This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Khan Academy

### From Mathematics Is A Science

Khan Academy is company that maintains a depository of short video lectures on a variety of topics all presented by Sal Khan. The mathematics part is about a half and most of it is pre-college.

## Contents

## 1 It's tutoring

Picture this. A senior math major is helping a freshman with calculus. After a few frustrating minutes of “what?”, “OK…”, “hmm” from the freshman the senior gradually becomes more and more animated. He raises his voice to emphasize some important words (these are actual quotes):

“givenanyepsilon, I canalwaysspecify delta…” “aslongas you pick an x, I canguaranteeyou…”).

He is furiously pointing at an especially important spot on the paper (if this is a blackboard, you can hear chalk pounding). He forcefully underlines and circles some important letters and formulas, again and again (if this is a blackboard, the chalk might break at this point). All this time he stares at the freshman with an intense expression on his face.

I always feel like this freshman when I watch Sal Khan’s videos.

Seeing it as a tutoring service explains the popularity of Khan Academy:

- It's popular as good tutoring would be.
- It's a revelation to those who have never tried such a service.

After a lecture in a room for 300, a ½ hour with a decent tutor will feel much more personal. If the tutor is any good, the student usually becomes a fan, and sometimes a user, of this service -- and complains to the tutor about the bad professor. If, on the other hand, the tutor is bad, the student never returns -- and complains to the professor about the useless service.

Just about every college offers tutoring services to its students, at least in the US. I always recommend them to my students, but virtually none ever tries it. I suspect this is not uncommon. Good students don't go there because they feel they don't need it and bad students because it feels like extra work.

Compare this also to a recitation run by a TA.

## 2 The good

The Khan Academy has a few good things that make the service useful:

- The best idea is to deliver the lectures in 10-15 minutes increments.

This makes the collection more manageable. It's still a long way to go because the lectures aren't transcribed or annotated.

- Online exercises with guidance and data collection will be very useful if done right.

The low hanging fruit of area that allow multiple choice questions seems to be the main target at the time. The broader feasibility of this approach remains to be seen.

- The presentation is lively.

My guess is that Khan would become a good teacher if he has spent some time is the classroom. Unfortunately, this is never going to happen...

## 3 The bad

I am afraid the good things about the Khan Academy don't outweigh the bad ones.

- Salman Khan has never taught a class in his life.

This means two things. First, Khan has never *lectured*. What do you expect from a good lecture? Depth, insight, introspective. "Why?", not just "what?". A good lecture isn't just regurgitated material from a textbook or a "how-to" manual on tape. This shortcoming is an inevitable consequence of Khan's attitude, which is very common among non-mathematicians, towards mathematics: math is a tool. From this point of view, it's more important to be able to compute the derivative of a specific function than to understand the idea of the derivative. The result is a parade of computational examples that neatly fit into the mini-lecture format. Isn't this the most **boring** way to teach and learn math! (To be fair, let’s not forget about a different kind of damage inflicted by many mathematicians with their definition-theorem-proof style. That's second most boring.)

Second, Khan has never *taught*. Notice that his lectures, when recorded, are addressed to an empty room. This way you don't have to deal with the problems the student may be having. If the student in the "audience" is struggling, he is free to turn the video off and try something else, like a book. In either case, you will have only *satisfied* customers! In a real classroom, you don't have this option.

- Salman Khan lacks the domain knowledge necessary for developing a curriculum on the college level.

Khan uncritically follows the standard curriculum and emphasizes standardized tests. Compare to this project of mine as an example of the issues one has to face in order to develop something *new*. Also, developing a curriculum even for high school requires considerable background and careful thinking. Consider this recent article with a serious, mathematical discussion about how and what to teach about fractions, yes, *fractions*!

- Trying to build “a new paradigm in education” on such a foundation is a mistake.

That's my conclusion. Beyond that, the implied goal of covering the *whole* high school/college curriculum -- "in pretty much every subject" -- leaves me extremely puzzled...

## 4 The ugly

One may be able to overcome such a lack of background, especially with a few millions in the bank. But did Salman Khan surround himself with experienced educators? No. In fact, Khan Academy is hiring software developers. Teachers are welcome to contribute -- for free.

I am not saying it doesn't make sense business-wise; after all there is so much content online already and plenty of people would work for free if you promise to change the world.

## 5 Comparison of video lectures to online textbooks

Advantages of this site and similar over the video lecture format at the Khan Academy:

- search-ability,
- edit-ability,
- readability,
- print-ability,
- internal links,
- lower requirements on the bandwidth and better download speed,
- much easier for non-native English speakers,
- more useful for vision-impaired,
- it's cheaper.

Content-wise, the overlap with this site is minimal:

- Early calculus
- Elementary probability
- Elementary linear algebra
- Ordinary differential equations

For alternatives, see Math online.