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Khan Academy - http://www.khanacademy.org/ - is often cited as a great online resource for learning mathematics and other subjects. I have heard many good things about this website and was wondering in what depth are subjects covered?

I know Khan covers topics in (highschool) algebra and calculus. What other subjects are treated? and at what level? How rigorous is his treatment?

Some background: I teach at a university and would like to know if this is a good resource to point students to. I'm thinking primarily of students who are having trouble in college algebra, calculus I, etc. Not necessarily math majors.

To be crystal clear: I'm not looking for suggestions regarding other online resources. I just want an honest critique of Khan Academy from those who've explored what it has to offer.

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Khan (from south Asia) not Kahn (central Europe). –  Henry Nov 8 '11 at 14:52
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Accessibility, and breadth. For many people without access to a college education (say, because they're working), and who find the video format better than books, it's a way to get reasonably decent lectures on many many topics (he even teaches history and biology now), which is great. –  ShreevatsaR Nov 8 '11 at 14:58
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Regarding the math, some students like it because it doesn't sound authoritative and provides certain type of hand-holding for every level. That is something research level mathematicians have hard time to understand for their own reasons. –  user13838 Nov 8 '11 at 15:31
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Another point: it appears that the videos are split into small chunks, with each video having one main point and being short enough to sustain the attention of the average viewer. So even those whose attention spans have withered away (again, say, because they are no longer in a classroom setting) can get something useful out of these videos. In fact, one could say that the traditional long-form lecture fails such students, and Khan Academy videos fill that gap. –  ShreevatsaR Nov 8 '11 at 16:58
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A critique of the videos which, IMO, makes an important point of what's wrong with them: Khan Academy and the Effectiveness of Science Videos. I personally haven't watched enough of them to really be entitled of giving a judgement, but from what I have seen I strongly disapprove of the lack of motivation why stuff is done the way he explains it. That may be just fine for a student who's not interested in actually understanding anything but simply wants to pass some exam, but they will probably gain little benefit from this in the long run. –  leftaroundabout Nov 8 '11 at 19:28
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I find that the impressiveness of a Khan Academy video for me is negatively related to how much I know of the subject. As a math graduate student and calculus teacher, I find Khan's math/calculus videos the least impressive of the lot, his physics/chemistry/biology videos mildly impressive, and his history videos the most impressive.

What this suggests to me is that the Khan Academy is lacking in depth and clarity of presentation, as well as in addressing the subtleties and key issues that would be necessary to impress a person with some knowledge of the subject. Watching the Khan Academy is roughly akin to having a smart kid in your class (who is learning the subject along with you) explain to you what he/she has understood of the subject. It is not really comparable to how an expert teacher would convey the material.

This may not be completely a minus, because the lack of polish and the chumminess of the videos might itself be an endearing factor that makes people more comfortable with the videos. It also makes it easier to scale up and make a larger quantity of videos. Also, the low intensity of the videos makes it easy for a person to watch them when tired and distracted without missing out on too much.

Here are some examples of sloppiness:

(i) In the calculus videos, when I viewed them, the graphs were drawn very shakily, extremely hard to understand, and not well labeled. (ii) In a video on classical mechanics, there were some inaccurate statements about normal force, describing it as a reaction to gravitational force in the action-reaction sense (this was fixed later, I think). These weren't merely careless errors in speaking, but reflected a deeper lack of understanding. (iii) The examples and symbol choices are often confusing.

If you are recommending watching Khan Academy videos, I suggest you add the caveat that they should not expect a lot more (in terms of accuracy and quality of explanation) than they would expect learning from their colleagues.

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> "Also, the low intensity of the videos makes it easy for a person to watch them when tired and distracted without missing out on too much." I think this is an important point. It means that the average multiply-distracted internet users of today can get something useful out of the videos, which they may not be able to get from books or longer-format videos. –  ShreevatsaR Nov 8 '11 at 17:01
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Shreevatsa, not sure you're right. If a user remembers 40% of Khan's video, and 20% of another video that is thrice as dense, the arithmetic supports the denser video. It's unclear how the trade-off works in practice, it could go either way. –  Vipul Nov 8 '11 at 18:29
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I agree, but besides %, another point is viewers feeling they've learnt something (and thus being motivated to continue watching more videos). If someone watching a longer video in their normal internet-distracted way realises they're not following much (or gets bored), they may just give up, while if they somehow complete watching a Khan video they may feel they've actually learnt something or passed a milestone, and continue with another small Khan nugget video at some later time. Of course, this is all speculation: some students are more patient and even Khan length is too much for some. :) –  ShreevatsaR Nov 12 '11 at 16:13
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I like the videos.

But I don't think they are what is special about khanacademy: instead it is the combination of the self-study videos together with the machine-graded and assisted exercises, where a human tutor can monitor progress on the exercises. In a sense this might be seen as the reverse of traditional education where the tutor teaches and the student does exercises alone. Time will tell whether it is a better model.

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I've looked around khanacademy a bit and I'm not really impressed. There's certainly nothing wrong with it, but it gets too much hype. There are math tutors on youtube (look up PatrickJMT) who do a better job.

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What are you not impressed with? Depth? Rigor? Explanation? Number or quality of exercises? –  Srivatsan Nov 8 '11 at 15:08
    
Just the clarity of presentation in the videos. I admit I only looked around a little, and this was a while ago. I'm not saying it's not a good resource, it certainly is. I just feel like it gets too much hype. Youtube is full of great math tutors, MIT's opencourseware videos, etc. –  Brendan Cordy Nov 8 '11 at 15:46
    
After reading Henry's post, I realize I may have missed the point though. I didn't know there was any student-tutor interaction going on through the website, so I can't comment on that. –  Brendan Cordy Nov 8 '11 at 15:51
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I've used Khan Academy videos from time to time, and my biggest complaint would be the lack of professional oversight. For example, in his video about the sodium-potassium pump he is just wrong about how the membrane potential is generated, and how the action potential is transmitted. In this case, there is a correction video posted, but I remember there were some other videos with smaller mistakes that were only pointed out in the comments, or not at all.

That said, I still think it's an excellent learning resource, because the short videos are easier to watch than reading the same content in a book, and Khan is very good at explaining things.

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I think it's weird that he's the only one doing videos. If he could get more funding, which he probably can and does, he should hire experts to do videos. Or, they could volunteer. He could pick people known to be good teachers as well. –  Graphth Nov 8 '11 at 17:36
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