Pixar senior scientist Tony DeRose was faced with a problem that animators had never solved — how to make the hand of an old man look lifelike. It was 1998 and he was working on the experimental short film “Geri’s Game.” DeRose needed to figure out how to make a sculpture hand model with many angular planes look smooth and skin-like on the screen. To do this he developed an algorithm using weighted averages that won him a Scientific and Technical Academy Award in 2006.

Pixar is constantly solving new technical challenges that allow its artists, designers and storytellers a broader range of movement and texture in the movies they make. Now the company is teaming up with Khan Academy to use examples like DeRose’s discovery of surface representation to show students how the math and science they’re learning in school is applied by Pixar animators.

Khan Academy is best known for its modular videos explaining various curriculum topics that students can use to better understand and practice a concept. But, like many other groups working on reaching large numbers of people through online video lessons, its content producers have discovered that lots of people stop watching partway through.

A combinatorics lesson shows how many kinds of robots can be made by animators with just a few parts.
A combinatorics lesson shows how many kinds of robots can be made by animators with just a few parts. (Pixar in a Box)

When Pixar started looking around for a distribution partner, Khan Academy content producer Brit Cruise got excited that this partnership, now known as Pixar In A Box, might keep people interested in the content longer.

“The place we intersected was this need to pull people in,” Cruise said. “I wanted to do better, but that required a paradigm shift.”

The Pixar In A Box lessons start with a technical problem that animators face and work into the math from there. In each video a real Pixar animator lays out the technical problem, and then students get to experiment with interactive elements to better understand the problem. Gradually the video works towards a more explicit explanation of the math involved, and by the end the student is calculating to solve the actual problems faced at Pixar.

For example, in the character modeling lesson, based on the surface representation work DeRose pioneered, students learn about weighted averages. An animator lays out the problem DeRose faced and then students get a chance to play with 2-D and 3-D shapes, manipulating different functions to create midway points and move them in ways that might smooth the shape. As they play, they begin to intimately understand the challenge.

The lesson then turns to an explanation of why weighted averages help create the smoothing effect needed to make skin look more real. Students then return to the same tool they used before, but the math behind it is exposed, in this case simple algebra.

“They have this more interactive intuition lesson,” Cruise said. “They’re not just calculating.”

He is also working to add hands-on activities to enhance the video lessons. Right now only two of the 12 modules have an interactive lesson, but Cruise is working with a group of teachers to develop others that can be done simply, in 40 minutes, with cheap materials.

“We really are trying to intersect art and math, and you don’t often see those things represented really well in hands-on activities,” Cruise said. The hands-on activities are meant to push both the artistic elements and the math concepts a little further, challenging students to continue applying the information to more complex situations.

The emphasis on art isn’t a coincidence. While the video lessons are currently about only math topics, Pixar In a Box producers are working on science lessons now (mainly computer science) and hope to make others for the humanities side of Pixar’s work as well.

“At Pixar, art and technology go hand in hand,” said Elyse Klaidman, director of Pixar University, an internal department that encourages Pixar employees to continue their learning. In school, math and science often seem completely divorced from the humanities, but at Pixar the storytellers, artists and sculptors must work hand in hand with computer scientists like DeRose, tasked with figuring out how to animate those ideas.

Klaidman said the creative demands of stories push the technical innovations that allow the studio to represent those ideas, but just as frequently a new technical innovation will spur the storytellers and artists to dream up new things.

“It’s the interplay between the two sides that’s essential to what we do,” Klaidman said.

The Pixar In A Box videos also do a good job of taking viewers inside the world of Pixar, into the offices and studios of real employees. And kids like feeling on the inside. “One of the things we found from eighth-graders was they were hungry for more of the Pixar personality,” Klaidman said. “At that point we were focused on the content.”

The Pixar in a Box videos show glimpses of what it might be like to work at Pixar, including an office designed to feel like a jungle.
The Pixar in a Box videos show glimpses of what it might be like to work at Pixar, including an office designed to feel like a jungle. (Pixar in a Box)

The videos show the people behind careers many kids have never considered. Students liked meeting real Pixar employees and getting a sense of who they are and where they work. This feedback prompted the content producers to add a “Getting to Know” section at the end of the videos, where viewers learn about the backgrounds of Pixar professionals and how they landed their jobs. The people featured in these interviews are intentionally diverse to help kids see themselves in many kinds of jobs.

While some teachers are already getting excited about the Pixar in a Box lessons, it’s worth noting they were designed for the individual user, who isn’t necessarily a student in a public school. Cruise was clear that in order to make the videos feel authentic, they wanted to start from real technical problems Pixar has solved and explain the math behind them. Not all those problems are explicitly related to the Common Core, although some are. Every module has a lesson guide, which maps the lesson to Common Core standards when applicable.

Instead, these videos are meant to delight, to ask people to be creators as well as learners, and to push users to finish online lessons. Cruise said he hopes teachers might consider assigning the video lesson at home so class time could be used for the hands-on activities and a deeper dive.

“I honestly think you don’t actually start learning until that stage,” Cruise said. “I’m a huge proponent of hands-on learning.”

All the materials are free and the initial lessons are often suitable for all ages. The follow-up lessons are more grade- and standard-specific and range from fourth grade through high school.

Pixar In A Box Teaches Math Through Real Animation Challenges 3 September,2015Katrina Schwartz

  • mpstreeeter

    Interesting project but in the TED talk you’ve included, knowing how to calculate midpoints isn’t actually that important. The software tool already does the calculations, so why should we spend time teaching students how to calculate midpoints? With so much technology available to do these calculations for us, there isn’t much of a reason (beyond standardized tests) to teach students these “basics”. Instead, we should spend time giving them authentic opportunities to apply them – like making an animated short film when they’ll really need to use the core ideas and related technologies.

    • Brit Cruise

      If you dig into our lessons you’ll see just that: an opportunity to create your own shapes & animations. We also think it’s important to reveal the underlying mathematics so that the world doesn’t feel like a ‘black box’. In the same way, it’s important to understand how to bake a loaf of bread even though we can just grab a bag of a shelf. It’s important to build a battery from scratch even though we can buy them easily. Doing these things builds confidence so that when you confront future ‘black boxes’ you can do so with curiosity and excitement instead of fear and the assumption that “technology will do it all for us”.

      • I’m glad to hear that they’ll get to make shapes and animations. That’ll be a great experience for them. My point is that the TED video explains how to calculate a midpoint then immediately removes the need for that understanding by using the animation software. The same animation could’ve been created with just an explanation of midpoints without teaching the formula. At a high level, a midpoint is a straightforward idea – the middle point of a line. Knowing the formula didn’t add much, if anything.

        Just like, knowing how to bake bread isn’t super useful until you’re actually trying to bake some interesting kind of bread and you can’t buy the mix at the store. IMO it’s not something worth knowing until you absolutely need it. Knowing how to bake bread or build a battery is not inherently interesting for most people, and aren’t skills that will ever come up again in their lives. The added value of the confidence is not enough for most students, so we shouldn’t ask them to spend time on that. There should be more value than confidence.

        While I’m glad that these Pixar lessons are happening because we certainly need more practical applications of math for students to see, there seems to be more focus on teaching math in the same ways we’ve been teaching them but just using different word problems. I’m proposing starting with the goal/question in mind (how do I animate this hand? I need it to look like more naturally curved) and then working through the problems like a professional would. In the case of animating the hand, the professional doesn’t actually need that much understanding of a midpoint to do this work so trying to force a discussion of midpoints is doing what we’ve always done in education – crafting careful problems – when we should instead be looking for problems where actually knowing the formula adds real value.

        • Brit Cruise

          Cool! I think you’ll really enjoy the lessons. These gave Tony a chance to break free of TED talk limitations (such as interactivity and working towards a goal). You’ll love the Character Modeling lesson where we ask the question “how do you make a hand, or character, and turn it into a beautifully smooth rendering.” If you get a chance to go through it send your feedback to piab@khanacademy.org to reach the creative team. We are always looking for ideas

        • Tracy

          I’m just glad you weren’t one of my teachers. That is one of the biggest problems with teachers and schools today … thinking that a computer can take the place of actually knowing how to do something. Don’t you wonder why our country is falling behind ? Our children are not being taught the basics. Math is still math even if a computer does it for you. Understanding the concept helps to solve the problem and I think that is a big part of what Pixar in a Box is trying to show.

          • It’s fine that you disagree about what students should learn, but you don’t have to attack me as a teacher. You also can’t deny that kids are generally bored in school regardless of the teacher because we bog them down in basics, most of which none of us don’t use again, beyond the very basics of adding, subtracting, multiplying and dividing. (Perhaps there are a few more – don’t get distracted) When was the last time you graphed something by hand, factored a polynomial or used the midpoint formula? Sure it would be helpful to know the formulas and proofs, but we’d be in school for much more than 12 or even 16 years (including college) if we needed to prove every single formula we learn in school.

            Using technology doesn’t mean that students won’t understand the underlying core ideas. That can be covered in shorter, proof-free conversations. Instead, using technology in math (and in school in general) means they can focus on answering deeper, bigger, more complex questions. This conversation that we’re having wouldn’t be possible without technology and we don’t need to understand how any of it works in order to take advantage of it to do something purposeful – i.e. debate important ideas about math education. Pixar wouldn’t be possible without technology and I’m sure that most people working there don’t spend that much of their day actually doing any of the math that’s used in their software. If they did, we would get at most 1 movie a year because they’d spend so much of their time integrating complex functions and graphing by hand. Sure they likely have some underlying ideas of the math because they went through our public school system, but how many of them do you really think reference back to any of that when they’re working on a movie? A handful at best. The rest are thinking about the story itself, the design of the characters, the music, etc.

            Embracing technology doesn’t mean that students learn less. Well, that depends on how their teacher is using the technology. But used “correctly”, technology can empower students to do a lot more and be a lot more engaged than they are now, which are what I hope we both want. If you’re not sure what that might look like, you should consider reading more articles here on Mind Shift about incorporating technology into school – they’ve got some good stuff.

    • Nooneh Kradjian

      Think about the training of averaging two numbers… the midpoint is a stepping stone to developing abstract reasoning. I agree with what you’re saying, but the dismissal of midpoints is a weak argument to your point.

      • I’m not saying that there aren’t problems where knowing the formula of a midpoint isn’t useful. I’m saying that the problem in the TED talk did not require knowing the midpoint formula. It required a high level understanding of what a midpoint is (that it’s the middle point of a line), but beyond that, the animation software actually did the work. We, as teachers, always talk about math as something that builds confidence and abstract reasoning but math is actually useful in doing practical work. We shouldn’t limit the purposefulness of math to “building our brain muscles”.

        Using Pixar is definitely a step closer towards showing the true value of math, but it’s still seems to approach the teaching of math in traditional ways – i.e. forcing math into situations where knowing the details is barely useful because the computer does so much of the work. We don’t teach kids how the graphite in pencils works before they can learn to write or how books are bound before they can learn to read. We should embrace the technology for what it does and focus on the mathematical skills (some of which is computation and more of which is question asking and analysis) that students actually need in the 21st century. Maybe if a student were building a treehouse and needed to calculate midpoints of beams, then actually knowing the midpoint formula would be helpful. But even then, there’s certainly some 3D computer modeling software that will determine those measurements for you. We need to distinguish what students need to know at a high level and where knowing the formula is practically useful.

  • Gail Wright

    IMHO, the student should understand the theory and application behind the technology. I wish this computer animation was around when I was suffering through algebra in middle school.

  • Nooneh Kradjian

    When I was in undergrad, I switched from computer science to graphic design because I found a place to apply my math. During my stent, I read a school article breaking down the SAT scores by department. Second to Math and Engineering students were the Art students. Second to the English and History majors, were the Art students. Once I processed the joy and validation as an art student, I decided to become an educator. I love math, I love art; but above my two loves is the brain! Escher rocks! Euclid’s my man!! Van Gogh is amazing and DaVinci is my absolute favorite dead guy!!! Thanks for the article! PIXAR^nth!

  • Debra Garek Parkes

    Is there any interest in partnering with a school for a pilot? I am a teacher at an idependent school and am constantly working on integrating STEAM innovative learning. The students would love this. We are open to pilot a program like this! Looks like the possibilities are endless.

  • Debra Garek Parkes

    Is there any interest in partnering with a school for a pilot? I work in an independent school and we are always searching for new innovative ways to integrate STEAM into the curriculum and engage our students with authentic learning experiences. Our school would love to be a pilot school for Pixar in a Box, especially the younger grade levels.

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Katrina Schwartz

Katrina Schwartz is a journalist based in San Francisco. She’s worked at KPCC public radio in LA and has reported on air and online for KQED since 2010. She’s a staff writer for KQED’s education blog MindShift.

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