Vertical Learning
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Vertical Learning

Igniting a Culture of Powerful Ideas

The first time I remember thinking about my own education was as a college junior studying physical chemistry. School had always come easily to me and my plan was to pursue a PhD in chemical engineering as I figured out what I wanted to do in life.

That all changed once I started to apply physics to model chemical systems. Suddenly, I had discovered a powerful idea which would forever shape how I saw and understood the world: complex behaviors can emerge from simple and local interactions. This led me to another epiphany: complex behaviors are much easier to understand if we drill down to underlying mechanisms; and then another: we should live in a world where we are continuously discovering our own powerful ideas.


I don’t remember exactly when I first read Mindstorms: Children, Computers, and Powerful Ideas. It’s a must read for anyone with a deep interest in STEM education. But I definitely didn’t understand it in the same way I did reading it again a couple of years ago after developing some of my own ideas in the course of my practice as learner, thinker, scientist, and educator. Here is how I would summarize Seymour Papert’s main thesis today:

  1. We learn anything naturally and easily as long as there are abundant materials in our environment with which we can construct the necessary intellectual structures.
  2. A subject only seems difficult if the materials we need to understand it don’t exist. The only effective way to encourage understanding is to build and provide those materials, not through teaching.
  3. Building the materials we need is a challenge because we grow up in a culture that distorts our understanding of what we need.

At the end of Mindstorms, we still don’t know how to build the materials we need to establish Mathland—a world where children learn math as naturally and easily as children in France learn French. Papert suggests that children, less encumbered by the surrounding culture, might do that themselves using computers. But how? What are the underlying mechanisms?

In his talk, Rethinking Ideas, at the Thinking about Thinking about Seymour symposium at the MIT Media Lab, it was clear Alan Kay has spent the past few decades thinking about this very question. His powerful idea? We can build the materials we need if we develop processes to methodically identify and then see around our blind spots.

Defining terms

When Seymour Papert talks about materials, he doesn’t mean textbooks, worksheets, or classroom manipulatives. In the forward to Mindstorms, he shares how he constructed the intellectual structures he used later in life to make sense of math by playing with and thinking about gears as a child. He’s not arguing that all children should play with gears; he’s only pointing out that a powerful idea which appears inaccessible to children can be made concrete if it is embodied in an object children can relate to through their own experiences.

An idea is powerful if it changes how we understand things we thought we already understood and if it changes how we see and think moving forward. According to Alan Kay, powerful ideas create “new contexts for thinking” by eliminating blind spots and expanding our perspective. We create powerful ideas from mediocre ones by debugging them—testing and revising ideas to improve them.

Most of us never have the insight that comes from fully understanding how complex behaviors can emerge from simple and local interactions. We may know it on some intellectual level, but that’s not the same as experiencing it directly. As I child, I had an ant farm. The behavior of ants in an ant colony is highly coordinated—from relocating and building a new nest to foraging for food. On the surface, it appears that the ants are being directed by some central authority. But that’s not what’s happening. The ants act individually, responding only to stimuli in their immediate environment.

I remember reading how ants coordinate the foraging of food by laying down pheromones and thinking: “Wow! That’s really cool.” If I’d continued studying ant colonies and had access to other similar materials, I may have had my powerful idea earlier. But the idea never really sunk in and the ant farm didn’t change how I thought about other complex behaviors because I couldn’t see complex behaviors emerging from simple, local interactions for myself—that was all happening beyond my vision. It makes me wonder what would have happened if I had been able to program virtual or robot ants to forage for food? Then I could see complex behaviors emerging directly from the simple condition-action rules I had created. That’s an idea we explored while working on Teaching a Robot How to Dance.

Culturally, we have a massive blind spot when it comes to learning. Because we believe children aren’t capable of understanding very much, we tend to water down the ideas we share with them, removing any power those ideas might hold. In the 1990s, an activity designed to help children understand states of matter became popular. It was described as both constructivist and bodily-kinesthetic. Children moved randomly around a room, bouncing off of one another. Then, when signaled, they would gradually slow down and, at some point, they would find themselves clumping up—transitioning from a gas state into a liquid state. Emergent behavior, right?

Not quite. The children only clump up because they know they’re supposed to—they already know that’s how a gas turns into a liquid. Try the activity again, but this time, place the children in blindfolds and padded suits with their arms strapped to their sides (I’m not recommending this!), and then tell them to move in a random direction after bumping into something. They won’t clump up. Particles which don’t attract one another form ideal gases. Not only are the children not discovering something for themselves through a bodily-kinesthetic activity, we are tricking them into falsely believing ideal gases condense into liquids. How did thousands of educators and scientists vet this activity without any of them raising a red flag? It’s because we have a massive blind spot when it comes to learning.

Nuclear fusion

Nuclear fusion is a naturally occurring reaction. In the center of a star, the gravitational forces generated by the mass of the star are strong enough to overcome the electrostatic forces pushing positively-charged atomic nuclei apart—and if the distance between two atomic nuclei is small enough, they fuse together and energy is released. To ignite a nuclear fusion reaction, all we need is a cloud of hydrogen gas with sufficient mass. Given time, the cloud will collapse under the force of its own gravity and the atomic nuclei in the cloud’s center will start fusing together, turning the cloud into a star.

Seymour Papert and Alan Kay theorize that, for a Mathland or a culture of powerful ideas to emerge, all we need to do is seed the environment with enough of the needed materials. Once a critical mass of materials has been achieved, gravity takes over, nuclear fusion begins, and the cloud becomes a star. But the question remains: How do we build those materials? Because of our blind spots, almost all of the materials we build today are basically made of neutrinos—particles with near-zero mass that pass through regular matter and don’t contribute to the cloud. As long as we keep producing neutrinos instead of the materials we need, a Mathland or a culture of powerful ideas will never be born.

Particle accelerators

I am a careful and curious fellow. Because I’m careful, I want to know, not just assume, the materials I’m creating hold some power and aren’t made of neutrinos. While I design my materials with leverage and scalability in mind, I’m also aware that I have blind spots when it comes to learning. I feel the need to test if my materials can actually ignite and sustain a nuclear fusion reaction. Because I’m curious, I’m not satisfied by our current understanding of nuclear fusion. What are the underlying mechanisms? How do individual people interacting with individual materials in their immediate environment cause a new culture of powerful ideas to emerge? And finally, because I care about children, I can’t look a child in the eye and say: “In a few generations, all of this might be a star, but for now, you’ll have to settle for this cloud of cold hydrogen.”

There are two basic techniques scientists use to artificially produce nuclear fusion in the lab so they can study it. In the first technique, some material is confined in a small space, and it is then heated and compressed. In the second technique, a few hand-picked materials are accelerated close to light speed and smashed together. I’ve been using the second technique to try to ignite nuclear fusion in the classroom for years.

In From Pennies to Ohm’s Law and Beyond, I describe a model children can use to simulate chemical systems using random particle motion. Simply by playing with this model, with no instruction or guidance, children would make numerous discoveries on their own: from Ohm’s law and the behavior of circuits in series and parallel to rates of diffusion, dynamic equilibrium, and the propagation of information throughout a system after the system is perturbed.

If I wanted to artificially accelerate this natural process in the classroom, I would start by organizing the classroom as a scientific community. Then, I’d ensure the students had sustained and prolonged contact with the model. The students would naturally use the model to develop hypotheses, conduct experiments, analyze results, and draw conclusions. That’s the scientific method as it’s commonly defined in schools. But in our scientific community, we’d take the process further.

The scientific process is iterative. We don’t just study a phenomena, develop a theory for it, test the theory, and then move on if the theory appears valid. Theories are extended, generalized, and improved over time. When I say we act as a scientific community, I mean we work together to develop an integrated set of coherent theories we are continuously testing and revising. It’s through this rigorous debugging process that we arrive at powerful ideas as a community.

Because I haven’t figured out how to fit it into a traditional middle school science curriculum yet, this specific material is untested. But I have written an article describing the first particle accelerator I built as a second-year teacher. I set up a structured community that enabled students to discover five powerful ideas as they crafted their own résumés:

  1. I can frame my story in different ways.
  2. The words I choose matter.
  3. My actions reflect who I am.
  4. I can learn about myself by studying what I do.
  5. I can be the person I want to be by doing what that person would do.

This particle accelerator has a special place in my heart because it’s my first and because I only designed the material with the first four powerful ideas in mind; individual students arrived at the last powerful idea by themselves.


I can see three interrelated processes at work when nuclear fusion occurs. The first process is the discovery of the powerful ideas in the material itself. Ideally, there are many powerful ideas to be discovered and some of those ideas are more general or build on top of others. The second process is the development and functioning of the scientific community. This is where we learn to debug our ideas and theories, enabling us to create powerful ideas regardless of the material. And the third process is the discovery of a set of powerful ideas about ourselves:

  1. Shaking up things that I thought I already knew and learning to see and think about things differently isn’t scary, it’s powerful.
  2. I am capable of debugging my own ideas and turning them into powerful ideas. This is the person I want to be moving forward.

Inside a star, nuclear fusion passes through several stages. Initially, hydrogen atoms fuse together to form helium atoms. Then, helium atoms fuse together to form carbon atoms. Eventually, heavier elements are formed.

I believe individuals go through similar stages in a culture of powerful ideas:


For example, a coherent learner strives to align himself with his core values where a strategic learner also strives to align the world.

Moving forward

Some people are uncomfortable with my use of particle accelerators. I do recognize particle accelerators are unnatural and they won’t help us ignite a self-sustaining nuclear fusion reaction to fuel a culture of powerful ideas. That won’t happen until we have a critical mass of the needed materials. At the same time, I am a careful and curious fellow who cares about children in the here and now—and I’m far more interested in identifying and seeing around my blind spots and creating powerful ideas than in worrying about what’s natural or unnatural.



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