Seymour Papert: The Gears of my Childhood

Original: The Gears of my Childhood

How can we restructure maths to make it more lovable and learnable!? What would success look like?

Seymour covers a lot of ground brilliantly in his 4 page Preface to Mindstorms! His personal learning story which then morphs into a pathway to universal powerful, learning opportunities

He traces his personal learning journey from early childhood when he played around with car gears in the back shed. Seymour fell in LOVE with the gears. He found “particular pleasure” in the differential gear due to its complexity, “the motion in the transmission shaft can be distributed in many different ways to the two wheels depending on what resistance they encounter”. He argues that this love affair became a vehicle for him to later on master school maths. “I clearly remember two examples from school maths. I saw multiplication tables as gears, and my first brush with equations in two variables (eg. 3x + 4y = 10) immediately evoked the differential.”

Another CRUCIAL piece of information about the gears. Good learning materials have a dual nature. They can carry both advanced maths ideas AND sensory motor ‘body knowledge’. You can be the gear.

So far, this is a story of one person’s unique pathway to maths mastery. But not everyone will fall in love with gears:

“One day I was surprised to discover that some adults – even most adults – did not understand or even care about the magic of the gears”

This led him to think:

“How could what was so simple for me be incomprehensible to other people?”

Seymour’s reflection on this question is revealing. He rejected the viewpoint of his proud father that he was clever because he knew people who could do other things he found hard who didn’t understand the differential.

But it slowly led him to what he still sees as the fundamental fact about learning: “Anything is easy if you can assimilate it to your collection of models. If you can’t, anything can be painfully difficult.”

This leads to further questions for educators: How can we create conditions where learners develop useful mental models? How do intellectual structures grow out of one another?

Having a physical manifestation helps here – be it a floor turtle, a Robocup competition vehicle made from LEGO or an attractive shape designed in Turtle Art and then 3D printed.

And to repeat: Seymour fell in love with the gears. He stresses that you need love. He gently criticises Piaget here who focused more on the cognitive than affect.

By the way, later the slogan became hard fun. Whether you prefer love, hard fun or play is ok the underlying message is the important thing: if we like it we will persist in learning it.

When computers came along Seymour envisaged that they could play the role for everyone that the gears played for him. His belief is that many more will fall in love with a cleverly constructed computer based learning environment that taps into natural ways of learning. Hence Seymour helped to invent Turtle Graphics. The computer (Protean machine) can take on a thousand different forms. It can be the universal machine for learners to fall in love with. An incredible leap! Profound yes, True? We shall see.

Of course, since the computer can take on a thousand different forms it can also be used in bad ways:

• Computer as universal machine
• Children’s learning machine
• Game playing machine
• School administrative systems
• Surveillance capitalism machine
• Tik Tok trivial and sinister machine
• Some blame social media for the mental health decline in youth (Jonathan Haidt, The Anxious Generation)

Spawner of revolutions …universal communication and computation (internet, smart phone – banned in schools because too distracting for the youth.

Seymour’s optimistic pathway is one amongst many. Creative learning systems are always there but never dominant in society overall.

I understood this part of Seymour’s message, that the turtle is body syntonic and offers an engaging, a path to mathematical abstraction. Logo / Scratch provides students with a far better chance of falling in love with maths.

What I didn’t grasp firmly enough was the embodiment aspect. I did run a LEGO TC logo group for a while in the 80s but drifted off that path because of the logistic / cost factors of establishing that in the curriculum. More recently, I've corrected that error, after reading Gershenfeld's book, Designing Reality.

In our age, where individual data points have taken on more importance how do we measure or evaluate the mental models that Seymour sees as the most fundamental measure of learning new, useful things? This question was unresolved in Seymour’s view:

“If any ‘scientific’ educational psychologist had tried to ‘measure’ the effects (of Seymour’s encounter with gears) he would probably have failed … A ‘pre-’ and ‘post-’ test at age two would have missed them.”

It’s hard to measure mental models! I see that as the most important challenge arising from Seymour’s article:

“Thus the “law of learning” must be about how intellectual structures grow out of one another and about how, in the process, they acquire both logical and emotional forms”

This is the subject of Marvin Minsky’s book Society Of Mind