Sal Khan, responding to our #mtt2k contest in a (paywalled) article in the Chronicle of Higher Education:
There’s always the critique that Khan Academy is not pedagogically sound, that we’re procedural-based, focusing on mechanics without base understanding but I actually think we’re the exact opposite of that.
With procedural, worked problems: That’s how I learned, that’s how everyone I knew learned. But we do have videos explaining the ‘why’ of things, like borrowing, or highly rigorous concepts like college-level linear algebra, so it’s kind of weird when people are nitpicking about multiplying negative numbers.
Maybe something got lost in the edit, but I can’t seem to reconcile those two statements. On one line, Khan Academy is the opposite of procedural learning. In the next paragraph, Khan offers a full-throated endorsement of procedural learning through worked examples.
We will never say that our visual library is perfect. And we’re constantly trying to improve. But I think it’s a straw-man argument to pick one video and say, ‘This is a procedural video, it is not conceptual, they’re all like this, these people don’t have an understanding of pedagogy.’ That is, frankly, a bit arrogant and disparaging.
The statement “this should have been better” isn’t the same as “this should have been perfect.” Khan has god-knows-how-many videos at this point, some of which he made with only his cousins in mind, and we should expect a wide distribution of quality.
Setting aside any of our concerns about the best place for video lectures in a math classroom, we all have an interest in Khan’s video lectures being as mathematically correct as possible. But Khan thinks it’s arrogant and disparaging for people who have spent decades witnessing and cataloging every possible misconception about negative numbers to step in and say, “Your video may lead to misconceptions about negative numbers.” That’s a pity. I encourage Khan and his staff to find a more productive way to engage this deep bench of unpaid, well-informed critics.
BTW. If Khan is wondering why math teachers worry about his pedagogical content knowledge, this is the sort of decision that gives us the heebie-jeebies:
Mr. Khan says he intentionally mixed up the transitive and associative properties to show that understanding that a times b is the same as b times a is more important than the procedural process of memorizing vocabulary.