Seymour Papert’s Powerful Idea

In Mindstorms: Children, Computers, and Powerful Ideas, Seymour Papert writes about powerful ideas without ever attempting to define them—except to say that powerful ideas are ideas which are powerful. He argues that we can only know an idea is powerful by experiencing that power for ourselves. And then, if we experience enough powerful ideas, we’ll gradually learn how to recognize a powerful idea by developing a mental profile of what powerful ideas feel like on an intuitive level. Any conscious definition we may arrive at later will only come if we have an intuitive understanding of powerful ideas, based on our own experiences, first.

Thirty-seven years later, at the Thinking about Thinking about Seymour symposium held in honor of Papert at the MIT Media Lab, Alan Kay chose to share his conscious definition for a powerful idea: An idea is powerful if it changes the context in which we think. Because Kay’s definition happened to match my own intuitive profile of a powerful idea, it resonated strongly with me—and I ran home to bang out a series of articles on powerful ideas.

New contexts and Newtonian mechanics

A few days ago, I was discussing Kay’s definition of powerful ideas when my friend, Henry Kim, shared his own conscious definition. Framed in statistics, I’m afraid it flew over my head a bit and didn’t resonate with me in the same way. I was going to ask Henry for an example of a powerful idea so I could try to wrap my head around it, but then, out of the blue, he shared this postscript on Newtonian mechanics—and I could see what he was saying.

From my perspective, Henry’s not proposing a different definition, but one possible mechanism to explain how we can change the context in which we think—and why we experience that as powerful. In my mental model, I see Henry drilling down into Kay’s definition, grounding it and making it more concrete and functional.

In Henry’s example, he explains that Isaac Newton developed his laws of motion for a context which we almost never encounter on Earth. For example, he stated that a body in motion will remain in motion until some external force acts upon it. But on Earth, where friction and air resistance are difficult to eliminate, especially in the 1600s, we don’t experience objects remaining in perpetual motion until they’re visibly acted upon. It goes against our intuition, and it seems rather pointless to theorize about the physics in some abstract, alternative universe. Well, by thinking in Newton’s alternative context, we’re able to gain valuable insight into our own context, coming up with new ways to see and think about motion in the real world. By imagining what’d happen in context B while living in context A, we can eventually change context A by seeing context A from context B—and then merging the two.

New contexts and learning French in France

While Henry’s definition of powerful ideas was starting to make sense to me, it still wasn’t fully resonating. It didn’t feel wrong, but it also didn’t feel quite right. I had to test his definition by applying it to another idea which I already knew was powerful: Papert’s theoretical Mathland.

Just as Newton imagined a context with no friction or air resistance to gain a deeper understanding of motion, Papert imagined a context in which math is embedded into the culture to gain a deeper understanding of learning. Because everything we know about learning math is based on experiences in a mathophobic culture, our perspective on learning is highly limited. But we can widen that perspective by imagining what learning math might look like in an alternative context.

What Papert noticed is that learning math feels a lot like learning French in a middle school classroom in America. Instruction is direct and formal, many students struggle, and only those students gifted with aptitude become fluent. However, unlike for math, we know of a familiar context in which learning French is an entirely different experience. In France, almost all children learn to speak French fluently with ease and minimal instruction. Could math be as easy to learn as French in France? Papert tested this hypothesis by embedding powerful ideas about differential geometry into Logo, a language used by children to program the movement of a turtle both in the real world and on a computer screen. Children became fluent in differential geometry by playing with and thinking as the turtle.

If learning math in Mathland can be as easy and natural as learning French in France, does it change how we see and think about our current context? Let’s take a short quiz and find out. Decide whether each statement below is true or false.

Children in France learn French more easily and fluently than children in a middle school classroom in America because:

  • The standards in France are higher.
  • There are more high-stakes tests in France.
  • France has more charter schools.
  • There’s more competition in the French educational system.
  • French students are tracked earlier on.
  • France has a national curriculum.
  • French schools aren’t unionized and it’s easier to fire teachers.
  • French teachers are paid more and better prepared.
  • More students in France participate in an Hour of French.
  • French schools use adaptive learning software to personalize learning.
  • In France, students have more access to MOOCs and online resources.
  • French students engage in more project-based learning.
  • French schools are more democratic and innovative.
  • French students pursue their own interests and design their own learning.
  • French parents are more involved in their children’s education.
  • Students in France are born with a natural aptitude or passion for French.

When looking at how we’re pursuing education reform in America from the context of Mathland, I see us nibbling around the edges—treating symptoms of our mathophobic culture instead of addressing the culture itself. We’re debating how much say students should have in their own education, but how much does that even matter when the culture doesn’t provide the basic raw materials students need to learn? As Papert points out, we will learn almost anything if it’s embedded in our culture, but trying to learn something which the culture doesn’t support is toxic to our system. The constant tug-of-war between traditional and progressive education suddenly seems like a massive waste of time and energy. Papert’s Mathland is definitely a powerful idea for me because it changes how I see and think about learning in our context. Has it changed how you see and think about learning as well?

Moving forward

Unfortunately, most people who read Mindstorms often see and think about Mathland from our context rather than the other way around. Ignoring the role of culture entirely, they view Mathland as an argument for empowering children to learn on their own through technology. For example, the Scratch programming language has largely supplanted Logo at the MIT Media Lab. It is designed to enable children to play with programming at a young age, not to experience powerful ideas and develop intuitions about them. My gut tells me that Scratch isn’t as powerful as Logo—and it won’t generate the cultural change which Mathland tells me is necessary.

A red flag that Papert would have picked up on, but the Scratch community hasn’t, is the lack of traction among adults. Millions of children are working on Scratch projects on home computers. Why aren’t parents learning Scratch, too? Sure, parents are busy, but I’d expect at least 5% of parents to engage in Scratch for their own purposes, not just to support their children, if Scratch is truly as engaging, accessible, and powerful as claimed. In fact, this is a trend I’ve seen when it comes to most Mindstorms-inspired STEM activities: parents who are engineers will participate in STEM activities with their children, but parents who don’t have a STEM background won’t, even as they shuttle their children between STEM activities every day. Are we changing the underlying culture or simply layering new things on top of it? A reasonable hypothesis is that today’s children will be more engaged in STEM as parents, and they will change the culture—we just need to wait. But anyone who is considering our context from the perspective of Mathland would be concerned, and we’re not.

Papert’s strategy was to place powerful ideas in a child’s environment so the child might independently: (1) discover how some ideas are powerful; (2) learn to distinguish between mediocre and powerful ideas; and (3) figure out how to debug mediocre ideas so they become powerful. He was attempting to enable children to develop a taste for powerful ideas through experiences. But there’s a causality dilemma within Papert’s strategy. How do we fill a child’s environment with materials embedded with powerful ideas if few people have the intuition to recognize and debug powerful ideas? The vast majority of the materials in a child’s environment will be embedded with mediocre ideas, not powerful ones.

When I think about how I developed my own intuitions about powerful ideas, I feel as though I discovered powerful ideas through my intuitions about knowing if things make sense. As a child, I just knew if something made sense or not—and it felt wrong when it didn’t. Over time, I learned how to make sense of the things that didn’t, and this led me to seek out, recognize, and then debug powerful ideas. While filling a child’s environment with materials embedded with ideas that make sense still involves a causality dilemma, I feel as though the hurdle is significantly lower. I believe more people intuitively know if something makes sense or not—and as educators, we should be able to enable students to have more experiences where things make sense, so they can develop their own intuitions. That’s the theory, at any rate. Hope it makes sense!