It's kind of an interesting question. Is it better to educate masses with an inferior product that breeds misconception, or fewer people with a better product that limits misconception?
Perhaps the word "breeds" is strong. I would argue that even though Khan's lessons are very imperfect, the accessibility offered may be a worthy trade-off.
If knowing math at a superficial level opens doors for other learning, it's hard to argue that it's NOT a worthy trade-off.
We as math teachers strive for perfection, but the truth is that having a deep understanding of what an equals sign is and how it should function isn't important for most people in their lives. Sure those in math careers will want that depth (and they'll get it, since Khan alone can't prepare them for that career), but everyone else will be fine whether they use the equals sign properly or not.
In a lot of ways it's like prescriptive vs. descriptive linguistics. Are we going to be the equivalent of a grammar nazi and come down hard on everyone we see that uses improper notation? Or can we be satisfied if there is some understanding there, even if it's imperfect or communicated poorly?
