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..."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.
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)
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.