Sunday, October 4, 2009

Mindstorms: Children, Computers, and Powerful Ideas

I have a new hero. Seymour Papert writes so brilliantly about math, learning, and how it all fits together, I think I'll have to read his book a few times to absorb it all. He wrote Mindstorms: Children, Computers, and Powerful Ideas back in 1980. (Why I never read it until now is a mystery to me. I've taught programming and math since the early 80's and could have used these ideas.) I expected a book about computers from the 1980's to be pretty severely dated, but the ways in which it's dated are surprisingly trivial. Papert's notions about why programming a turtle is valuable are still true, powerful, and not widely applied. But the book goes way beyond programming turtles.

He starts the book with a story from his childhood, about how he was in love with cars, and at two knew about "the parts of the transmission system, the gearbox, and ... the differential" (more than I know even now). He adds:
I became adept at turning wheels in my head and at making chains of cause and effect: "This one turns this way so that must turn that way so..."
Gears, serving as models, carried many otherwise abstract ideas into my head... I saw multiplication tables as gears, and my first brush with equations in two variables (e.g., 3x+4y = 10) immediately evoked the differential. By the time I had made a mental gear model of the relation between x and y, figuring how many teeth each gear needed, the equation had become a comfortable friend. (page vi)
But of course not all children will fall in love with gears the way he did, hence his "attempts ... to turn computers into instruments flexible enough so that many children can create for themselves something like what the gears were" for him. He points out many ways in which the gears encouraged his understanding of mathematics, including affect (he loved them), body knowledge (he could turn his hand or body the way the gear turned while he was thinking about it), and flexibility as a model for mathematical structures. His creation on the computer, the LOGO language, included a turtle on the screen (or a robotic turtle) that could be moved around.

He worked with Piaget for years, and has a similar clarity about the deep learning that must happen for children to understand things that seem very basic to us adults. He has differences with Piaget, though, and the most salient here is his conviction that the cultural environment makes a difference in when kids will learn things. To learn formal systems like mathematics, it helps for kids to have a fun "world" to play in that uses formal systems, like LOGO. So Piaget saw the 'formal reasoning' stage of development happening around 12, and Papert thinks much younger children can do formal reasoning if given the right environment.

He has a lot to say about the damage wrought by the culture associated with schooling:
Our children grow up in a culture permeated with the idea that there are "smart people" and "dumb people". The social construction of the individual is as a bundle of aptitudes. There are people who are "good at math" and people who "can't do math". Everything is set up for children to attribute their first unsuccessful or unpleasant learning experiences to their own disabilities. ... Within this framework children will define themselves in terms of their limitations, and this definition will be consolidated throughout their lives. Only rarely does some exceptional event lead people to reorganize their intellectual self-image in such a way as to open up new perspectives on what is learnable. (page 43)
Of course kids in school hate making mistakes, and want to throw the mistakes away, or run away themselves. But if they're doing programming on a project they care about, the mistakes become bugs that need fixing, not testaments to their inadequacy, and they become willing to debug. The more they get into that habit, the more willing they'll be to deal with future 'mistakes' that way.

Most of us learned Euclidean geometry in high school, with its axioms, straightedge and compass, and our first taste of proofs. (There are alternates to this, non-Euclidean geometry and Origami geometry, that still use a system of axioms and step-by-step deductive proofs.) Analytic geometry uses the x and y coordinate system to connect algebra and geometry. Papert mentions those two and then talks about how turtle geometry is both easier for kids to connect with (tell the turtle how to move in a circle, by figuring out how you'd do it) and more sophisticated (it has a deep connection with calculus). Once a child has really played with turtle geometry, they're likely to feel more at home as they learn about other geometries. Papert goes into how using turtles to think about physics is likely to lead into some deep science learning, too.

Reading Mindstorms motivated me to find and download Scratch, a modern descendant of LOGO, and start learning it. Scratch has 'sprites' instead of the turtle. You can create as many sprites as you want, and give each one a script. This week I've brought my computer in to Wildcat, where I teach kids in a very free-form environment, so they can play with Scratch. They are loving it. I'll probably post soon about that.

While I was online, searching for more information about Papert's recent work, I discovered that he'd been in a tragic accident. While in Hanoi in December 2006 for a conference, he was hit by a motorbike and suffered a severe brain injury. There is hope he will eventually recover, but he hadn't yet as of July of 2008. Here's the news article from then. I've searched and haven't found anything more recent. I'm wishing him well.

I want to include so many quotes, but I think I'll just write more posts on this later. If you want to think deeply about how children (and adults) learn, read this book. If you want a fresh perspective on how computers might be used with children, read this book. If you want more reasons to shake your head over the current testing craze in the public schools, read this book.


  1. Here's the email I just sent to the parents at the school I work at:

    Well, I have mixed feelings about using computers with kids. There is some evidence that lots of screen time isn't good for their development. (For example, the eyes need to change distance focus lots when playing with a ball, and they don't get this practice when watching something on a screen.) The Waldorf folks say no screen time before 8 years old. They're more rigid about it than I want to be, but I am torn... So I've avoided doing a whole lot of computer stuff with the kids until now.

    Then I read Mindstorms, by Seymour Papert. I am blown away! I wrote a blog post about it here.

    He developed a computer language called LOGO especially to help kids learn to think. One of its main descendants is an environment called Scratch. You can get that here. You may have to set up an account, but it is free. It's easy to learn, and kids can do lots of cool projects with it. They can create Sprites (there's a painting portion of the program for that or they can ask the system to surprise them), and each Sprite can get a script that makes it do things.

    I've been bringing my computer to school this week. J, E, and T already had played with Scratch, and were excited to get to do it at school. Lots of other kids gathered around my computer and watched and then took their own turns. D (much younger) signed up for time today, and came running when I called her. She had been watching earlier, and just needed a few nudges to get going on what she wanted to do. Her mom was watching, and wondered how she'd already learned so much. She learned from the other kids. And that's how it goes with Scratch. Check out this video of an experiment in India to see how much poor kids would teach each other given access to a touch screen computer set into a hole in a wall. (Link:

    I highly recommend reading Mindstorms. But if you don't have time, and you're wondering what this has to do with math, let me give you one example. In the book Papert refers to turtles, which is what LOGO controlled. But I'll refer to sprites as I give an example from the book. Kids wanted to make their sprite go in a circle, and weren't sure how, so he suggested they go in a circle themselves and describe what they had done. A child's description of that might be, "I took a small step and then turned a little, and I did that over and over until I got all the way around." They learn how to put together a script (from available tiles) for their sprite that does this, and they've come to understand circles in a new way.

    Try it out yourself. See if you can make a sprite go in a circle. It's fun! (There's a pen down command, so you can see the circle itself.)

    We'll still do the more usual sorts of math lessons, but I may have to tear kids away from their turn at the computer for it. ;^)

    There are 3 computers in the computer room that do not have internet access. If someone could help me get Scratch installed on those, the kids would be grateful, and I think we'd see some amazing creativity. I'm going to try downloading the installer for those older operating systems onto my computer, then putting it on my flash drive, then maybe getting it on the macs. I don't think the PC even has the right place for my flash drive to plug in.

    If this keeps the kids' interest, I'll keep pointing out the math connections.


  2. As you know, Seymour Papert has long been my hero. I've read Mindstorms at least 6 or 7 times and I always find something new that I can think about and apply to my work. I'm glad you've discovered him.

    I've been using a newer version of the original floor turtle at my math center. It's a robot called Roamer and is produced by Valiant Technology. Roamer has a small computer onboard but hidden from view. On the outside, there are button symbols that students use to create programs. When students press the Go button, Roamer follows the procedure. Roamer is simple enough for a 5 year old to program but is capable of procedures that would challenge a 12 year old. Roamer can also be equipped with sensors that detect touch, sound, and light.

    A friend of mine works with students who have processing issues. She visited Papert at his home in Maine last summer and tried to help him. He had a lot of difficulty expressing his thoughts but she could tell that he understood. She felt that he may not be getting the therapy he needs. It's really sad.

    Now that you've read Mindstorms, you may want to delve deeper and read his published articles as well as the work of Idit Harel, one of his doctoral students. Gary Stager has worked with Papert and has an extensive list of articles on his site. If you need links, let me know.

  3. I would love links to things you think are good.

    Hmm, I wonder if there's anything we can do to help send Papert the therapy he needs to recover.


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