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Sal Khan responds to critic (washingtonpost.com)
292 points by danso on July 27, 2012 | hide | past | web | favorite | 154 comments

Disclaimer: I'm part of Khan Academy. Not going to chime in w/ my deeper disagreement w/ the original critic and the other article on the frontpage.

I would like to correct a persistent misconception or two.

Persistent misconception: "...we suggest that Khan Academy desperately needs voices of teaching experience. Khan could tap into any number of existing networks..."

Truth: We have four ex-teachers as full-time employees. We have two high school math teachers as consultants. One Harvard Doctoral candidate in Education and one post-doc in neuroscience at Stanford are in residence. One UPenn Professor is also likely to begin a sabbatical with us. We have a 3 person team dedicated to working with and getting feedback from our 50 pilot classrooms and the 15,000 teachers actively using KA in classrooms.

Persistent misconception: "...it certainly requires more than just “two minutes of research on Google,” which is how Khan describes his own pre-lesson routine."

Truth: Go read Sal's AMA response (includes the sentence "When I did organic chemistry, I spent 2 weeks immersing myself in the subject before making the first video") before taking one of these "two minute" snipped quotes at face value: http://www.reddit.com/r/IAmA/comments/ntsco/i_am_salman_khan.... I've seen Sal's face light up when he gets an unwieldy new shipment of textbooks to start studying in preparation for his videos. Does he dive right into some videos? Absolutely. Is claiming that his "pre-lesson routine" can always be dismissed as two minutes of Googling disingenuous and patently false? Absolutely.

It's good to know that you guys are a non for profit and that you're just looking at improving in any way possible the current education system, whether as a supplement, or as a self learning tool.

I personally think that Khan's response was one of tact and class, as is your comment. Keep up the good work.

I agree that Sal is a class act. I'm glad he's doing what he's doing. I suspect we'll see some (more) great things from Khan Academy. I can say that and still believe that it might be a good idea for him to treat these videos as version 1 and consider upgrading them to version 2. In particular, if there are resources for creating more videos, some of those resources might better be spent on upgrading the existing videos.

I've tutored math in Korea, observed the schools in Japan and Singapore, was observing math class in Shanghai most recently, and have used curricular materials from Singapore, Japan, and China to homeschool my own kids in math.

What I observe in the Asian programs I've seen that differs starkly from the vastly inferior curriculum here in my own country (US) is meticulous care put in to the development of:

1) a strategically-ordered, cohesive sequence of topics,

2) explicit list of the ideas that need to be mastered in each topic before moving on, and

3) rigorously field-tested teaching techniques, examples, assignments, and assessments for each idea.

The whole sequence is constantly being experimented with, tested, and optimized like a Japanese industrial, or Apple consumer, product.

In contrast to this meticulously crafted approach to incremental mastery, our US approach is one of each teacher throwing her own bowl of math spaghetti at kids and whatever sticks sticks. Whatever doesn't stick today, well, don't worry, we'll be doing something different tomorrow. Maybe you'll do better with that. And someone else will throw the whole bowl at you again next year, and the year after that. If you run out of years and a lot of things still haven't stuck, well, we did all we could. You're just not a "mathy type" (claim the teachers who couldn't solve a Singaporean 5th grade word problem if their lives depended on it.)

What Sal has produced in version 1 reminds me more of the American way than the Asian way, but that's no surprise. It started off as an act of personal generosity, not a NASA space project. If it stays the way it is, I'll be grateful for the moral equivalent of free pizza. I'll gladly eat some, and I won't fuss that my free pizza doesn't have my favorite toppings.

But if he's planning to go forward, I think the next step might be to back off a bit on the quantity of videos and consider upgrading some of the old ones to a more deliberately designed, cohesive video sequence.

I am an Asian myself, but that doesn't stop me from saying that teaching is an art. If you put too much rigor into the style and methods of teaching, the whole thing becomes a military exercise, and kind of kills the creativity in kids. If this is not true, why does creativity still stay with western countries and not Asia (in terms of industry)? I think Sal's spontaneousness is his strength. I don't think he is a loose canon. His style may be casual, but he is always moving towards a clear goal in the videos. That casual tone encourages the user. It piques their curiosity. That's why maths reference books are very structured and rigorous, but people don't read them.

Creativity is not hampered by a rigorous, well-designed curriculum. Just look at the Florentine artists, who trained hard at their art under their masters, then produced creative masterpieces themselves. Creativity is hampered by lack of skill (a problem for Western kids who aren't taught math well) and by social pressure to conform to expectations, do as you're told, and not question your superiors (a problem rife in Asian cultures and classrooms).

You can combine a well-designed, coherent curriculum for skill training without imposing the crushing baggage of "your worth as a human being depends on the brand prestige of the university you get into."

Don't have much to say about the relative merits of Kahn Academy specifically, but I think there's a balance to be had here.

If you want to train people to be inventive in finding new ways to apply mathematics, and new mathematics to solve problems, then you need a process which leaves some room for questions, creativity, for open-ended challenges, and for some context around mathematics as a creative process.

The industrial production line approach may be efficient, but perhaps requires a lot of external pressure and discipline on kids to keep it on track, and can result in people who are strongly technically skilled within the relatively narrow boundaries of material they've been drilled on, but utterly lacking in imagination or passion for the subject.

In practise I suppose you need something in the middle. It takes disciplined study to develop the fluency to be creative in maths at a given level, but the discipline is a means to an end not an end in itself, and if it's so strong that people are discouraged by shame from asking the questions they need to ask to develop a deeper than rote understanding of the material, then it's got to be counter-productive.

I say this as someone who was almost put off maths for life by the latter approach, but is now doing a second masters in a mathematical field...

As a grad student I've TA'd several first-year courses and run into what is produced by, what independent studies tend to agree, is one of the best high-school systems in one of the best provinces in one of the best countries in the world for math and physics education. To be blunt, students are frequently taught things that are just plain wrong. Not short-cuts or half-truths. Not nit-picks like the slope mentioned in the article. Things that they should never have been taught at all. Whether it's bad text-books or teachers who majored in psychology being roped into teaching math, even one of the best high-school systems in the world doesn't get it right all the time.

I haven't viewed any videos from Khan academy, but I think a public repository of lectures that are rigorously checked for correctness can only be a good thing. Is that what Khan's academy really is though? Teachers are trained to engage young minds. Is it realistic to expect flawlessly correct lessons from someone with this background after just two weeks of immersion in a given topic, especially when reference materials (e.g. highschool textbooks) are so often riddled with mistakes? If you're teaching math or physics, why not collaborate with a mathematician or physicist? Let Khan's teachers handle how to structure lessons and provide engagement while experts in their field provide the material. There are plenty of experts out there who would jump at the chance to help, if only to save themselves from headaches when teaching first-year courses!

I also think people often overlook the fact that Khan Academy isn't really meant to be a revolution for the worlds privileged students. What KA really does is provide access to learning materials to people all over the world who do not have access to good teachers. People like to point out that recorded lectures do not provide the interactive element that real teachers do, and that's absolutely true. However, there is no substitute for homework. To learn math, one must do math. No amount of interactiveness can change that. If KA provides good exercises along with its lectures then it could indeed provide disadvantaged (but motivated) students with a road to academic success anywhere in the world.

Care to give examples of the wrong stuff being taught?

Anyway, I agree with you on KA. My big thing is, and I think Khan is an awesome, amazing, but when we get down to brass tacks does KA help students really "get it done?" I don't know.

I feel like there's always all this talk about Khan Academy and how great it is and all of this. But if you get down to it and watch the videos for hours, not just talk about watching them, how much is it helping? Maybe it is but I've showed it to a lot of people and have tried, and this is just my anecdote, to get people to learn via KA and their results haven't been amazing or anything.

But there's no reason it can't improve and get better. I just get this feeling that we have all collective gone "OMGZ MATH VIDEOS!!!!!!!" and haven't done a critical examination.

It's not designed to be a replacement for traditional teaching though. It's an additional supplement. In hiS TED talk Khan gives details of how teachers are using it as homework, freeing up class time for more interactive discussion. It seemed like an interesting pattern to me but I have no experience with it do I can't comment on how effective it is.

> Care to give examples of the wrong stuff being taught?

That glass is liquid and old panes of it are thicker on the bottom because it flowed. (The definition of a 'solid' is a bit technical, but panes of glass do not flow.)

That raindrops have a 'raindrop' shape. (No. Wrong. Not possible to salvage this one, as it is entirely incorrect.)

Is that not the case with glass? That's exactly what I was taught at school by my science teachers.

Also a good argument to counter the "why is it thicker at the bottem then?" point - if you were incapable of producing perfectly flat glass, just as they were back then, and you wanted to put this glass into a window - which side would you have pointing up?


> I was made aware of the fallacy of the glass flows myth many years ago by the late great glass chemist, Nick Labino. Nick offered this simple analogy, "...if the windows found in early Colonial American homes were thicker at the bottom than the top because of "flow" then the glass found in Egyptian Tombs should be a puddle."


> Many years ago, Dr. Chuck Kurkjian told me that an acquaintance of his had estimated how fast—actually, how slowly—glasses would flow. The calculation showed that if a plate of glass a meter tall and a centimeter thick was placed in an upright position at room temperature, the time required for the glass to flow down so as to thicken 10 angstrom units at the bottom (a change the size of only a few atoms) would theoretically be about the same as the age of the universe: close to ten billion years.

I can find more if you want.

Edited to add: Oh what the Hell:



(The FOA is the Fiber Optic Association. It seems every serious group that works with glass has debunked the flow myth.)

Which is obviously completely reasonable in retrospect.

I guess my point was that it's just as likely for a teacher to accidentally feed you misinformation as it is for KA. More likely even, given that KA is transparent and open for scrutinization.

Agree. Good work. Let me add one more thing.

A Usually Persistent Truth: the farther you are from when you learned something, the worse you are at teaching it. Khan's ability to learn something and turn around and teach it is likely the reason it's accessible and enjoyable for students.

> "When I did organic chemistry, I spent 2 weeks immersing myself in the subject before making the first video"

I'm sorry, but 2 weeks is not that much time. Most TA's for ochem classes have at least taken 2 quarters (and yes, I can assure you, they also are 'immersed') of the subject, and they aren't in charge of the lecture.

Meanwhile public school teachers teach math without understanding the subject at all, and we question whether or not Khan is doing a better job? I'm pretty sure he can do a better job than teachers regurgitating the textbook.

Can it be said that his organic chemistry lessons have suffered for this?

Honest question. I have not seen them and I am not in a position to evaluate them even if I had.

Organic Chemistry is not rocket science. I haven't seen those videos, but if they are introductory subjects, 2 immersed weeks sound about enough to me. I'll take a look at the videos today and see.

Actually, as documented in Ignition!, a great deal of rocket science is, in fact, chemistry — and although the oxidizers are not usually organic, the fuels are.

Rocket science is not "rocket science". The expression has been coined as part of a propaganda campaign for the US public to accept a Nazi war criminal (Wernher von Braun) in an important post on the US government.

Maybe it's not "science", but it's horribly complicated, with then new vibration modes up the wazoo, and look up the fun efforts that were required to F1 engines for the first state of the Saturn V.

And look at how many still blow up or otherwise fail to put their payload in the desired orbit (although maybe in general we're getting better at that).

I would suggest that the chemistry parts of rocket science are some of the easier parts (how complicated can burning kerosene and LO2 be?), but I suspect I would piss off a few rocket scientists. ;)

Read Ignition!. It is, in fact, fairly difficult to find a combination of fuels that ignite exactly in the manner one wants them to, in a reasonable range of temperatures, and can be stored without decomposing or eating the storage container.

Of course, today, in large part thanks to a large number of people who died horrible deaths investigating this during the time period documented in Ignition!, it's not hard at all. But it was sure hard until the 1960s.

I think I will check that out. Thanks!

Apparently, it's not the complexity that kills you. It's the unexpected explosions (who knew titanium could be explosive?), the deadly poisons, and the times where you discover that the oxidizer tanks for all the rockets you manufactured seven years ago are leaking fuming nitric acid, and you haven't changed the design in seven years. The solution for that problem was truly astonishing.

We're done here.


I'm not a programmer. If I read a book on programming for two weeks, should I then teach the world how to program? Maybe, but I imagine HN would not necessarily agree...

Regardless of whether or not he should have thought it possible, he did it. That means that we have the luxury of evaluating his capability by evaluating the product instead of merely considering hypotheticals.

You can have as many theories as you want on this matter; I have many of my own. However I'm asking if anyone in a position to actually evaluate what he already did can tell us how well it worked.

Most TAs in organic chemistry classes aren't Salman Khan.

Even if they aren't perfect, it's better to have them on the web as a starting point. From there, KA can iterate and make them better.

But not everyone is a genius

Many a times the main points in a Khan Academy criticism get totally eclipsed by such misconceptions.

The points made about the specific videos may be valid, but those points about specific videos and ideas, can be put across more effectively if the authors get these facts correct.

Having the debate framed as 'Sal Khan is the future of education' and 'No, he isn't, teachers are' is bogus. It's a ridiculous dichotomy. It does a disservice to both Khan and teachers to debate this in that way.

There will be many teachers who will use Khan's videos in their teaching (or to augment it), and I imagine that over time Khan will change the way he does things based on his own education about education.

It's self evident that the 'sitting in front of a machine watching videos' isn't the solution to the education. If it were the multimedia revolution wouldn't have petered out as it did. Children (and adults) need a variety of approaches. Khan's is just one.

> There will be many teachers who will use Kahn's videos in their teaching (or to augment it), and I imagine that over time Kahn will change the way he does things based on his own education about education.

Sal Khan(it' khan, not kahn) himself mentioned he is not looking to replace classrooms. He wants to invert the classroom. Traditional classroom has passive lectures followed up with problem solving which is to be done at home. He says it's better if people can do the passive things at home at their own pace, and use the classroom for problem solving.

The problem with passive lectures in classroom is many a times students are sitting through lectures they don't follow because they don't know the prerequisites; and often times students by themselves aren't able to figure out if they can't make heads and tails of probability problems, what is it that they need to know so that they can understand it. In his talk, Khan demonstrated the software(I haven't used; I might be off) which can track your deficiencies. For example, you are struggling at basic probability. The framework will drop you down to permutation/combination problems. You still are struggling; introduce fundamental principle of counting. You are doing fine now. So explain permutations based on counting principle.

Lacking the prerequisites is one of the problems. We have people who learn at different rate, people who aren't fluent in the language the lecture is delivered in, people who are shy/under-confident to speak up, people who are smart and are bored and feel left out, people who aren't very smart(lack the fundamentals, slow learners...) and are lost and feel left out.

If Khan Academy, or any other self-paced learning resource can solve these problems; coupled with classroom guided problem solving and projects, that will make a huge difference.

As a child of the multimedia revolution, it was strongly ingrained in us that going to college was the only route to getting a job that wasn't flipping burgers. To even consider learning in non-traditional ways would make you the laughing stock of not only your peers, but the older generations too. I'm not sure learning through multi-media ever stood a chance.

I do feel that those times have changed dramatically. Now all we hear about is the college dropouts who went on make billion dollar companies. It has almost become cool to not go to school. I think the time is finally right for these non-traditional educational services and it just helps that the internet is now widely available to act as the conduit for it.

I sort of want to just say Poppycock to this. How many billionaire dropouts do you know? I don't know any myself. OK, fine if you happen to be connected in SV and know MZ or whatever then you're an outlier.

These billionaire dropouts like Zuckerberg and Gates, ... where did they drop out from? Although I don't think it makes a lot of sense to equivocate those two, it will suffice for now.

I don't think times have changed that much. Learning purely from these things is also going to be likely only for autodidacts. There happen to be many of autodidacts in our little world (or at least autodidactic enough to put together a website in Rails or something) but this is not true of that many people.

In fact, how far do you get with this online stuff? Not far, if you look at most places like Khan and so forth, you're talking about sophomore, maybe junior year stuff for the most part. OK, sure there's the occassional machine learning course that gets popular online that a lot of people that don't have any sort of mathematical background take and can say they are a part of the "cool kids" group, but let's be honest. Even then, we're still talking about this small segment of autodidactic or semi-autodidactic types.

A lot gets said of "big bad college" and how the "fresh new hip information revolution trumps traditional learning" but I don't see it. Sure, you could put up a few tutorials about learning to make Hello World in Javascript but I'm just not seeing this education revolution here.

I feel you've perhaps read too far into what I wrote. The fact is that the vast majority of the population couldn't care less about education. The only reason they go to college at all is because they've been told that they won't be able to find a job without it.

With people like Zuckerberg, Jobs, and Gates frequently in the news as of late, people are starting to question those long-held beliefs. They see that people are successful without the education, despite what they've learned to not be true. The stigma of not going to college is starting to lift as a result. Knowing those famed people personally is completely irrelevant here.

If spending a couple of months reading up on Rails will get you a decent job, that's exactly what people will do. They really do not care about deep CS topics. They care about providing a decent home and comfortable living conditions. That is it.

I respect the academics, but you are as rare as the autodidacts.

I didn't really read too much. Again where did Gates and Zuckerberg drop out from? We're not talking about East Savanah Technical College here. Gates, Jobs, and Zuckerberg are the worst examples you could pick to show that people are shedding long held beliefs about education. They are outliers in several different senses.

Who cares where they dropped out from? All people hear is "you must have a degree to be successful" and then they hear "oh, these people didn't have degrees and are still successful." You give too much credit to believe the vast majority of people actually consider the backgrounds of these so-called outliers. These are the same people who previously bought into the "you must have a degree" line in the first place.

There has to be something regional/cultural about this that I'm missing since I hear this complaint a lot, but don't know anyone personally that experienced it until very recently.

When I went to high school in Pennsylvania the 90s people were still encouraged to into the trades. I have some friends from high school that have gone on to be very successful electricians and welders. Even when my brother went to the same school and graduated in 2007 he was never pushed to go to college. He ended up getting his AA at a local university and is now a paramedic/fire fighter for the same city.

>When I went to high school in Pennsylvania the 90s people were still encouraged to into the trades.

I graduated in 2002, at the time any Georgia high school graduate with a B average got full tuition and fees paid for with the HOPE scholarship (still exists, but it only pays about 80% now).

Possibly as a result, almost everyone who wasn't a terrible student was encouraged to go to college.

The only people pushed into the trade direction were people with less than a B average, and with grade inflation you really had to be pretty lazy not to get by with a B.

Interesting. I too have heard it so many times I had assumed it was fairly widespread across North America, but I guess that is not true. I'm from Canada, for what it is worth. Maybe it limited to Canadian culture? Though another reply to you seems to indicate that it is also true across the western US.

Is that not the same principal? Person X chooses career Y and must obtain a certification through path Z.

The complaint is that teenagers are being told the only way you'll be a member of the middle class is that you must go to a four year university. People were saying that going into a trade or getting "just" an Associates degree would leave you in the dust of everyone else.

HN isn't remotely representative of the population at large. You're primarily getting bay area and a bit of Pacific Northwest culture here. A touch of NYC businessfolk sentiment that HN entrepreneurs envy but can't actually pull off.

If you think the folks commenting here have any idea what life outside the bubble is like, think again.

The point though is that Khan is free, is a non-for profit and is more than just sitting and watching videos. They are followed by exercises which track the progress of the user and can even be reviewed by teachers if a teacher chooses to do the teacher account - student accounts setup. All of that is very valuable and very disruptive to something like Mathalicious, a for-profit site not many have heard of.

Not sure if there's a reason you mention it that way but his last name is Khan, not Kahn.

My mistake.

>An effective math teacher will point out that “rise over run” isn’t the definition of slope at all but merely a way to calculate it. In fact, slope is a rate that describes how two variables change in relation to one another:

What a dumb thing to argue about. I'm not a historian (or a mathematician), but the term "slope" seems pretty obviously adopted from a physical slope/incline/hill. Why? Because it's the easiest visual analogy for us apes to grok. It doesn't come from an earlier term meaning strictly "a rate that describes how two variables change in relation to one another."

If you're trying to teach someone a complex concept, are you going to use a phrasing that has zero significance to them? Rate? Variable? What? The people learning about slope aren't programmers or engineers. Give me a break.

Why not use a visual analogy that makes perfect sense and is still a valid definition: rise over run on a section of a hill, road, roller coaster, etc. I hope whoever is teaching this is relating it to a real world object. Just talking about a line on paper isn't going to help much, but neither is an overly complex definition.

Wait till they start learning Calculus - by this point it would be extremely useful to have understood that slope is a rate that describes how two variables change in relation to one another!

From the article that sparked Khan's response:

>Take Khan’s explanation of slope, which he defines as “rise over run.” An effective math teacher will point out that “rise over run” isn’t the definition of slope at all but merely a way to calculate it. In fact, slope is a rate that describes how two variables change in relation to one another: how a car’s distance changes over time (miles per additional hour); how the price of an iPod changes as you buy more memory (dollars per additional gigabyte).

Followed by this in her response to his letter:

>As math was not my subject in school, I don't know who is right but would love to hear from mathematicians out there.

I had to reread all 3 articles multiple times. Then I lamented the sad state of journalism as well as the complete willingness of our society to tolerate the "I'm just not good at math so I won't bother to understand it because I don't think it's worthy"-attitude. What angers me about the first article is not that it went by some editor without the editor saying, hey, this seems suspect, but rather the fact that the journalist decided to write about something she had little knowledge about with a tone that suggests that she thinks she knows knows more than Sal or someone else educated on the subject. An unapologetic combination of ignorance and condescension.

The original article criticizing Khan wasn't written by the person who wrote this response.

"A guest post I published Monday critiquing the Khan Academy..."

Right. She published it as a guest post, but it wasn't written by her. She didn't "write about something she had little knowledge about"

Oh my mistake.... you're right. I suppose this is why I'm not a journalist.

On a related subject; note to WP: do not have guest posts published under an editor's byline. Instead of

"By [editor]

[italicized paragraph explaining that this is a guest post published by an editor]

By [actual author]"

Have 1 byline... the person who wrote the article.

From the article:

> Below is Khan’s e-mail to me, which I shared with the author of Monday’s post, Karim Kai Ani, a former middle school teacher and math coach who is the founder of a company called Mathalicious. He said Khan is wrong.

So, to summarize, "Khan is wrong, but I won't bother to explain why, he just is, and I have a self-proclaimed expert that says so."

More so, Khan's free model has the potential to interfere with my paid model, so I'm going to sling some FUD around.

There were some cogent points in Kai Ani's critique; the biggest one I think Khan would completely agree with: education problems aren't going to go away because of videos on YouTube.

education problems aren't going to go away because of videos on YouTube

Moot point since the Khan Academy is much more than about YouTube videos now.

The videos may have kickstarted it; but to offer the above as a critic to Khan just shows that you are debating on an outdated version of what the Khan Academy is up to.

People debate about outdated versions of companies all the time. Why should Khan be any different?

Yes, people debate moot points all the time out of ignorance. What's your point?

For any equation in the Cartesian plane, Khan is right.



I cannot stand people who leave things at "just because". I can't remember who said it, but it goes "people who have explanations will explain".

The Cartesian plane does not contain equations.

I think what you mean is that a two variable linear equation over the reals describes a line in the Cartesian plane.

Try thinking of a line's slope (as you've described it) as just one measure of that line's "steepness" in the Cartesian plane. Thinking like this, we could use any number of measures to describe "steepness" (for example, angle of inclination provides a measure for the "steepness" of any line)

So it's sort of a philosophical difference. However, there is a a very subtle elegance at work here.... we have this geometric concept of "steepness" which -- very interestingly -- turns out to be related an algebraic concept.

Actually, we can go further. The geometric concept of "steepness" is related to algebra via a simple quotient, which is further related to an analytic concept (rate of change).

It seems so trivial, but a good number of mathematicians make a living by finding small connections between geometry, algebra, analysis, etc.


Not to suggest that credentials are everything, but, lacking any other information, they do provide useful signaling indicators, from http://en.wikipedia.org/wiki/Khan_Academy

"After earning three degrees from the Massachusetts Institute of Technology (a BS in mathematics, a BS in electrical engineering and computer science, and an MS in electrical engineering and computer science), he pursued an MBA from Harvard Business School"

One would hope that his education background might have given him some insight into what "slope" was, and how to best explain it to someone in the 8th/9th grade.

I can _recall_ when it was introduced to me, and I didn't really grok it until a few years later - "rise over run = slope" was complex enough for my brain back then - I can just imagine if people started yacking about "Ratios of variables" - my head would have exploded.

From the article criticizing Khan:

> An effective math teacher will point out that “rise over run” isn’t the definition of slope at all but merely a way to calculate it.

Depends on the level. For introductory algebra, or classes before calculus, where the "slope" concept is used exclusively with linear functions, "rise over run" is a perfectly adequate definition.

For calculus, you can rigorously define slope as the limit of (f(x+h) - f(x)) / h as h -> 0 (or any of several other equivalent definitions). The subtleties of the proper definition are likely to be more confusing than enlightening to a beginner.

But even the rigorous definition is still a "rise" term f(x+h) - f(x) divided by a "run" term h. The phrase "rise over run" is an easy-to-remember mnemonic which actually does a really good job of capturing the underlying idea without going deep into more technical issues involving limits (calculus) or the guts of exactly what a real number is (real analysis).

Once the linear case is completely understood and the student has some basic facility with both mathematical reasoning and algebraic manipulation, THEN is the time to introduce the more general definition of "slope". Even then, mathematics teachers tend to use the word "slope" mainly in the linear case, and "derivative" in the general case.

As far as I know, this has been the standard way to teach high school / early college level mathematics for decades.

How often do you need signaling indicators, though? If someone has sufficient competence at a given field, they should be able to demonstrate that competence by delivering satisfactory work.

The proof should be in the level of understanding of the concept of slope acquired by students using various methods; it doesn't matter at all who is "right" with respect to some formal definition.

Totally agree with you that what matters is whether the students eventually grasp the material. What I like about Khan, is he is fundamentally interested in teaching students so they _understand_ the material. He doesn't get caught up in theories of pedagogy or mathematical models or precise correctness - he sees his job is to communicate a concept in a way that the student says, "Oh, I get it."

Now, with that said - there _is_ a danger in that model of teaching, in which the student gets lured into a zone of comfort. So there _absolutely_ is a place in teaching for instructors who are going to challenge, upset, and disturb the student - resulting in a form of stress that pushes to the student to new heights. This can be a very uncomfortable (and, indeed, upsetting/stressful) learning environment - but it does give students deeper, and sometimes much more meaningful insight into topics.

But that's not what Khan's about. He is the guy you go to when you just want to get over some hurdle about a topic that has frustrated you.

"One would hope that his education background might have given him some insight into what "slope" was, and how to best explain it to someone in the 8th/9th grade."

That leap you made there at the end of your sentence is the crux of the issue. Most educators argue that being an expert in a subject is not even remotely sufficient qualification to teach it effectively, especially to children.

No, she presented Karim's argument in another column. This is Khan's response.

I don't know if she has a position on Khan herself.

"Khan is wrong" is actually Karim's response to the email:

"Below is Khan’s e-mail to me, which I shared with the author of Monday’s post, Karim Kai Ani, a former middle school teacher and math coach who is the founder of a company called Mathalicious. He said Khan is wrong."

I think it just may be poor paragraph structure.

"Below is Khan’s e-mail to me, which I shared with the author of Monday’s post, Karim Kai Ani, a former middle school teacher and math coach who is the founder of a company called Mathalicious. He said Khan is wrong. This won’t be the end of the debate."

It was part of the recap, I understood it to mean "Khan responds to this guy who posted the other day who said Khan was wrong" and then "stay tuned for his response to Khan's response" rather than "And then he replies Khan is wrong in his response. Stay tuned."

"As math was not my subject in school, I don't know who is right but would love to hear from mathematicians out there."

Go find a professor, you sorry excuse for a "journalist".

You mean the two who are sitting there disagreeing?

Which ones are the "professors?" I'm not trying to be flip but I don't think it's unreasonable to ask for the blogger or whatever it is to go find an expert. It's not like this debate is occurring between Einstein and Feynman.

No need for inflammatory language here.

This kinda stuff gets me fired up. Do your job, blogger!

Anyways, edited.

The way I've understood it, Khan isn't trying to disrupt the idea of teachers or schools per se, only alter it.

Basically, the traditional schooling model consists of "lectures" in class, where the teacher presents you with information for an hour, and homework, where you work on problems relating to that content alone in your own time.

Khan says, that's cocked up-- we should let students consume the raw informational content on their own time, where they can pause, rewind, and go over it as many times as they need to in order to understand it without disrupting anyone else, and then do "homework" in the classroom, where there's a focused environment that encourages exploration and somebody who can help each student with their individual difficulties.

Which has always struck me as a pretty straightforward, good-common-sense approach to at least try. Why is this concept so opaque to so many people?

That approach (students working at their own pace) isn't very novel when you consider the fact that home-schooling has been around for a while.

Except that the notion of homeschooling is hugely co-opted by cultists who brainwash their kids. It's hard to get a serious dialogue on homeschooling going when most people equate it to a stand-in for Bible study and avoiding science education.

I've heard this said often enough, but most of the homeschoolers I actually know or know of indirectly are pretty lefty or libertarian. Most Christian extremists go to little private schools which are scattered all over the place.

There is actual data to look at here: http://nces.ed.gov/pubs2009/2009030.pdf

Desire to provide religious or moral instruction is at the TOP of the list of reasons people homeschool.

...among those who answered the survey.

This is a survey by the NHES, a government organization - do you think there is some reason for selection bias?

Here is the survey's remark on their estimation methodology:

"When applied to survey data, weights allow for the generation of national estimates from a sample of respondents. They also adjust for characteristics of the survey design, nonresponse, and noncoverage. However, biases may exist in the data if weighting procedures have not adequately adjusted for these issues. A large-scale bias study was conducted in conjunction with the 2007 data collection. Readers interested in the findings of the bias study, as well as detailed information on NHES survey methods, weighting, and response rates, can refer to the Data File User’s Manuals published online at http://nces.ed.gov/nhes ."

I think that the fact that the survey was conducted by a government organization and that the targets of the survey were families who had decided not to participate in government-run education, for one reason or another, makes a certain selection bias seem likely.

I'd expect a measure of homeschooling families to want nothing to do with the federal department of education.

I was homeschooled in 7th and 8th grade. It was totally because my parents thought I wasn't getting a good enough education. I still had hebrew school on sunday(jewish), but religion never entered my curriculum at home. I had a much greater focus on science & tech. (I had a programming "class" taught by my dad where I programmed micro-controllers)

edit: (actually... It wasn't a heavier focus on science & tech... it was just more intense in general... I had a hefty literature portion (I read many Dickens books...) and some sweet art history books)

I've no idea to what extent homeschooling has been co-opted by 'cultists', but I think it's a fair statement to say that families who engage in the practice do so out of some mistrust of the prevailing institutional model of education for one reason or another, and that it may be relatively likely that, for the same reasons, they're unwilling to allow their children's education to be the subject of some public 'dialogue'.

And unless I'm mistaken, home-schooled children tend to consistently outperform their public-schooled peers in testing, yes?

I'm sure if you had that kind of student-teacher ratio in normal schools students would perform better anyway.

A big part of a child's success in school has to do with parental involvement. Home schooled children, almost by definition, have highly involved parents. It would be interesting to compare home schooled children with regular children whose parents are actively involved in their education to see how that matched up.

Traditional schools are built on an industrial batch model where the goal is to get a certain percentage of the class to basic competency. So students are grouped in classes, taught for a semester, graded, and then moved on.

The Khan and homeschool model, in contrast is the mastery model. Students are individually taught at their own pace. They are not graded and pushed on. Instead they keep learning a topic until they know it. In traditional classroom education, the learning is variable while the time to learn is constant. Khan makes the learning constant and varies the time. Some students will learn faster than others, but all students learn to a high standard.

Khan is not just delivering a better classroom. He is offering a wholly different model of education.

To over-generalize: one-on-one teaching results in results that are about 2 standard deviations better than normal. Home schooling results are about 1 standard deviation better than normal.

This does not sound like an argument against home schooling. If it sounds unfair, that's kind of the point.

My issue with home schooling is the lack of variety and specialization. With only one teacher, the child just isn't going to be exposed to as many viewpoints as they would in a traditional school setting.

Homeschooling and un-schooling are actually quite varied. Un-schooling, specifically, is usually very specialized. Take Erik Demaine, for instance. He is the youngest professor in MIT's history - he was un-schooled until he entered college at 12. He specialized in mathematics because he loved it.

Homeschooling is still regulated by the state. Students must still pass certain tests, and often homeschoolers have a community of parents and children who get together to learn with each other at educational events geared specifically to their education. Both models have evolved, though they still have some cons. So, too, do public and private schools. Personally, I'd like to see us picking the best parts of various educational systems and putting them together.

What Khan is doing is great. For some students, it is very effective. For other students, not effective whatsoever. Thankfully, dozens of similar offerings have appeared (40 by one count), as well as tools to help teachers create their own video lessons (ie. Educreations). And that's not even mentioning all the other students for whom video is not the best way to learn these topics.

The real problem is the media. And by that overarching term, I mean the rhetoric that various journalists, bloggers, and others have let themselves use for whatever purpose (ie. sensationalism, pageviews, linkbait, etc).

It's understandable that there's been a backlash to Khan. He got overhyped. The pendulum swung too much one way. Now it's naturally swinging the other way.

In the end, this is going to turn out better for students. As critics lash out in both directions (supporters and detractors both have gotten pretty vicious in this debate), there are a bunch of for-profit and non-profit efforts that are creating alternatives. Khan has a smart team too. I'm sure they're steadily improving their offerings.

Frankly the response only addresses a small part of the criticism (the definition of slope) and then launches an attack on the critic's motivation. The main point in the original article [1] was that Khan's preparation for his lectures is deficient ("I don’t know what I’m going to say half the time") and often resumes to "two minutes of research on Google".

[1] http://www.washingtonpost.com/blogs/answer-sheet/post/khan-a...

I agree that it would have been nicer to see that issue addressed head-on. I think Karim is conflating the words unscripted and unprepared.

From what I understand, Khan keeps the videos unscripted so he can maintain more of a conversational style, but he's always careful to understand the material very well before doing a video on a subject.

My lad (now 7) has done some of the maths problems and we've used the videos to provide the background to attempting those problems. IMO from the half-dozen videos I've seen they were both 'unprepared' and unscripted - but that might not be bad. They're the sort of thing I think one would come up with if someone puts you on the spot and says "teach me how subtract". Obviously these are low level maths subjects. He's not unprepared in being able to do this sort of basic stuff but I think a little more polish would make such videos a lot better.

One thing I found quite frustrating was the lack of technology applied to making the video - in the few I've seen he takes ages drawing out number lines (for example) and the writing is quite unclear; it doesn't appear to be too hard to have a marked axis that you can paste in when it's needed. Petty issue but something I didn't expect to find on this much touted resource. Another example would be hand drawing bunches of marbles/tins http://www.youtube.com/watch?feature=player_embedded&v=D...; I guess it naturally limits the pace, which may be good.

I found Mr. Khan's response really odd for the same reason.

He's addressing an EXAMPLE the critics used to illustrate their actual point, and fails to completely address the bigger issue.

I thought the critics' points were completely valid, and raise pretty serious issues about the quality and usefulness of the Khan Academy material.

I find this line of discussion dubious. What you want to know is _not_ if he has spent hours preparing but if what he is saying is correct/the best way to explain something. He might be so gifted that everything just comes to him. Or he might be the person that might suck at math even with hours of preparation. Just because he said "I dont prepare for my lessons" (paraphrased) does not mean what he's teaching is no good. There is a reason why the videos have been watched as many times as they have.

The thing that annoys me about Karim's argument is 1. There is no constructive criticism. He does not tell Sal (or me the reader) how one can make SA better 2. He has a competing for-profit venture that is a direct conflict of interest with SA and leads me to question his motives 3. He is a self-proclaimed expert with no proof of his own expertise 4. From his rant, I don't get that there is something structurally wrong with SA videos in general as his claims make them out to be

How many of Khan's videos have you watched? I've gone through about 100+ of them, and the material has been universally excellent, and certainly met, (and in most cases exceeded) the lecture material that was presented to me at High School/Simon Fraser University.

"Quality and Usefulness of Khan Academy Material?" - you must have gone to an incredible school if you find his material lacking.

You didn't read the criticism, did you?

I didn't say anything about how I view Khan Academy content.

I don't use Khan Academy, because I have no use for it. That doesn't, however, preclude me from assessing critique made by others about it.

Absolutely I read the original criticism - carefully. It was (in my opinion) complete nonsense by somebody who clearly has an axe to grind.

I have seen over 100 of Khan's videos. On many occasions he was able to clearly communicate a topic that I had been gated on. Doing so in a clear, concise manner. I have colleagues at work that use Khan to help their children through Math. If Khan had existed when I was in university, it would have eliminated 90% of the tutors costs associated with things like linear algebra. So, as I read his criticism, I was asking myself, WTF - this feels like it has _nothing_ to do with the content that I've viewed, which has been _excellent_ in explaining topics that very few (if any ) of the lecturers I had in High School/University were capable of doing.

What it actually reminded me, was of Encyclopedia Britanica's FUD against Wikipedia when it was coming out. The criticism _sounds_ accurate, unless you've actually looked at the content being attacked.

My point is - you can't read the criticism, and make a judgement, until you've spent some time looking at the material to see if the criticisms are sound.

Sounds to me like he chose to ignore the ad hominems and focus on the complaints for which there is a factual definitive answer.

My son has been watching Sal give lessons for the last year. Sal makes mistakes sometimes. My son usually notices and asks for clarification. We end up with a nice discussion about the topic at hand and arrive at a correct answer. If it's math related, I've got it covered. If it's not, we do some research.

Classroom teachers make mistakes. Textbooks make mistakes. But the system is set up to disallow question of these two authorities. Example: Math class is the first class of the day; teacher follows textbook and textbook is wrong; child questions and is waved off; is that kid gonna remember at the end of the day that she needed to ask mom about this problem? No.

I much prefer when Sal makes a mistake because it makes for a learning experience. What's nice is when my son comes back some time later and tells me that Sal's video has been corrected.

No, I think that's great. Is it really like that though. I always feel like this is kind of a caricature: "The teacher would not dare let me question the authority of the textbook." That doesn't seem very serious. I'm sure, and this may sound mean, that this goes on some very bad rural or inner city schools but it's just such a ridiculous thing to say that I find it hard to believe it occurs in more reasonable scholastic settings. But people always bring it up ...

It seems to be a matter of convenience. It shouldn't be, but that what it looks like. It disrupts the flow of the teacher's classroom. It's viewed as yet another disruption, but the worst kind of disruption: the legitimate kind that gives the rest of the class an opening to continue disrupting the class. And that could affect perceptions about how this teacher handles a class. No, can't have that so just sit down and shut up.

A good teacher can handle the book being wrong. A good teacher will tell the students that the book has a mistakes on this problem well before they have the chance to discover it themselves. A good teacher will have gone over the material in advance and know what's correct. Instead, we have teachers thrust into roles that aren't near their specialty; teachers that can get a degree and qualify for a paycheck because they can work the system, not because they know how to teach students. And interfering with that teacher's conveniences is not a good thing for a student to attempt.

You are one awesome mom :)

Thanks for the compliment! (you assumed incorrectly on the gender, but I'm accustomed to that with the nick :-)

Looks to me like a feeble attempt by Karim Kai Ani of Mathalicious to generate some PR for his for-profit website. What better way to drive traffic then to "build up some controversy" by hating on Khan? Sal's noble efforts have allowed countless people obtain a first-class education at virtually no cost. Shame on The Washington Post for promoting this hidden agenda. Seems like they also have an agenda of their own.

1) Post a controversial guest article bashing a guy whose actually trying to do something good in the world.

2) Act like the neutral party so they don't have to take any blame. Allow Karim to be the scapegoat.

3) Sit back and enjoy while traffic explodes to their site.

I see you Washington Post. You ain't fooling me!

Wow, nailed it. I totally missed the Washington Post incentive angle.

Can anyone weigh in on their differing arguments regarding the definition of slope? I am not a maths expert by any means, but am genuinely curious who is correct here. Or is this a matter of one being technically correct versus the other being correct in practice?

(Cross posted from the original thread because I genuinely would like an opinion more informed than my own and the totally unhelpful "conclusion" provided by Valerie Strauss.)

*Edit, I missed that he (Khan) posted a video defending his definition http://www.youtube.com/watch?v=TNaQJjLAhkI

I'm not a math expert either, but rise over run sounds like a perfectly good definition of slope to me, at least for the purposes of an introduction to high school algebra. It is certainly how I was taught about slope, and I went on to graduate from MIT, so whatever nuance this definition allegedly didn't catch did me no harm.

Once you get to calculus, things get a little more complicated, as the slope at a given point is defined using derivatives, but I'm pretty sure that ends up being the same as the rise over the run of a tangent line.

In any case, anyone who would make such a lame criticism, should just STFU. If that's the best criticism they can come up with, they surely can't have much of value to say. Also, when teaching something like algebra, it's more important to make the material approachable and comprehensible, rather than define everything to a level of rigor that would make Russell and Whitehead happy.

>It is certainly how I was taught about slope, and I went on to graduate from MIT, so whatever nuance this definition allegedly didn't catch did me no harm.

In that case, this debate really isn't about you. You were probably an exceptional student, who saw the connections between mathematical concepts easily, regardless of instruction. You probably found yourself predicting the next concept a teacher would introduce, because it just "makes sense." Not all students are that way. Most are not.

The two people involved here are fighting over two different ideas. Sal is being pedantic, but is right, slope is defined as ∆x/∆y. What the other guy was saying is that slope represents rate of change, which is a much more important concept to early algebra, and the underpinning of why you actually care about slope in physics and calculus. You probably made the connection effortlessly. I assure you, many students do not.

I teach high school mathematics to both honors and special needs students, and it's important to keep in mind that the instruction is very different between the two populations.

I'm still not sure I understand the criticism. I'm sure that Kahn must eventually get to rate of change in his algebra course. The criticism is then supposed to be that Kahn didn't motivate his students on why they should care about slope soon enough?

If so, that's a completely different criticism, however, from the criticism that Khan is putatively making an alarmingly dense stream of gross factual errors.

I think that we can all agree that Kahn is not the best possible teacher that exists in the world for each given subject. Is that a decent argument against what he has done? Hardly! That would be letting the perfect be the enemy of the good.

Considering that so many people learn from the Kahn Academy these days, an argument can certainly be made that Kahn's lectures should all eventually be replaced with lectures by the actual best teacher in the world for that given topic. For all we know, this is already in the works.

"slope is defined as ∆x/∆y"

Do you mean ∆y/∆x?

Yup. Caught the typo when I wrote the post, even, but I apparently retyped it the same way.

> slope represents rate of change

You may as well say it represents a tangent. (Pun not entirely intended.)

You could say that, but it would be wrong. A tangent is an equation of the form y = ax + b at point P, which just happens to have (well, by definition) a value for a that equals the rate of change at P (of the original equation).

Usually when you talk about slope we're assuming "slope of a line". In that case, Khan's definition is fine. If you're trying to really rigorously define "slope", which is fairly silly since you should just start using the term "gradient" which is more rigorously defined, then I could see this going two ways:

1. You could argue that if you're talking about slope, you mean slope of a line. If you want to talk about the generalized notion of slope of a line, you should use terms like gradient, derivative, etc. If Khan had taken this stance, I would have been fine with his defense.

2. You go with the fully rigorous definition of slope as basically being a synonym for gradient. This is what mathworld actually does. This is where Khan's reputation gets really knocked, in my opinion. He quotes mathworld (http://mathworld.wolfram.com/Slope.html) but only selectively. What he failed to mention are these key points:

- The very first sentence defines slope this way: "A quantity which gives the inclination of a curve or line with respect to another curve or line." - The sentence he did quote begins with "For a line in the xy plane..."

For the vast majority of his students, including those other points when they're first learning about slopes would do more harm than good. He shouldn't be judged on his rigor, but on how effectively he enables learning and understanding. They wouldn't know what to do with gradients.

Sure, but I'm not talking about how effective his teaching is. I'm simply addressing the technical definition of slope.

I am perfectly fine with Khan teaching it as "rise/run". I thought criticizing this was silly on Karim's part. But then Khan was the one who came back to argue that his definition was correct and Karim's was wrong. I think Khan's wrong here and shouldn't have even engaged in such a trivial dispute...

I'm not a mathematician, but I think that the initial response by Karim saying that Khan was incorrect about the definition is really nitpicky and petty. Karim is saying that "Rise over run" is how you calculate it, but he claims it's not the definition. Even if it wasn't the precise definition, for most people, rise over run is good enough for a basic understanding.

Khan saying that Karim was wrong, is wrong and actually made him look worse in my eyes. In the video he said "Slope can present rate of change." No, slope is the rate of change. Him saying Karim was wrong about the price vs gigabyte being the inverse if you switch the axes is ridiculous. By definition, you always say the first variable vs the second variable, where the first variable is the y axis and the second is the x. Khan should have left it at that instead of trying to twist things around to make Karim look wrong, it was a poor and transparent attempt at being vindictive.

"Slope" implies that the denominator is a distance. In the context of a graph on paper or screen, it is clear how rise and run are mapped to distances. It's a totally sensible definition: slope only makes sense given a choice of axes.

"Rate" implies that the denominator is a timespan. This does not make sense, as there are many slopes which are not rates and which are not presented as rates.

It's kind of a silly thing to worry about, but Khan's answer is unequivocally better.

In math, is not accurate to say the "definition" and the "calculation" are one in the same? Sometimes we require ambiguous non-math language to start understanding a concept but ultimately, once understanding has happened, the calculation and the definition are identical.

Definition and technique to calculate are not the same thing. Consider integer division, which is defined by an equation, but calculated by an incremental long division algorithm.

Most definition use a phrase like "such that", which says nothing at all about calculating.

Khan’s definition is fine. Karim Kai Ani is being foolish by insisting that “slope is a rate that describes how two variables change in relation to one another.” No, that’s a rate of change. A “slope” is a commonly used rate-of-change in which there’s a reasonably clear “rise over run” relationship implied between the variables of interest.

But when that relationship isn’t so clearly implied, sensible people don’t try to describe it by calling it a “slope.” Instead, they say what relationship they really care about: Is it the instantaneous rate of change at a specific point? Or at all points along a curve? (Or surface?) Or is it the average rate of change over some interval? Or the weighted average rate of change over some interval of varying density? Or the weighted average rate of change over constant-width intervals centered at certain (or all) points along a curve? Or is it really that they care about—?

You get the drift: If you care about rates of change, you’ll use the term “slope” to describe them only when the context implies a clear “rise over run” relationship between the variables of interest. Kahn seems to get this; Karim Kai Ani, not so much.

This point is an interesting crux of disagreement about methods, not just nitpicky. Technically, slope is the rate of change of the tangent to a function, and the disagreement is about how to communicate that to students.

Approach 1, Mathalicious: "Unless you give students the right information from the first, even if it is a bit more abstract, they won't be prepared later on."

Approach 2, Kahn: "The best way to prepare students is to keep things simple. Later you can give them refinements about tangents and derivatives and such."

This is an interesting point, and I'd be pretty surprised if there isn't already a wealth of knowledge surrounding it in educational research. (Neither Kahn nor Ani appeals to such research in the articles.)

I think this debate does sadly just come down to semantics, and I tend to side with Kahn on that merit. Once I got past a certain point in my math education (first half of intro of calculus 1) "slope" wasn't used anymore. We moved to derivatives and gradients. In my education we've always used slope as a purposefully simple/geometric term for 1 dimensional lines plotted in two dimensional x-y planes.

Agreed, "slope" is a rather useless concept beyond algebra. When you're plotting, say, a position function, the slope of the function at any given point is of limited meaningfulness--the velocity, on the other hand, much more so! Likewise, the slope of the velocity curve at any given point is of little import, but the acceleration is very meaningful.

Of course, the slope of the position curve is the velocity; what I'm suggesting is that referring to it as slope detracts from understanding, while referring to it as velocity enhances understanding. Consequently, getting all wrapped around the axle over the canonical definition of slope is a shining example of majoring in the minors.

Sal is right but I understand the critique... which I might clarify as the importance of understanding the larger concept that slope is a comparison of the rate of change of one variable to another in specific order.

To take the example of price of an iPod vs. more memory. The slope is inverse depending on which variable you choose to plot on which axis. If you just watched Sal's one video, you would not understand why that is... your only context is 'rise over run'. If given sample data points and asked for a slope, you might not be able to figure out which way to plot it based on the question.

To be fair to Sal though, this was just a single video subtitled "Figuring out the slope of a line" and so Sal may have covered the larger concept and its importance in a different video.

Thats the old response to this critique http://www.washingtonpost.com/blogs/answer-sheet/post/khan-a...

The original critical piece was written by someone with a vested interest in defaming Khan, as he runs a company that is (in a way) a direct competitor. That alone should be enough to dismiss his critique.

I disagree that critiques from those with vested interests should be dismissed out of hand. I do believe that their points should be reviewed more carefully, though.

My comment was a bit sensationalist... I agree with you 100%, I just stated it a little more black and white than I should have.

I wasn't aware that KA was a non-profit. Where do they get their money? Entirely donation-driven?

Just ask KA for a current IRS Form 990. It will show you just about everything. Here's an example from 2010 - http://dynamodata.fdncenter.org/990_pdf_archive/261/26154496...

Bill Gates.

Among others.

What's missing from this argument is that traditional education dogma has the same plight. Is anyone ready to state, on record, that any educational platform is perfect and free from error? Khan deserves/requires criticism, but let's not forget that these criticisms apply across the board.

Either the people who watch Khan's video's find them useful, and can do things they couldn't do, or understand things better than they did, or not.

Most public school teachers are awful. They have degrees in education, and most university programs in the teacher pipeline are intentionally easier and less demanding than the equivalent 'real' degree in a given subject. 'Math-ed' is a very undemanding degree compared to 'Mathematics'. If high-school teachers were placed under this kind of scrutiny we would be forced to completely re-evaluate how teachers are credentialed and licensed. They aren't put under this or really any scrutiny at all, and probably they never will be. Teacher unions fight as hard as they possibly can to prevent any measurement or evaluation of teacher performance.

Students will continue to try to fill in the gaps in their understanding of these topics, and if there are free resources available to them to do so, even better!

The problem is partly economic. Most people very advanced in mathematics, I don't think would choose low salaries teaching kids Algebra or "AP Calc" in the inner city. Sure, there are the "heroes" out there but it's a reality.

I never understood why Sal Khan does all the videos himself. Shouldn't they get the best Linear Algebra teacher that they can find for the Linear Algebra series, the best Calculus teacher for the Calculus series, the best Marine Biology teacher for Marine Biology, and so on? Maybe even get two sets of teacher with different lecture styles for each subject?

I've had dozens of amazing teachers throughout my education, all of which were excellent at gripping my attention, having a passion for their subject, and a knack for explaining it extremely well. If I thought my teachers were this good, can you imagine how good the best in the country would be? And what it could do for education to makes those lessons available for the entire world?

It's a shame he does it entirely himself. It's not for lack of funding, that's for sure. Maybe it's an ego thing?

This article is emblematic of the hardest challenge Khan Academy faces, IMO, as it tries to change the educational system from the current 'lecture at school, practice at home' approach used by virtually all schools today, to the 'learn at home, tinker and interact at school' championed by Khan Academy.

The hardest challenge is this: disrupting the educational experience requires buy-in from teachers, administrators, regulators, academics, and existing service providers, but all these parties are nearly always resistant to change and well-entrenched in their positions, making large-scale change very, very, very slow and difficult.

The optimist in me wishes Sal Khan and his team only success as they take on, and attempt to co-opt, the educational establishment. The realist in me thinks they face a long, tough battle.

The educational establishment won't "buy in" it Khan, just like the traditional encyclopedia establishment didn't "buy in" to Wikipedia. But change will happen regardless because the users of education, the parents and students, will ask themselves the same question that the users of encyclopedias asked themselves: "Why are we continuing to pay for the same old product when a much better product is available for free?"

I found quite a bit in the original article that seemed to point to a misunderstanding of the site for someone who hasn't used it. Karim doesn't even mention one of the most valuable areas: the practice area. It isn't just about watching videos, and maybe I'm alone, but I use the practice first and the videos as supplements. Furthermore, the actual videos seem to often feature explanations in a clear way that does not merely point to following a series of steps (see "why division by zero is undefined")

Frankly, I don't know why he even bothered to respond. What KA is doing might not be perfect but it is one serious attempt to move education forward in some form. They deserve nothing less than admiration and support. I am sure that they welcome and encourage constructive criticism.

Aside from that, the only way the "(highly unionized) teachers do it better" argument can hold water is if the (highly unionized) teachers start producing students that actually place in a reasonable range in international comparisons.

The author of the criticism is the founder of a for-profit start-up competing with Khan Academy. Khan Academy itself is a non-profit.

These incentives should frame everything we hear about this exchange.

this also is reminiscent of this nytimes op ed: http://www.nytimes.com/2012/07/20/opinion/the-trouble-with-o...

that conveniently forgets to mention all the collaborative/interactive components built into coursera - the community TA's, the forums, chatrooms, etc etc etc.

moral: don't criticize unless you've actually read the book/seen the movie/etc. or maybe beware of hidden agendas.

Mathalicious is doing this just to get popular, I never knew they exists before this debate. Google might improve page rank of mathalicious.com as well due to back links.

The critique was written by a competitor. Isn't the motive obvious?

This is a storm in a tea cup.

First they ignore you, then they laugh at you, then they fight you, then you win.

Then you get to shove mind-control worms into their ears.

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