Five Principles of Extraordinary Math Teaching: Dan Finkel (Transcript)

Here is the full text of Dan Finkel’s talk titled “Five Principles of Extraordinary Math Teaching” at TEDxRainier conference. In this enjoyable talk, he invites us to approach learning and teaching math with courage, curiosity, and a sense of play.

Dan Finkel – TEDx Talk TRANSCRIPT

A friend of mine told me recently that her six-year-old son had come from school and said he hated math. And this is hard for me to hear because I actually love math.

The beauty and power of mathematical thinking have changed my life. But I know that many people lived a very different story.

Math can be the best of times or the worst of times, an exhilarating journey of discovery or descent into tedium, frustration, and despair. Mathematical miseducation is so common we can hardly see it.

We practically expect math class to be repetition and memorization of disjointed technical facts. And we’re not surprised when students aren’t motivated, when they leave school disliking math, even committed to avoiding it for the rest of their lives.

Without mathematical literacy, their career opportunities shrink. And they become easy prey for credit card companies, payday lenders, the lottery, and anyone, really, who wants to dazzle them with a statistic.

Did you know that if you insert a single statistic into an assertion, people are 92% more likely to accept it without question? Yeah, I totally made that up.

And 92% is — it has weight even though it’s completely fabricated. And that’s how it works.

When we’re not comfortable with math, we don’t question the authority of numbers. But what’s happening with mathematical alienation is only half the story.

Right now, we’re squandering our chance to touch life after life with the beauty and power of mathematical thinking. I led a workshop on this topic recently, and at the end, a woman raised her hand and said that the experience made her feel — and this is a quote — “like a God.”

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That’s maybe the best description I’ve ever heard for what mathematical thinking can feel like, so we should examine what it looks like. A good place to start is with the words of the philosopher and mathematician René Descartes, who famously proclaimed, “I think, therefore I am.”

But Descartes looked deeper into the nature of thinking. Once he established himself as a thing that thinks, he continued, “What is a thinking thing?”

It is the thing that doubts, understands, conceives, that affirms and denies, wills and refuses, that imagines also, and perceives. This is the kind of thinking we need in every math class every day.

So, if you are a teacher or a parent or anyone with a stake in education, I offer these five principles to invite thinking into the math we do at home and at school.


The ordinary math class begins with answers and never arrives at a real question.

“Here are the steps to multiply. You repeat. Here are the steps to divide. You repeat. We’ve covered the material. We’re moving on.”

What matters in the model is memorizing the steps. There’s no room to doubt or imagine or refuse, so there’s no real thinking here.

What would it look like if we started with a question? For example, here are the numbers from 1 to 20. Now, there’s a question lurking in this picture, hiding in plain sight. What’s going on with the colors?

Now, intuitively it feels like there’s some connection between the numbers and the colors. I mean, maybe it’s even possible to extend the coloring to more numbers. At the same time, the meaning of the colors is not clear. It’s a real mystery.

And so, the question feels authentic and compelling. And like so many authentic mathematical questions, this one has an answer that is both beautiful and profoundly satisfying.

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And of course, I’m not going to tell you what it is. I don’t think of myself as a mean person, but I am willing to deny you what you want.

Because I know if I rush to an answer, I would’ve robbed you of the opportunity to learn.


It’s not uncommon for students to graduate from high school believing that every math problem can be solved in 30 seconds or less, and if they don’t know the answer, they’re just not a math person. This is a failure of education.

We need to teach kids to be tenacious and courageous, to persevere in the face of difficulty. The only way to teach perseverance is to give students time to think and grapple with real problems.

I brought this image into a classroom recently, and we took the time to struggle. And the longer we spent, the more the class came alive with thinking.

The students made observations. They had questions. Like, “Why do the numbers in that last column always have orange and blue in them?” and “Does it mean anything that the green spots are always going diagonally?” and “What’s going on with those little white numbers in the red segments? Is it important that those are always odd numbers?”

Struggling with a genuine question, students deepen their curiosity and their powers of observation. They also develop the ability to take a risk.

Some students noticed that every even number has orange in it, and they were willing to stake a claim. “Orange must mean even.” And then they asked, “Is that right?” This can be a scary place as a teacher.

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