Math tends to inspire groans, moans and a fair amount of anxiety. But is there any way to make math enjoyable? Or, dare we say … fun? First, we have to heal the generational trauma, says educator and puzzle aficionado Dan Finkel.  We sat down with Finkel to talk about how to fix mathematics education and how his organization, Math 4 Love, aims to help.

The problem: a broken system

What problems were you seeing as a math educator? 

Fundamentally, I was seeing a huge disconnect between the sense of the beauty and the excitement and the dynamism of mathematics that I had known in my life, and what other people got. Most people just have such a negative experience with it. I don’t think we’re going to see math education magically get better. It’s a long-term, slow-to-change problem around a system with a lot of inertia.

“Somehow we found a way to use math to make everyone’s life worse. It’s done damage to whole generations.”

Math is this subject that is one of the most beautiful, powerful, empowering things. It’s part of your inheritance as a human being — like art and music. And it should only make your life better. Instead, somehow, we found a way to use it to make everyone’s life worse. It’s done damage to whole generations. So it feels like it’s this quiet tragedy that plays out, and we need to figure out how to just get in there and interrupt the cycle. There’s so much good and so much joy that’s waiting to be unleashed.

“If you can give students a really positive experience as their foundational experience, that actually sustains them as they go into middle and high school and beyond.”

That’s really the challenge — if I go into a group of teachers and I say “I’m going to share what’s beautiful and wonderful about mathematics”– if you’ve never had that experience, you literally just think I’m talking gibberish.  Because to them, that’s not what math is. Math is the thing that’s made them cry when they were a sixth grader. So that fundamentally is, from my point of view, the largest structural impediment. We need as a culture to give people positive experiences with mathematics.

“There’s no teacher who wants their students to not like math; everybody wants their kids to have a positive experience with it. But, again, if you haven’t had that yourself, what does that even mean?” 

It’s almost like a kind of therapy. And people need a human being with them holding their hand, just for the first time through because it’s so traumatic. That is the difficulty. There’s no teacher who wants their students to not like math; everybody wants their kids to have a positive experience with it. I feel like right now the most anyone can reasonably hope for is one really inspired teacher every 3 to 5 years and that’s enough to keep the spark alive. And what’s sad is that often we don’t even get that.

The solution: make math fun again

Math 4 Love: bring play into education

What was your inspiration to start Math 4 Love?

I started blogging under the name Math 4 Love. It felt like this was a problem that I was ready to take on: trying to communicate what mathematics could be, and what the possibilities for teaching and learning it could be. To give teachers and parents and students a positive experience. And also to provide a kind of pathway towards helping teachers transform what they’re actually doing in the classroom.

There’s three main things we do at Math 4 Love. We work with teachers and run workshops, and go to classrooms and run demo lessons. We write curriculum; we’ve written the summer intervention program that Seattle public schools use for their Summer Staircase program. The idea is, it’s a play-based intervention. You get kids playing with math at a young age. It actually allows them to learn more deeply. We have two math games, one is called Prime Climb, the other is called Tiny Polka Dot. If we can get kids and families to see math as something they can play with, it’s a totally different way to interact.

“Get kids playing with math at a young age. It actually allows them to learn more deeply.”

What do you think it is about games and puzzles that make them such effective teaching tools?

One of the reasons that there’s a problem is people basically say, “Ignore your own common sense. Ignore your way of doing things. I’m going to just show you this method. Don’t worry about why it works, just memorize it, and then you’ll get the right answers.” But mathematics is a way of supercharging your common sense. And that means it needs to start with common sense. The way that you create ownership is often through play. It’s counterintuitive in a way because we have this weird cultural bias about how when you’re playing you’re not learning. But that couldn’t be further from the truth. Playing is nature’s way of helping you to learn.

“We have this weird cultural bias about how when you’re playing- you’re not learning. But that couldn’t be further from the truth. Playing is nature’s way of helping you learn.”

So when we have games and we have puzzles as something we’re doing in the classroom, we’re extending an invitation saying “Hey, play with this, make it yours. Make this subject belong to you. Make it something that you own.” What teachers, both with our games and also the puzzles, tell me over and over again is “I threw this puzzle out to the kids and I was just blown away by all the stuff that they came up with.” It suddenly unleashes that sense of personal relationship, a playful relationship with a problem, and that generates the engagement and sense of ownership, which is what really does transform students’ relationships with the subject.

“It’s like having the experience of “do I get to be the one who shows you the color yellow?” I get to add this whole dimension to your life. There are just not many places where we get to do that. That’s how teaching math can be.”

Watch Dan Finkel’s TEDx talk here:

Stop-motion animation is a visual storytelling form that conjures up the illusion of movement by combining art, motion and metaphor to convey an idea. It’s also really fun to create, as 100+ first-time animators recently discovered during a workshop led by the TED-Ed Animation team. Ready to create your own stop-motion animation at home? Here are a few suggestions from TED-Ed Animators to help you get started:

Start with the basics. Before you begin filming, get inspired by the animated lesson shown above, which was produced with the help of first-time animators during the TED-Ed Summit animation workshop. Some of the stop-motion techniques used to visualize this lesson idea include pixilation, cut-out animation and puppet animation. Which one will you choose to try first? You can learn more about each technique — and how to do it yourself — by exploring the TED-Ed Animation Basics lesson series.

Embrace your constraints. You don’t need a lot of equipment and supplies to start creating stop-motion animation. One set-up might include props (such as Legos, Playdoh or magnet letters, etc), an iPad or laptop, a stop-motion app, table, black tablecloth, two lights, and a tripod or mount to stabilize the camera. Another set-up might include a flipbook of photos and your phone camera. For your first animation project at home, the idea is to start with the resources you have available and experiment. If needed, you can even fold your own origami iPhone stand.

Experiment with software. iStopMotion is the stop-motion software that new animators used to help create that animated lesson. It’s easy to test out on a MacBook Pro, and also available for iPad or iPhone. Other apps that you might try for iOS include: iMotion, Stop Motion Studio. For Android, try StopMotion Maker. Pro tip: remember to read through the software guide for whatever app you decide to use to capture animation.

Keep a growth mindset. Stop-motion animation projects can flex your creative problem-solving skills and help you to practice patience. Whether this is your first animation or your 15th, there is always something new to learn or try. So keep a growth mindset — and remember to have fun!

For more ideas at the intersection of education and animation, sign up for the weekly TED-Ed Newsletter here >>

How is it that Beethoven, who is celebrated as one of the most significant composers of all time, wrote many of his most beloved songs while going deaf? As Natalya St. Clair explains below, the answer lies in the math behind Beethoven’s music.

The standard piano octave consists of 13 keys, each separated by a half step. A standard major or minor scale uses 8 of these keys with 5 whole step intervals and 2 half step ones. Using the “Moonlight Sonata,” we can begin to understand the way Beethoven was able to convey emotion and creativity using the certainty of mathematics.

The first half of measure 50 of “Moonlight Sonata” consists of three notes in D major, separated by intervals called thirds that skip over the next note in the scale. By stacking the first, third, and fifth notes — D, F sharp, and A — we get a harmonic pattern known as a triad.

But, these aren’t just arbitrary magic numbers. Rather, they represent the mathematical relationship between the pitch frequencies of different notes, which form a geometric series. The stacking of these three frequencies creates ‘consonance’, which sounds naturally pleasant to our ears. Examining Beethoven’s use of both consonance and dissonance can help us begin to understand how he added the unquantifiable elements of emotion and creativity to the certainty of mathematics.

For a deeper dive into the mathematics of the “Moonlight Sonata,” watch the TED-Ed Lesson: Music and math: The genius of Beethoven:

Animation by Qa’ed Mai/TED-Ed

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Mathematician Eduardo Sáenz de Cabezón suspects that when people ask him what’s the use of math, they’re really asking why they had to study math in school. As a mathematics professor at the University of La Rioja in northeastern Spain, Sáenz de Cabezón (TED Talk: Math is forever) has come up with a spirited defense of his chosen profession. Math, he believes, is nothing less than a quest for eternal truth. Here’s why:

Math reveals unfathomable truths. Take a regular sheet of paper and start folding. If the piece of paper were big enough to be folded 50 times, Sáenz de Cabezón says, “its thickness would extend almost the distance from the Earth to the Sun.” If you’re now trying to imagine how a sheet of paper, folded 50 times, can rise nearly 93 million miles into space, you’re experiencing the strange thrill of a mathematical proof. “Your intuition tells you it’s impossible,” he says. “Do the math and you’ll see it’s right. That’s what math is for.”

Math can be as beautiful as poetry — or love. “Science operates on intuition, creativity. Math controls intuition and tames creativity,” says Sáenz de Cabezón. He admits that his colleagues fall into two camps when they’re asked why math matters: attackers and defenders. “The attacking ones are mathematicians who would tell you this question makes no sense, because mathematics have a meaning all their own,” Sáenz de Cabezón says. “There’s no point in constantly searching for all possible applications. What’s the use of poetry? What’s the use of love? What’s the use of life itself?” They have a point, he says — and so do the defenders. “Those who stand in defense tell you, ‘Even if you don’t realize it, friend, math is behind everything.’ Those guys, they always bring up bridges and computers. ‘If you don’t know math, your bridge will collapse.’” Also true. But Sáenz de Cabezón suspects that neither answer conveys the private thrill that mathematicians experience with every breakthrough in their field — and every push to help us better understand the world.

Math endures. Anyone can posit a theory of how the universe works, but math leaves no room for conjecture. Consider how long mathematicians puzzled over a proposal by Pappus of Alexandria, who theorized in around 300 A.D. that a hexagon was surely the most efficient shape for covering an infinite flat field. “But he didn’t prove it,” says Sáenz de Cabezón. “It remained a conjecture: ‘Hexagons!’” The debate raged for 1,700 years, until in 1999 American mathematician Thomas Hales offered decisive proof of what Pappus had discovered and what bees instinctively know — the most efficient shape is indeed a hexagon. “We mathematicians devote ourselves to coming up with theorems,” says Sáenz de Cabezón. These, in essence, are “eternal truths,” discoveries that are possibly the most enduring things we will ever encounter in our lifetimes.” You probably said or were told at some point that diamonds are forever,” Sáenz de Cabezón says. “That depends on your definition of forever. A theorem? That really is forever.”

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Image credit: Emilie Soffe + How Big Is Infinity?/TED-Ed.

Editor’s note: This article is adapted for TED-Ed. A longer version appeared first on Ideas.ted.com.