Mindstorms and Seymour Papert are the reasons for LOGO in schools. That is, it's the reason my primary school had a robot which would drive forward, turn a right angle, and drive forward a little more, in front of a set of bewildered children, and why the BBC micros at my prep school occasionally ran programs that let us draw squares.
The premise of the book is that we could use computers to teach children how to think. Specifically, it would provide an opportunity for children to learn how to both formalise things (i.e. how to program) and how to think through hard problems by refining partial solutions (i.e. how to debug). Papert complains that most education is about right vs wrong answers and rote practice, without developing understanding (so children practice thousands of sums without ever really seeing the algorithm). So, the maths in school is no more like real maths than a spelling test is like writing literature.
Indeed, his ideas are very powerful. Children are very rarely taught (or perhaps let learn) ways of thinking, and I think that's what distinguishes the best teachers. It's ambitious and interesting. He thinks it could succeed where 'New math' failed. Unfortunately, experience has shown it to be the new 'New math'. The LOGO way of working takes time. Children have to be let loose experimenting, discovering rules and ideas in their own way, with subtle guidance. One robot shared across a classroom of children doesn't cut it. When it came to LOGO on the BBC B, I do remember doing some pretty cool stuff with it, but this was perhaps despite the infrastructure, not because of it. Looking back, so much more could have been achieved.
In the end, what Papert was after was pretty much achieved with BASIC! It's a horrible thought, but that's what introduced a whole generation of now-professional programmers and mathematicians to the world of computational description. Even that was a fleeting world, as modern computers hide the computation from the user.
Indeed, one of the fallacies of the book was 'there will be more computers, so there will be more programming'. Computers are ubiquitous, but they've hidden programming. They've become fantastically powerful typewriters and easels, but for the majority of users, that's it. If you want to do the same things lots, you better hope your software supports it, as scriptability is rarely exposed. This is not how the future was meant to be!
So, in the end, this book reminds me how much the potential of computers has been lost. Independent of the argument about dumb GUIs or esoteric programming languages, the main point is that computers have been dumbed down to the average person, rather than providing a way to lift the average person up. *sigh*
The idealism in the book, though dated, is still catchy. Fundamentally, schools were never going to change that much. I very much doubt David will see LOGO at school, but I'm seriously tempted to wave a LOGO turtle at him when the time comes.