Where Seymour Papert Got It Wrong
And where we continue to misunderstand him
Two articles about Seymour Papert crossed my desk this week and a friend invited me to the Thinking about Thinking about Seymour symposium at the MIT Media Lab.
A line from the second article prompted me to write this article:
The core premise of Mindstorms is that children learn best when they are in charge.
Seymour Papert was a professor of applied math and education at MIT. He was a protégé of Jean Piaget, co-invented the Logo programming language, and wrote Mindstorms, a book which has shaped educational thinking about technology for decades. There is a lot to learn from Papert and his amazing body of work—but not if we continue misunderstanding him.
Mathland
Papert puts forward two central theses in Mindstorms. The first thesis is there’s no such thing as easy or hard subjects, only domains with abundant materials or sparse materials. He compares learning French in an American middle school classroom with learning French in France. If everything we knew about learning French was based on observations of American middle school classrooms, we would conclude that French is very difficult to learn and few students have the aptitude for it. But we would conclude the exact opposite if we observed young children in France.
Why the difference? According to Papert, if materials are abundant and diverse enough to fulfill a wide range of needs, children learn naturally and easily. Children in France are immersed in an environment rich in materials for learning French, while children in the United States are not. It’s access to these rich raw materials that enables French children to construct their own understanding of the French language. American children can’t do the same because the materials available to them are poor and limited.
Papert argues we can learn math as naturally and easily as children learn French in France if we grow up immersed in an environment rich in math materials. He called this environment “Mathland”. To test his hypothesis, he co-invented the Logo programming language, enabling young children to learn geometry and computer programming by directing a turtle to move on a computer screen. Mathland embodies Papert’s vision for education. His thesis that we can learn anything if we have access to the materials we need to construct our own understanding is both profound and transformative.
Mathophobia and the Proteus of machines
If the key to establishing Mathland is more and better math materials, then why not simply build them? The problem is we exist in a culture that is not neutral to math, it is deeply mathophobic—and any materials we build will carry the germ of that mathophobia within it. Even adults who love math and study it their entire lives inadvertently build materials that perpetuate our fear of math because they grew up in and internalized this mathophobic culture. To put it bluntly, people who grow up in a mathophobic culture are generally incapable of building Mathland materials.
To get around this seemingly insurmountable obstacle, Papert advances a second thesis. Because a computer can be programmed to take on different functions, maybe children can use computers to build their own materials, bypassing adults and inoculating themselves from the mathophobic culture. He describes the computer as the “Proteus of machines”.
The blindspot
It’s clear this second thesis is a Hail Mary pass. Papert doesn’t propose that children in France build their own materials for learning French. It’s access to raw materials that matters, not who provides them. If children have access to the materials they need to construct their own understanding, they will. He only proposes children use computers to build their own Mathland materials because he knows the adults can’t.
Unfortunately, Papert has a blindspot when it comes to children. He fails to recognize that children also begin to internalize the mathophobic culture at a very young age. They are no more capable of building Mathland materials than the adults around them.
When children learned geometry and computer programming naturally and easily working directly with him, but not in the mathophobic environment of schools, Papert blamed the schools. But he knew going into the experiment that schools and adults would act to perpetuate mathophobia. That’s why he developed his second thesis. Can children use computers to inoculate themselves from the surrounding culture and build their own materials? Not simply use Logo, but build new materials better than Logo? The results seem to indicate they can’t. But instead of acknowledging he was asking too much from children, he blamed the schools.
A basic misunderstanding
To me, Papert’s second thesis is hopelessly naive, but I understand why he would run an experiment to test it. He could see no other path to Mathland. It’s our misinterpretion of the experiment that troubles me. Papert believed learning needs to be active, relevant, and personal. I believe the same. But putting children in charge of their own learning is not the core premise of Mindstorms. If it was, why would Papert use learning French in France as his analogy for Mathland? How would putting American students in charge of their own learning in French help? Would they learn as naturally and easily as children in France? Agency is necessary, but completely insufficient if the raw materials for learning aren’t even available.
In his experiments with Logo, Papert never distinguishes between children who do and don’t have a passion for geometry and computer programming. Just as all children learn French in France, all children would learn math in Mathland. Immersed in an environment rich in math materials, you will find personal and relevant connections with some of those materials, and you will construct your own understanding of math. That is Papert’s first thesis and the basis for his vision of Mathland.
A fear of learning
I find it interesting how no one talks about Papert’s first thesis any more. Somehow it’s been erased from our collective memories and only the second thesis remains. We are still trying to complete Papert’s Hail Mary pass, but we’ve lost sight of the reason why the pass was thrown at all. I believe this is mathophobia at work, co-opting Mindstorms.
When Papert discusses cultural mathophobia, he makes it clear he means the fear of learning, not just the fear of math. “Math” is the root word for learning in Greek. The idea that anyone can learn anything naturally and easily is a mortal threat to mathophobia. Learning is supposed to be hard. It takes grit and passion. And make no mistake about it, passion is code for aptitude. Our current fixation with passion-driven learning is incompatible with Papert’s vision of Mathland in Mindstorms.
I understand why no one talks about Papert’s first thesis any more. It seems unachievable. We focus on the Hail Mary pass because at least it may be possible. So what if it results in a pale imitation of Mathland, a place where only students with a passion and aptitude for math can learn math? We can always pretend the students who lack aptitude also lack grit and passion, that they used their agency to focus on something else. Plausible deniability.
That doesn’t work for me. There must be some way we can overcome our mathophobia and build the Mathland materials our children need and deserve. We can’t transform education and learning if we leave this cultural mathophobia in place—and the surest way to undo it is to embrace Papert’s first thesis. Another Hail Mary pass isn’t going to work. Neither is punting. It’s time to draw up a new play.
