I work in a small start-up making educational software, and this is exactly the kind of thing I want to achieve.
A couple of months back I read John Holt's famous book 'Why Children Fail' which had a profound effect on me and my work. What he says, and what I agree with due to my own experience and observations is that school can be a fundamentally scary experience for children. Self-esteem is so central to learning, because how you react to failure and your own progress (or lack thereof) defines the way you learn. Kids who are afraid of looking stupid, of being compared to their peers, and of having to work hard without the promise of success are the ones who are branded as lazy, unimaginative, or just 'stupid', when in fact they are just afraid of trying hard.
The internet and self education offers an opportunity for kids to escape that fear, and to truly experience the joy of learning. I'm sure many HN readers will relate to my belief that the greatest joy of hard work is not when you appear smarter or harder working than others, but when you achieve something for yourself, or learn something new. Many programmers get to experience that joy all the time.
Holt became so disillusioned with the inability of schools to provide a comfortable and secure learning place for children that eventually he became an advocate for home schooling. I believe in schools' potential and what teachers have to offer, and my company's software is built accordingly, but we have reached a point where there is too much focus on comparing students; through frequent nation-wide testing, intense competition for prestigious colleges, and through insecure parents who push their children an unhealthy amount. To balance that, the schooling system has lost sight of the original reasons for its existence. The judgment-free zone of the internet and self directed learning is giving us a chance to undo the bad learning habits of our current students, and ensure that the next generation of students do not ever need to learn them.
The Khan academy is not about taking the power away from schools and administrators, it is about putting the emphasis back on why we have them in the first place; which is because for all the good of self education, the greatest help you can give a student is a teacher who understands them and the way they learn.
First, it was usually the assumed knowledge that got them. They'd mess up at calculus because of algebra; or get algebra wrong because they couldn't add. When you don't know the basics, you get the wrong answer even when you do all the new stuff right. The whole thing starts to seem futile, like climbing a mountain of sand.
Second, just as above. Most of my students had no idea that math, like weightlifting, is supposed to hurt a bit. They thought that heavy, stretching sensation you get when you learn new concepts meant they were stupid, that they couldn't do math. They didn't realize that every feels that, if only briefly. If you're in the bottom third of the distribution, and a third of people are, you never get to the other side of that feeling before the class moves on.
The answer isn't magic teachers. It's for kids to learn that learning is possible. You do that with practice, and feedback, until they get it right.
It is all about relating things and explaining in a way that can be easily referenced in your mind.
By the way...several of these people who could not pass the TABE tests at the time went on to get their GED's because of that one little step with fractions.
See this BBC article, which is about a good school teaching pupils that it's okay to fail.