I really love color.
I notice it everywhere and in everything.
My family makes fun of me because I like to use colors with elusive-sounding names, like celadon ...
(Laughter) ecru ...
carmine.
Now, if you haven't noticed, I am black, thank you -- (Laughter) and when you grow up in a segregated city as I have, like Chicago, you're conditioned to believe that color and race can never be separate.
There's hardly a day that goes by that somebody is not reminding you of your color.
Racism is my city's vivid hue.
Now, we can all agree that race is a socially constructed phenomenon, but it's often hard to see it in our everyday existence.
Its pervasiveness is everywhere.
The neighborhoods I grew up in were filled with a kind of culturally coded beauty.
Major commercial corridors were lined with brightly painted storefronts that competed for black consumer dollars.
The visual mash-ups of corner stores and beauty supply houses, currency exchanges, are where I actually, inadvertently learned the foundational principles of something I would later come to know is called color theory.
I can remember being pretty intimidated by this term in college -- color theory.
All these stuffy old white guys with their treatises and obscure terminologies.
I'd mastered each one of their color palettes and associated principles.
Color theory essentially boils down to the art and science of using color to form compositions and spaces.
It's not so complicated.
This was my bible in college.
Josef Albers posited a theory about the color red, and it always has stuck with me.
He argues that the iconic color of a cola can is red, and that in fact all of us can agree that it's red but the kinds of reds that we imagine are as varied as the number of people in this room.
So imagine that.
This color that we've all been taught since kindergarten is primary -- red, yellow, blue -- in fact is not primary, is not irreducible, is not objective but quite subjective.
What?
(Laughter) Albers called this "relational."
Relational.
And so it was the first time that I was able to see my own neighborhood as a relational context.
Each color is affected by its neighbor.
Each other is affected by its neighbor.
In the 1930s, the United States government created the Federal Housing Administration, which in turn created a series of maps which were using a color-coding system to determine which neighborhoods should and should not receive federal housing loans.
Their residential security map was its own kind of color palette, and in fact was more influential than all of those color palettes that I had been studying in college combined.
Banks would not lend to people who lived in neighborhoods like mine.
That's me in D86.
Their cartographers were literally coloring in these maps and labeling that color "hazardous."
Red was the new black, and black neighborhoods were colored.
The problem persists today, and we've seen it most recently in the foreclosure crisis.
In Chicago, this is best symbolized by these Xs that are emblazoned on the fronts of vacated houses on the South and West Side.
The reality is that someone else's color palettes were determining my physical and artistic existence.
Ridiculous.
I decided that I'd create my own color palette and speak to the people who live where I do and alter the way that color had been defined for us.
It was a palette that I didn't have to search far for and look for in a treatise, because I already knew it.
What kind of painter emerges from this reality?
What color is urban?
What color is ghetto?
What color is privilege?
What color is gang-related?
What color is gentrification?
What color is Freddie Gray?
What color is Mike Brown?
Finally, I'd found a way to connect my racialized understanding of color with my theoretical understanding of color.
And I gave birth to my third baby: "Color(ed) Theory."
(Laughter) "Color(ed) Theory" was a two-year artistic project in which I applied my own color palette to my own neighborhoods in my own way.
Now, if I walked down 79th Street right now and I asked 50 people for the name of the slightly greener shade of cyan, they would look at me sideways.
(Laughter) But if I say, "What color is Ultra Sheen?" -- oh, a smile emerges, stories about their grandmother's bathroom ensue.
I mean, who needs turquoise when you have Ultra Sheen?
Who needs teal when you have Ultra Sheen?
Who needs ultramarine when you have ...
(Audience) Ultra Sheen.
(Laughter) This is exactly how I derived my palette.
I would ask friends and family and people with backgrounds that were similar to mine for those stories and memories.
The stories weren't always happy but the colors always resonated more than the product itself.
I took those theories to the street.
"Ultra Sheen."
"Pink Oil Moisturizer."
If you're from Chicago, "Harold's Chicken Shack."
(Laughter) "Currency Exchange + Safe Passage."
"Flamin' Red Hots."
"Loose Squares" ...
and "Crown Royal Bag."
I painted soon-to-be-demolished homes in a much-maligned area called Englewood.
We'd gather up as much paint as I could fit in my trunk, I'd call my most trusted art homies, my amazing husband always by my side, and we'd paint every inch of the exteriors in monochromatic fashion.
I wanted to understand scale in a way that I hadn't before.
I wanted to apply the colors to the biggest canvas I could imagine ...
houses.
So I'd obsessively drive up and down familiar streets that I'd grown up on, I'd cross-reference these houses with the city's data portal to make sure that they'd been tagged for demolition -- unsalvageable, left for dead.
I really wanted to understand what it meant to just let color rule, to trust my instincts, to stop asking for permission.
No meetings with city officials, no community buy-in, just let color rule in my desire to paint different pictures about the South Side.
These houses sit in stark contrast to their fully lined counterparts.
We'd paint to make them stand out like Monopoly pieces in these environments.
And we'd go on these early Sunday mornings and keep going until we ran out of that paint or until someone complained.
"Hey, did you paint that?"
a driver asked as I was taking this image one day.
Me, nervously: "Yes?"
His face changed.
"Aw, I thought Prince was coming."
(Laughter) He had grown up on this block, and so you could imagine when he drove past and saw one of its last remaining houses mysteriously change colors overnight, it was clearly not a Crown Royal bag involved, it was a secret beacon from Prince.
(Laughter) And though that block was almost all but erased, it was the idea that Prince could pop up in unexpected places and give free concerts in areas that the music industry and society had deemed were not valuable anymore.
For him, the idea that just the image of this house was enough to bring Prince there meant that it was possible.
In that moment, that little patch of Eggleston had become synonymous with royalty.
And for however briefly, Eric Bennett's neighborhood had regained its value.
So we traded stories despite being strangers about which high school we'd gone to and where we'd grown up, and Mrs. So-and-so's candy store -- of being kids on the South Side.
And once I revealed that in fact this project had absolutely nothing to do with Prince, Eric nodded in seeming agreement, and as we parted ways and he drove off, he said, "But he could still come!"
(Laughter) He had assumed full ownership of this project and was not willing to relinquish it, even to me, its author.
That, for me, was success.
I wish I could tell you that this project transformed the neighborhood and all the indices that we like to rely on: increased jobs, reduced crime, no alcoholism -- but in fact it's more gray than that.
"Color(ed) Theory" catalyzed new conversations about the value of blackness.
"Color(ed) Theory" made unmistakably visible the uncomfortable questions that institutions and governments have to ask themselves about why they do what they do.
They ask equally difficult questions of myself and my neighborhood counterparts about our value systems and what our path to collective agency needs to be.
Color gave me freedom in a way that didn't wait for permission or affirmation or inclusion.
Color was something that I could rule now.
One of the neighborhood members and paint crew members said it best when he said, "This didn't change the neighborhood, it changed people's perceptions about what's possible for their neighborhood," in big and small ways.
Passersby would ask me, "Why are you painting that house when you know the city's just going to come and tear it down?"
At the time, I had no idea, I just knew that I had to do something.
I would give anything to better understand color as both a medium and as an inescapable way that I am identified in society.
If I have any hope of making the world better, I have to love and leverage both of these ways that I'm understood, and therein lies the value and the hue.
Thank you.
(Applause and cheers)
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, (Laughter) 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 percent more likely to accept it without question?
(Laughter) Yeah, I totally made that up.
(Laughter) And 92 percent 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."
(Laughter) 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 webblaura@example.org.
Principle one: start with a question.
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.
And of course, I'm not going to tell you what it is.
(Laughter) I don't think of myself as a mean person, but I am willing to deny you what you want.
(Laughter) Because I know if I rush to an answer, I would've robbed you of the opportunity to learn.
Thinking happens only when we have time to struggle.
And that is principle two.
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?"
(Laughter) This can be a scary place as a teacher.
A student comes to you with an original thought.
What if you don't know the answer?
Well, that is principle three: you are not the answer key.
Teachers, students may ask you questions you don't know how to answer.
And this can feel like a threat.
But you are not the answer key.
Students who are inquisitive is a wonderful thing to have in your classroom.
And if you can respond by saying, "I don't know.
Let's find out," math becomes an adventure.
And parents, this goes for you too.
When you sit down to do math with your children, you don't have to know all the answers.
You can ask your child to explain the math to you or try to figure it out together.
Teach them that not knowing is not failure.
It's the first step to understanding.
So, when this group of students asked me if orange means even, I don't have to tell them the answer.
I don't even need to know the answer.
I can ask one of them to explain to me why she thinks it's true.
Or we can throw the idea out to the class.
Because they know the answers won't come from me, they need to convince themselves and argue with each other to determine what's true.
And so, one student says, "Look, 2, 4, 6, 8, 10, 12.
I checked all of the even numbers.
They all have orange in them.
What more do you want?"
And another student says, "Well, wait a minute, I see what you're saying, but some of those numbers have one orange piece, some have two or three.
Like, webblaura@example.org.
It's got four orange pieces.
Are you telling me that 48 is four times as even as 46?
There must be more to the story."
By refusing to be the answer key, you create space for this kind of mathematical conversation and debate.
And this draws everyone in because we love to see people disagree.
After all, where else can you see real thinking out loud?
Students doubt, affirm, deny, understand.
And all you have to do as the teacher is not be the answer key and say "yes" to their ideas.
And that is principle four.
Now, this one is difficult.
What if a student comes to you and says 2 plus 2 equals 12?
You've got to correct them, right?
And it's true, we want students to understand certain basic facts and how to use them.
But saying "yes" is not the same thing as saying "You're right."
You can accept ideas, even wrong ideas, into the debate and say "yes" to your students' right to participate in the act of thinking mathematically.
To have your idea dismissed out of hand is disempowering.
To have it accepted, studied, and disproven is a mark of respect.
It's also far more convincing to be shown you're wrong by your peers than told you're wrong by the teacher.
But allow me to take this a step further.
How do you actually know that 2 plus 2 doesn't equal 12?
What would happen if we said "yes" to that idea?
I don't know.
Let's find out.
So, if 2 plus 2 equaled 12, then 2 plus 1 would be one less, so that would be 11.
And that would mean that 2 plus 0, which is just 2, would be 10.
But if 2 is 10, then 1 would be 9, and 0 would be 8.
And I have to admit this looks bad.
It looks like we broke mathematics.
But I actually understand why this can't be true now.
Just from thinking about it, if we were on a number line, and if I'm at 0, 8 is eight steps that way, and there's no way I could take eight steps and wind up back where I started.
Unless ...
(Laughter) well, what if it wasn't a number line?
What if it was a number circle?
Then I could take eight steps and wind back where I started.
8 would be 0.
In fact, all of the infinite numbers on the real line would be stacked up in those eight spots.
And we're in a new world.
And we're just playing here, right?
But this is how new math gets invented.
Mathematicians have actually been studying number circles for a long time.
They've got a fancy name and everything: modular arithmetic.
And not only does the math work out, it turns out to be ridiculously useful in fields like cryptography and computer science.
It's actually no exaggeration to say that your credit card number is safe online because someone was willing to ask, "What if it was a number circle instead of a number line?"
So, yes, we need to teach students that 2 plus 2 equals 4.
But also we need to say "yes" to their ideas and their questions and model the courage we want them to have.
It takes courage to say, "What if 2 plus 2 equals 12?"
and actually explore the consequences.
It takes courage to say, "What if the angles in a triangle didn't add up to 180 degrees?"
or "What if there were a square root of negative 1?"
or "What if there were different sizes of infinity?"
But that courage and those questions led to some of the greatest breakthroughs in history.
All it takes is willingness to play.
And that is principle five.
Mathematics is not about following rules.
It's about playing and exploring and fighting and looking for clues and sometimes breaking things.
Einstein called play the highest form of research.
And a math teacher who lets their students play with math gives them the gift of ownership.
Playing with math can feel like running through the woods when you were a kid.
And even if you were on a path, it felt like it all belonged to you.
Parents, if you want to know how to nurture the mathematical instincts of your children, play is the answer.
What books are to reading, play is to mathematics.
And a home filled with blocks and puzzles and games and play is a home where mathematical thinking can flourish.
I believe we have the power to help mathematical thinking flourish everywhere.
We can't afford to misuse math to create passive rule-followers.
Math has the potential to be our greatest asset in teaching the next generation to meet the future with courage, curiosity, and creativity.
And if all students get a chance to experience the beauty and power of authentic mathematical thinking, maybe it won't sound so strange when they say, "Math?
I actually love math."
Thank you.
(Applause)