Cathy Williams: “In math teaching, the power of ‘yet’ is transformative.”

Verónica Sánchez
Verónica Sánchez
28/11/2025|4 min read
Cathy Williams: “In math teaching, the power of ‘yet’ is transformative.”

You’ve spent more than three decades focused on changing the way the world experiences mathematics. Tell us about your journey.

I started out as a high school teacher in California. Then I became the director of K-12 mathematics in a school district, and together with Jo Boaler I co-founded Youcubed, the Stanford Graduate School of Education project that promotes a creative and humane vision of math teaching. I’ve devoted my entire professional life to putting research and neuroscience at the service of students’ infinite potential.

Looking back, what moments made you realize that math could be taught—and lived—in such a different way?

That’s a really good question. I think the biggest moments for me with recognizing different representations in mathematics with student learning really comes from my early days teaching students that were in the US, but English wasn’t their first language. I was teaching high school, and many of my students were older and had recently arrived. The dynamics of the class changed the day I gave them the agency to show me their way of getting to an answer. I learned so much from them.

Later, when I was working at the county office, I was asked to do a five-day training for teachers in a very remote area of California. I had twenty-five teachers in the group, and there were twenty different first languages. It became the most magical learning environment for all of us.

Those are two moments that immediately stand out to me: they showed me the global nature of mathematics across the world and how beautiful it is when we are all together.

We tend to think of math as an individual exercise. Why do you insist so strongly on its collective dimension?

Math is such a collaborative, communication-based, beautiful space to play—it’s like a big playground. When we bring people together with the right tasks and the right conversations, and we add what we know from educational research and neuroscience, they start to see that they can think mathematically in a safe environment. They can play mathematically, and the way they see things truly matters.

 In classrooms, even among teachers, we often hear the phrase “I’m not a math person.” Why do you think it’s so common, and how can we help students—and teachers—unlearn it?

Many teachers don’t talk about having a positive experience in mathematics, and that’s heartbreaking. I think we’re products of our system, right? So what helps them change is, I’m going to say, playful mathematics, a kind of gentleness. Low-floor, high-ceiling tasks where you build in real, authentic mindset messages, like: “I really do care about the way you see it. Let’s talk about the way you see it, and let’s work together.”

Math is such a collaborative, communication-based space to play. It’s like a big playground. I think bringing them together with the right conversations, the right tasks, and bringing in the research, the neuroscience—all of that educational research really helps them see, in a safe environment, that they can think mathematically.

And it’s not just a U.S. problem. This happens around the world. It’s global.

 So can all of us do math?

Absolutely. At least in the U.S., there’s been this belief that you’re either born with a “math brain” or you’re not. That’s simply not true. What matters are our experiences. If a child is struggling, there’s nothing wrong with them. If we think they can’t do it, that’s on us. That child can.

Our job is to ask: What do we need to do to support them in their growth? They’re just not there yet. And the power of yet—as students in Scotland like to say—is transformative.

If you could change one thing about how society perceives math, what would it be?

 My hope is that one day you can walk into a Starbucks, a bar, a pub—wherever you are—start talking about math, even doing math, and people don’t feel an aversion to it. Research shows that for many adults, the brain’s fear center lights up when math comes up. I would love to live in a world where everyone sees themselves as mathematical, and a math conversation doesn’t trigger fear. Whatever it takes to get there matters—helping people who already carry that fear move past it, and, with young children, doing everything we can so they never lose belief in their mathematical potential.

What things around you have given you hope lately?

I think the growth of research is a big part of it, especially the merging of mindset into mathematics. Mindset matters everywhere, but people are really focusing now on how students’ beliefs about themselves mathematically shape how they engage with math in content-specific ways. It’s a way of being. Helping students develop a mathematical way of being, and believing in themselves, gives me a lot of hope.