just enough to make room for the human part of it: the forgetting, the fumbling, the trying again.

To stand there not as the keeper of math, but as someone still learning it too.

"What a strange, lovely risk it is to admit uncertainty in the land of right answers."

What I Hope They Saw

If younger me had been standing at that board, she probably would have panicked.

I can still picture her so clearly: desperate to look competent, terrified of public mistakes, convinced that getting something wrong meant something was wrong with her.

She treated mistakes like proof that she was incapable.

I think many students still carry that same fear into math every day. You can see it in the hesitation before they answer. In the apology that comes before a question. In the way they say, "This is probably stupid," before they even begin.

So maybe what mattered most about that moment wasn't whether I corrected the problem later, but that they watched someone survive being wrong.

Maybe they saw that confusion didn't destroy the room.

That uncertainty didn't make everyone lose respect for me.

That mistakes are not emergencies.

Maybe they saw that thinking is allowed to be messy. That even teachers pause. Even teachers rethink. Even teachers begin again.

Delight in the Risk of Not Knowing

After class, I kept thinking about the students' faces. The laughter and little flashes of recognition when they realized even grown-ups get lost sometimes.

And when we get lost, it's okay to breath, pause, think, and begin again.

I kept thinking about all the times I’ve watched students physically relax at the math center (where I tutor) when I admit I don’t know something immediately. The way their shoulders loosen. The way their voice becomes steadier. The way honesty transforms the atmosphere of the room.

There’s a quiet beauty in that relief.

It’s the sound of trust forming, even if no one names it.

Maybe risk is less about stepping off cliffs and more about stepping toward each other: toward vulnerability, toward honesty, toward shared curiosity.

Maybe learning has always been less about proving intelligence and more about being willing to remain open even in uncertainty.

And maybe that’s why this moment stayed with me long after class ended.

Because for a few seconds, the room stopped being a place where everyone had to perform certainty. It became a place where people were simply thinking together.

So yes, there was delight in the risk of not knowing.

Delight in the stumble.

Delight in the pause.

Delight in the graciousness of recovery.

Delight in the small chorus of calculator clicks and pencil scratches that kept going even when I stopped.

Delight in the unexpected grace of discovering you do not have to know everything to be enough.

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