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Open letter to Sal Khan (christopherdanielson.wordpress.com)
177 points by ColinWright 845 days ago | 137 comments

This is the exact same kind of shit that got thrown at every person ever who successfully challenged a rusty status quo, especially when job security was at risk. Quoting the original piece in Washington Post:

We have great respect for the stated goal of Khan Academy — “A free, world-class education for anyone, anywhere.” Yet, we have some serious concerns about the quality of the instruction providing this education. Indeed, if either of us were supervising Khan’s instruction, we would point to some concrete and important gaps in his practice.

The key is "if we were supervising". That's the real problem. That someone is making something huge happen, and they are not playing a role in it. Guess what - nobody is stopping this guy or anyone else from producing a few hundred of educational videos with great content and making it available for free. However, some way or another, the people who are capable of a stunt like that are much fewer than those who can hate things on the Internet.


Look at it another way. You train for years. You spend more years, perhaps decades, working in a classroom. You read the research, you know just how hard it is to get kids to understand decimals. You work and work to find the right way for each child to understand this concept that trips up so many.

Then someone else comes along, teaches it badly, and gets lauded for doing wonderful things.

Well, it's true that KA is doing fantastic things, but I also have some reservations about some of the things that are said and done. Elsewhere it's been suggested that work is underway to help others contribute their direct working knowledge to help improve them, and I hope that happens. KA can be improved, should be improved.

Must be improved.

There are places where the way it explains things is in direct contradiction to solid research in pedagogy. I'm sure there are more people being helped by KA than hindered, but I look forward to seeing it acknowledge and absorb modern research.


I know it is a hard pill to swallow that such a pedagogical luddite such as Sal Khan is having such a broad and important impact on learning when the professionals are struggling mightily.

Maybe, just maybe, he's on to something that despite years of institutional training 'real' teachers are missing.

Maybe it's important for a student to be able to interact with a lesson over and over again in order to catch a key point they might have missed the first pass.

Maybe it's important for a student to be able to ask other students how they caught on to something on their time scale and in a way that is pseudo-anonymous.

Maybe what makes Khan a great teacher is his breadth and depth of knowledge and context thanks to being a triple undergrad from MIT with backgrounds in math, computer science, and electrical engineering AND a Harvard MBA.

Maybe the institution of teaching is due for an evolutionary shake-up and Khanacademy is it[or at least a taste of things to come].


You make great points, and much of what you say is absolutely true. But I have dealt with pupils who have severely broken concepts of decimal place, and whose potential for understanding basic arithmetic has been damaged beyond repair.[0]

I believe the KA is doing brilliant things, and opening up knowledge for all is fantastic. I would just like to be convinced that modern research about pedagogy is being integrated rather than ignored. The evidence suggests it isn't, and I very much look forward to the day when it is, so this resource becomes even better.

And lest you think that I am one of the ones feeling threatened, I'm not. I'm not a teacher, but I do go out and give presentations for the purpose of enrichment and enhancement. As such I am often asked to consult on questions of tutoring both the most able and the least able, and because of that I work closely with those active in pedagogy research.

[0] I can't, of course, say that the damage was irreparable, but despite many hours of effort, I and several colleagues found no way to dissuade the student that 0.35 was bigger than 0.4, no matter what we tried.


> found no way to dissuade the student that 0.35 was bigger than 0.4, no matter what we tried.

Out of curiosity, assuming you tried a number line, do you remember why that didn't work?


I think if I could ever have understood the difficulty, I would've had a chance of working around it. The problem seemed to be that they could place things on the number line, see that this was to the right of that, say that 0.4 was to the right of 0.35, say that hence 0.4 was bigger than 0.35, and then go right back to doing what they had always done.

My model of what was happening in the student's head is illustrated by this. A survey was conducted asking people:

    A. Which is true:
           (a) The Sun goes round the Earth.
           (b) The Earth goes round the Sun.


    B. How long does it take?
Of those people who gave the answer to A as (b), over 80% answered B with "a day" or "24 hours" or something equivalent. In short, they got the "right" answer to A, and then a completely disconnected and obviously "wrong" answer to B.

In this case I think people are answering A by reciting a fact they learned when young. We are told that the Earth goes round the Sun, so that's what people recount. By they don't connect that with their personal experience. Their personal experience is seeing the Sun going overhead. They "know" that the Sun goes round the Earth, and that it takes a day. They're told the Earth goes round the Sun, and that's what they parrot for question A, but when asked B, they answer from their own personal experience of seeing the Sun go overhead.

And that takes a day.

So I think the student could follow the things they had been told, and they could recite, parrot fashion, all the "right" things that would get them the marks on the test designed specifically to assess their knowledge of decimals places, and then when they had to put it into action, they fell back on what they felt things looked like, and were driven by their intuition and experience.

Which was completely wrong.

So that's my "theory" of where the disconnect lay. But maybe I'm wrong, because I certainly never fixed it.


Unlearning is always much harder than learning.

I know that when I'm debugging a piece of code, and I get an idea in my head about how it works or should work, and that idea is shown to be wrong by clear and incontrovertible evidence, it can still take between a few hours and a few days for me to stop thinking it.


A number line doesn't help some students decompose numbers. The key insight in this example is noticing that 0.35 is "3 tenths and 5 hundredths", in addition to being "35 hundredths". The former is a decomposition. Number line approaches more commonly rely on students being able to think of 0.4 as 0.40, which some interpret as an arbitrary rule, rather than as related to facts about equivalent fractions.

The particular approach offered by the Rational Number Project in the article I linked to in the original post focuses kids on that decomposition from the very beginning using area models and colors to highlight multiple ways of seeing (e.g.) 0.35


  > Sal Khan is having such a broad and important impact on
  > learning when the professionals are struggling mightily.
Are you sure he is having such borad and important impact? Are you sure that he won't fail at exactly the same spot where "professionals are struggling mightily"? Do you know the reasons they are struggling?

  > great teacher is his breadth and depth of knowledge and context thanks
  > to being a triple undergrad from MIT with backgrounds in math, computer
  > science, and electrical engineering AND a Harvard MBA.
Nothing in the list makes anyone a great teacher. You may have all the knowledge in the world and be a lousy teacher. What makes a great teacher is the skill of kindling the interest in the subject in your students and then having the skill to transfer you knowledge effectively. Khan Academy has none of that. It is just another attempt to solve the problem by throwing technology at it. The thing is, problem has little to do with technology. And Khan Academy has little of understanding ot that.


>I know it is a hard pill to swallow that such a pedagogical luddite such as Sal Khan is having such a broad and important impact on learning when the professionals are struggling mightily.

How are we quantifying Khan Academy's "broad and important impact" on learning? If someone learns from the KA videos, what do they typically accomplish afterwards?


In the space of 18 months ending Feb of this year the site has gone from reaching 1 million to 6 million students per month.

I quantify the value of the product by the demand.


That is a poor way to quantify the quality of an educational product. While quality can and sometimes does drive demand for a product it's frequently possible for demand to be driven instead by fads, trends, and hype.

If you want to measure the quality of something there are far more reliable metrics to use than demand.

With that said I like Kahn Academy. This is a single issue in a large body of educational materials. This one problem doesn't mean the qualify of the full product is bad just that is has room for improvement.


If we assume that students are rational actors making decisions between traditional teaching methods and KA...and we assume that KA, students, and teachers all have the same end goal of teaching the kids the material.

It sure looks like, at an increasing rate, kids are choosing KA. After all they are held most directly accountable for their academic success or failure. Wouldn't demand then be a reasonable gauge of value?


Students cannot possibly evaluate which of the teaching methods are better because they do not yet know what they are supposed to be taught. This lack of knowledge is a fundamental problem of markets in education.

Students might say that method A "feels better" or "is more fun" than method B. However, it is entirely possible that method A is worse because, in the end, students will actually not have learned what they would learn with method B.

This is not to say that students' opinions are irrelevant. After all, when students don't enjoy what they're doing, they will often block out the lesson and not learn anything due to the lack of fun.

Still, it is pretty absurd to think that students could ever be objective in evaluating the teaching methods they are subjected to.


> Students cannot possibly evaluate which of the teaching methods are better because they do not yet know what they are supposed to be taught. . . . it is pretty absurd to think that students could ever be objective in evaluating the teaching methods they are subjected to.

It's easy to recognize good teachers. They are first, understandable and second, motivating. If a teacher is not readily understood, or if they do not motivate the student to learn, then they are not very good. Children as well adults naturally use these metrics to evaluate not just teachers, but communicators in general.


It's easy to evaluate a Teacher by those metrics but that does not guarantee that the content the teacher is teaching is correct or accurate. Thus my point above.


The best way to ensure good content is to ensure smart teachers, which is what these metrics are designed for.

Fractions and decimals are not difficult. I doubt that kids who have been learning math with Khan have problems understanding them. But ìf Khan has been a little unclear for some percentage of students, the addition of a few exercises should solve the problem. The lacunae of a smart teacher are easily fixed, unlike the confusion caused by a teacher who doesn't understand the material.


> But ìf Khan has been a little unclear for some percentage of students, the addition of a few exercises should solve the problem.

You must realize that this is an incredibly simplistic view of learning? How students learn is an extremely complicated process. While decimals are not difficult, understanding exactly where students struggle with the concept and determining a sequence of learning activities to help them overcome that concept is extremely difficult.


Your assumptions don't account for whether the content being taught is correct or not. Goals and rational actors notwithstanding one of the most relevant metrics here is the correctness of the content being taught and that is something the student is not capable of assessing. As a result student demand is no indicator of quality of the content. It may be an indicator of the quality of the learning experience but that should not be conflated with the quality of the content.


Qualifications that are easy to obtain are often in higher demand than those that are harder. And yet the harder qualification may be of more benefit, more highly valued by potential employers, and bestow greater learning.

Demand is not an indicator of quality or value.

If you think popularity is an indicator of quality, this is an interesting read:



How are studnets "interacting" with his videos?

It's a hard pill to swallow that maybe he's not on to something; that THE EMPEROR HAS NO CLOTHES.


Have you been to the site and watched a lecture?

There are comments of other students who watched that video. These comments are questions and answers about what was discussed. There are also links to exercises covering the content. Each lecture is arranged in a logical order for each topic. There are capabilities to integrate the video lectures and exercise with real-world classes and ways for teachers to track their students progress and the areas where each student is struggling is highlighted.

It's phenomenal and worth closer inspection if any of this is news to you.


There is plenty to be criticized about KA, but this has politics written all over it, if the above Freudian slip doesn't convince you, consider the following bits:

Behind paywall, but someone at Khan Academy is an NCTM member, right? Right? If not, shoot me a note. We’ll get a copy to you.

Or from the other article:

Khan could tap into any number of existing networks of exemplary teaching, perhaps from recipients of the Presidential Award for Excellence in Mathematics and Science Teaching or the National Board of Professional Teaching Standards. He could seek these teachers’ advice and collaboration on issues large and small.

Meaning, they are not interested in contributing in any way, but they are feeling pity he did not ask for their permission before starting KA.


Perhaps a HN-appropriate analogy is in order here. Imagine someone came along who claimed that they could break the expensive stranglehold programmers have on software development and improve on the often mediocre code they produce by teaching anyone to program. Now imagine that it was widely lauded in the press and there was political pressure within the company you worked at to incorporate this new technique - except that the code produced was a bunch of dreck which you had to waste far more time cleaning up than it would've taken to do it right in the first place.

Further, imagine that every time you complained about this a bunch of people with no technical clue jumped on you and claimed you were just out to get the new scheme because it'd "successfully challenged a rusty status quo" and your "job security was at risk" if you didn't.

Of course the teachers are pissed off!


I think a more appropriate analogy is open source software which got described by the incumbents as an "un-american cancer" and is still being successfully fought off by many who are ripping off our governments and providing appalling service at a shockingly high price.

Is any random open source project perfect? No. Is open source the answer to everything? No. Is it obviously a better way to do things than the status quo? Yes. Are there people benefitting immensely from even the buggy projects? Yes.


"Behind paywall, but someone at Khan Academy is an NCTM member, right? Right? If not, shoot me a note. We’ll get a copy to you."

If I was supervising the way the NCTM goes about the dissemination of information via the internet I'd have serious concerns and would be pointing out some concrete and important gaps in their use of modern technology.


I have to agree with this, for sure.


What is the Freudian slip you are talking about? Do you mean the "if we were supervising" bit? A Freudian slip is a misspoken word that reveals unconscious intentions, often with a sexual implication. For example, you're sitting with someone who's eating a muffin and you ask, "Can I have a bite of your mother?"


Where is the politics?

Maybe you can find some between the discussion of the pedagogy, because you obviously aren't comfortable with that.


Then someone else comes along, teaches it badly, and gets lauded for doing wonderful things.

Are you arguing that KA teaches all or most things badly? If not, then I'd clarify because your statement above makes it sound like you are pissed that KA gets lauded even though its crappy.


This. From what I know, teaching is broken in the U.S. (and probably in many other places), and the way incentives and the balance of power is set up, what matters for most decisions on how things work is what is best for teachers, not what is best for students (the documentary Waiting for Superman shows a lot of this).

So it's not surprising to see teachers fighting back and trying to discredit KA, because success for them would mean a loss of status quo for teachers. If you get 99 things right and 1 thing wrong, those who feel threatened by you will minimize those 99 things and blow that 1 thing out of proportion.


I am thrilled that KA exists. I have read Khan's book and recommended it to others. I don't see anything in this post about "discrediting" KA. I think the author is making a completely valid point and I hope that KA addresses it soon.


> What we see in these two girls’ thinking is precisely the problem you set out to solve with Khan Academy. But you aren’t solving the problem, Mr. Khan. You are perpetuating it.

> Mr. Khan, you have a team of teacher advisors. If none of them can identify these gaps for you, you need to ask for help from the larger community (and then to reexamine your hiring practices).

> Or you could educate yourself (as we require of all licensed teachers) on what is known about how people learn mathematics.

Which of these contributed to his point? The whole thing is just entirely unnecessarily snide and personal. He has a simple and straightforward point that could have been explained in a concise and conciliatory manner, but he chose to use it as a platform to grind an axe. Also the "open letter to Sal Khan" title is confrontational linkbait. This is just not constructive.


The problem is that without the snideness/personal attack, we wouldn't be discussing the article, and Sal Khan would never have seen it.

Nobody wants to read a boring article about a better way to teach decimals. Sad but true.


That's why I read the article...


Okay, fair enough. The author did permit himself to go beyond constructive criticism and resort to pot shots in a few places. I don't think they invalidate his point entirely -- and I don't see the problem with writing an open letter -- but I agree, the pot shots are unbecoming, and suggest that the author is feeling threatened by KA.

Edited to add: the first quote is blunt, but not, I think, out of line. I do think I detect a bit of condescension in the latter two.


The point that there are gaps that hvae not been addressed? All of them.

Do you have any other suggestions as to how the pedagogical flaws could be addressed, since Khan Academy keeps basing all its exercises on these flawed materials?


> If you get 99 things right and 1 thing wrong, those who feel threatened by you will minimize those 99 things and blow that 1 thing out of proportion.

You nailed it perfectly, mate! ॐ


Could you find some things that he got right?

Oh. I didn't think so.

He also says in his movies that "two plus itself times one" is what "two times one" is. That's right, he gets 2 + 2 wrong.


Are you saying that all of the videos on Khan Academy are wrong?


This reminded me of a quote by Joe Armstrong, creator of the Erlang language. He said, referring to language design in general: "What you get right, nobody mentions it; What you get wrong, people bitch about."

Though I think the original author is making a valid point here, don't get me wrong, and Khan should address the issue.



It should be noted that the Washington Post owns Kaplan, which is effectively a Khan Academy competitor.


Kaplan Test Prep employee here. I of course don't speak officially for anybody but myself, but I will say that everybody I know at Kaplan all the way up to senior management has great admiration and respect for Khan Academy and all the other disruptive players in education these days. In fact, we have been hosting an educational technology startup accelerator with TechStars all summer.


You can admire your competitor but for the simple reason that its your competitor, you always have to try and one up them or keep them from eating your lunch. If senior management is doing its job right than they'd want to take on KA, not merely watch it take over the world.


Right, the whole tone reads as though he wants to impugn Sal's character and motive, as if he set out when he initially developed the vids as an attempt to pilfer money from the Gates foundation. He was a hedge fund analyst, for god's sake. As if he couldn't find a more financially profitable path through life.

He never stated the goal of the Academy was to be the end all and be-all of mathematical education, and anyone acting as though that were his stance is being disingenuous. These are supplemental add-ons to a wide range of important educational topics that I and my children have benefitted from far more than people who claim to have a better method but do nothing but blogbitch about KA.


For the record, ColinWright has contacted me via email in the past.

I want to say that it seems to me that while some of the tone in the blog seemed to be a little exasperated, it wasn't trying to impugn Sal's character. I can say that Colin is very constructive and encouraging to those who are new or trying to learn mathematics - certainly he was like that in the emails we sent back and forth.

I think evidence of his motives is on the comments section of his blog where one commentator did go too far, and he shut down the thread.

I think that the blog post wasn't "blogbitching" about Khan Academy. Just pointing out some perceived flaws. Criticism is good, and from what I can see Khan Academy are trying to address them.


Exactly. I have no time for those sniping from the sidelines at the doers of the world.


Khan Academy is putting out really flawed videos and spending millions and millions on 'em. Think VHS / Beta...

Guess what -- this is not a letter to you -- it's to the Khan Academy.

It's questioning its quality. Since you obviously can't address the well-grounded claim that it is very poor quality, you have to find something else to bring up.

It's 'way easier to say "you're a poor loser' than to address the actual claims, isn't it? Much harder stunt.


I am sorry you are downvoted. Alas, a lot of people on HN think technology is the ultimate solver of all the problems in the world. I guess to actually learn how to teach is too much work. Let's go making videos.


Your comment offers no value. Making videos, even if some of them are wrong is valid strategy as current educational system has, arguably, more elements that are wrong.


From a comment:

>I don’t want to fix KA. I don’t think it is possible to do so given Sal Khan. Sal Khan should not be the voice on his videos. He should not be the person putting together the actual content of his videos. And, I suspect, he should not be making any important decisions about either content or delivery of instruction, from the pedagogical side of the operation. I’m sure he’s a competent business/finance guy, but as long as he is engaged in making these borefests, they will be third-rate at best

That, friends, is why the "best minds of [this] generation are thinking about how to make people click ads".[1] That is why we're stuck building photo-sharing apps: because no good deed goes unpunished.

[1] http://www.businessweek.com/magazine/content/11_17/b42250609...


I find that pretty infuriating.

I'm reminded now of some years ago when I was in differential equations class and had trouble understanding my professor (his handwriting was terrible and incomprehensible, and his lesson structure very hard to follow). Khan's videos were an absolute blessing to me then.

In regards to the criticisms: as valid as they may be, don't assert that his offerings are not good -- it's better that they exist vs. not existing. We're at a more evolved state now with having had Khan's videos: now a new player can emerge who can produce better videos with the knowledge of what Khan's mistakes were.

I think it's actually a little bit irresponsible criticizing Khan's video like this in a public and confrontational way: it adds to the hysteria, now you'll have parents actively avoiding Khan's videos because of concerns of their pedagogical techniques. And that's not good: have you opened a standard calculus book these days? It's very hard to follow, don't these folks have some criticism for those (and their high prices, which often make it unaffordable for a lot of folks)? Video form of learning is still rather new, and Khan is a pioneer of it. Give it some more time to find its optimum form.


I used to teach English as a foreign language for a little while. My students were kids 10-13 years old. The most difficult task was to teach them things they were previously taught incorrectly. For example, I was struggling the whole semester to convince them "pizza" is pronounced "peetsə" although there is no visible "t" in it. The reason: Their last teacher told them it was pronounced "peeza". No matter how much I tried, they always went back to their pronunciation and thought I was an idiot.

As people working in tech, we are familiar with the concept of unlearning. Sometimes to make things right, we have to unlearn what we have learned and start from scratch. Unlearning is something that comes with experience. It's very hard for children to unlearn. You have to be careful what you say to them, because they're going to believe it for a long time.

I think what the OP is worried about is if these videos are someone's first introduction to math, they will struggle in this subject for foreseeable future.


  > The most difficult task was to teach them things they were previously taught incorrectly.
That is an easy thing to fix. If they take everything the teacher tells them at face value, they are bound to to repeat silly errors (and worse, biases,) in the teachers knowledge. If you teach them that the teacher might err (including you), then it is so much easier for you to demonstrate how they know wrong. Even better, if you fail at something while teaching (everybody do), they will be more likely to correct you, and you will learn something from them.


Despite what your comment says, it is not actually the case that people build cat picture apps because they'd be criticized for trying to build something more meaningful.


Trolls on the internet cause the best minds not to work on important problems? That can't be right. It's almost a self-contradiction.


This is not what I'm arguing. There are many different incentives for someone to do something: money, fame, respect from certain groups, the belief that you're doing something good, influence, following the wishes of your relatives/friends/mentors, economic stability or mobility, sense of entrepreneurship or ownership...

Now, everyone is entitled to their opinion and maybe I'm too sensitive to these things, but when someone abandons a lucrative career to start recording videos to help children and adults learn math and other subjects, and his enterprise gets popular because people got something from those videos, I believe this person deserves better than to be effectively fired from what he built.

Sal Khan isn't the best teacher. He's not a substitute for a great teacher. But he did something no teacher, parent or student had done before.

And now anyone can start a website like Khan started, record better videos and create better exercises. Maybe we'll see a Khan Academy-like CMS to help people do that.

It's not that nitpicks and criticism makes people not work on important problems, it's that if you can't even keep control of a project you started, even though it became popular and bigger than you, we're essentially left with money and recognition as the only rewards to do something.

Jane Doe starts a YouTube channel with math lessons, gets some praise and some flak. Jane Q. Public makes a cat photo app, gets some praise and some flak.

The photo app gets moderately successful, gets some VC money. If Jane Q. Public is ousted, at least she has the money, if that makes her happy.

The math lessons channel gets moderately successful and people want Jane Doe off, no money, no recognition, and she fades into obscurity.


It's a valid criticism. His videos are boring, but they're still some of the clearest instruction I've found, especially on math. I just have trouble staying awake through them.


Just goes to show that different people like different things (which seems to be forgotten sometimes). personally, I think his videos are fantastic, and quite the furthest thing from boring.


No. It is opinion at best. _You_ think his videos are boring; I find them engaging but not precise enough.


Strangely enough, opinion works as criticism. We're all just stating opinions here, including you. Get over yourself.


Has appending the phrase "Get over yourself" to an argument ever accomplished anything useful?


Yes. This is what we're doing here. Sharing our opinions. We rarely have the benefit of solid fact when criticizing things.


Is English your first language?

Saying that "A are B", particularly with emphasis and without a qualifying introduction isn't a typical way of expressing an opinion.


English is my first language, and I'm decent at it. "Boring" is inherently subjective, so stating that it's an opinion would be redundant. I don't usually need to open a statement like that with "It is in my opinion that..." to make it clear that it's an opinion. This is a weird outlier where a few people are taking it to be a statement of fact. At least as many picked up on the fact that it's an opinion without extra words.


>"This is a weird outlier where a few people are taking it to be a statement of fact."

I actually agree with you in general, but I don't agree with that bit.

I'd say that kind of interpretation is par for the course, particularly on the Internet. I expect it probably has about the same interpretation spread as sarcasm. Some get it, some don't, many learn to simply avoid it.

It would be nice everyone could understand and respect what all is inherently subjective, both in statement and response. Imagine many wars of politics, religion, culture and choice of smartphone would disappear overnight.

Until that happens, a simple "IMO" goes a long way.


Boring is generally a subjective word and when someone say "these are boring" I interpret that to mean that that's just their opinion. But when says "these are boring" I interpret that as the writer trying to overcome the inherent subjectivity of 'boring' by emphasizing the objective 'are', saying in effect "I found this boring and I expect almost any other reasonable person would too."


Eh, I don't really think that's why people are reluctant to do good/big things. I think the core reason is because it's a cached thought (http://lesswrong.com/lw/k5/cached_thoughts/) to make safe and familiar choices in life.


As if working to make people click ads doesn't draw any criticism :P


Someone should read how to disagree (http://www.paulgraham.com/disagree.html). He is criticizing something that Sal probably got wrong. Sal could probably do a better job of using findings in educational research to make his videos and exercises better. But the author seems to be implying that KhanAcademy as a whole is of poor quality. I think he's using a DH5 to argue something that requires a DH6.

I think Sal does an excellent job with his videos as a whole. He does a good job of explaining things in an intuitive and deep way. See http://www.collegeanswerz.com/rethinking-education for more information. Or read Sal's book http://www.amazon.com/The-One-World-Schoolhouse-Reimagined/d....


I think the criticism would be valid as long as Khan's videos were damaging education... but they are improving people's understanding of math.

Khanacademy is being optimized for effective learning. But that takes effort, and it might never be perfect.


Of course, the entire point of the blog is that they're actually cementing people's existing misunderstandings of math...


As Khan Academy makes lessons for younger students, I believe the argumentation will get more passionate like this article. Students increasingly learn to teach themselves as they get older, so I believe the media will let Khan "get away" with more perceived "flaws" in his Algebra and Calculus lessons than on something for younger children.


Thanks for that link to "how to disagree" - one I hadn't read.


Yeah, no problem! It's one of my favorites.


OP seems to be hovering around DH5/DH6. I don't see the problem.


He's (at least) implicitly saying that KhanAcademy sucks. I didn't really read it too too carefully, but that's the sense I get from it. He seems to be pissed about an error that Sal made, and is jumping to conclusions saying that KhanAcademy sucks. To make that claim, you'd have say what it means to suck, and why KhanAcademy does so (DH6).


Many of the comments here boil down to:

    At least he's doing something - let him get
    on with it.  If you think you can do better,
    then do so.
To some extent, I agree with that.

However ...

In the past I've been faced with students who have a serious mental block about some operation, or some process, or some concept, and upon digging deeper into what they believe and why, I have usually come across a moment in their past where someone has taught something badly.

The KA videos are generally great, especially because they teach things differently, and therefore provide an alternate approach, or an alternate viewpoint, and thus provide the opportunity to bolster existing instruction.

They are especially brilliant at providing access for those who are otherwise disenfranchised.

However ...

In some cases they give examples or exercises that experienced teachers know are fraught with the potential for misunderstanding.

I know there are some fantastic people on the KA staff, I have full confidence that problems like this will be sorted out over time, and I desperately wish this letter had been better phrased. But I suspect it wouldn't have got this level of attention had the writer written a respectful note pointing out that recent research advises against the methods being used.


The letter is blunt and to the point, but what's disrespectful about it?

I just watched the first included video, "Understanding decimal place value exercise", and I am flabbergasted. This is pointless; it conveys no understanding whatsoever. In fact, I agree with the letter writer: it gives completely the wrong impression about what the place values mean, suggesting that they're all of the same importance.

What would be better would be to have the student pick out a number on a virtual slide rule. You'd have to do some zooming even to get four significant digits; showing seven is probably not worth the trouble (well, maybe do it once to make the point). That would show very graphically the relationship between successive place values.


So why don't you just re-record it correctly and send it in? It would take about as much time as the blog post took to write up.


KA doesn't accept community-produced videos. Which makes sense if you think about it; it would take more time to vet them than they're worth, on average.

Edit: additionally, if he just sent a video with a quick note, KA may continue repeating the same mistake, as they have done over the past year.


Dear Open letter writer,

I am a parent of a 10 year old who likes Maths; my choices in fostering and encouraging this trait were to (A) enroll her in a really expense private school, (b) enroll ins Kumon (its a canadian after school private tutoring type of service) (c) private tutors -- which I can't afford. Please note that her teachers have shown no inclination to help advance her learning beyond the curriculum.

Sal and KhanAcademy make it easy for me to help her with learning above her grade level. I do the lessons with her -- last week we were working on advanced probability problems and the lectures were invaluable to me as well as my child. Sal and KA augment my capability and help me become an effective tutor to my child. Regards


I think that's fantastic, and I wish you all the very best. I think it's wonderful and amazing in equal parts when a parent takes the time to work with their child to reach their full potential. You are to be applauded - all too often I've had to deal with children who had amazing potential go completely unrealized.

But please, please take care with some of the Khan material. This letter highlights one specific place where the method of instruction can lead to major misunderstandings down the line. Undoing misconceptions can be incredibly time-consuming, and ultimately border on impossible. I just hope upon hope that over time the material is improved so it matches their ideals, and continues to enable parents like you.


Open letter writer here.

I am so glad to hear that your child finds Khan Academy videos stimulating and thought-provoking. I really do think that's wonderful and I am glad this resource exists for you and your child. I mean this in all sincerity.

At the same time, the popular press rhetoric around Mr. Khan is about his revolutionary teaching. The medium (free availability of instructional videos) gets confused with the message (hastily produced rehashing of low-quality traditional content). It is the medium you celebrate in your note here—that the videos are freely available and better than (a) nothing, or (b) very expensive alternatives.

In my letter, I was asking Mr. Khan to pay closer attention to the message. Mr. Kamens and others here have indicated that this is coming. I suppose I shall take their word on that for now.

Quickly about your 10-year-old? I suggest any of Martin Gardener's books, and "On Numbers" by Isaac Asimov as inexpensive ways to stimulate your child's mathematical mind. "On Numbers" may be tough to find—it has been out of print for years—but it will be worth the effort.

Either way, happy learning to you both!


The name is spelled Gardner.


Drat! Good catch. Martin Gardner it is.


This article is a partisan attempt to discredit Sal's great work. Pick one example where the content has a flaw and use it to claim that all of his content is therefore "useless". I don't know the author's motives. Is it an altruistic care about the children or a personal motive to protect his career and to defend the methods he uses to teach versus a new potential disruptive threat.

I'm really excited to see how the experiment in Africa of giving out thousands of tablets letting children self learn with limited teaching from a traditional teacher. Because of the number of students to teachers they are acting more as tutors in the case the children are stuck and can't figure it out with help from their peers.


Hi. Original poster here. I have amended the line in the post to make clear that the "useless" claim was not intended to apply to all of Khan's videos; only to the decimal ones.

As for motives, I would invite you to read deeper on the blog to get a sense of what motivates my work. See especially the "Talking Math with Your Kids" series, where you will find the following sentiment expressed in multiple ways:

"But I don’t want Griffin and Tabitha‘s mathematical educations to depend on better telling. I want them to explore and to wonder. I want them to commit to their ideas and see what the consequences of those ideas are, and to revise their thinking when their present ideas are not good enough to explain what’s going on in the world.

And what I want for my own children is no different from what I want for my students, and no different from what I want for all children.

There is a place for good, mathematically correct explanations. I want kids to experience those when they’re the right move.

More importantly, I want them to learn to think for themselves."


> As for motives, I would invite you to read deeper on the blog to get a sense of what motivates my work. See especially the "Talking Math with Your Kids" series, where you will find the following sentiment expressed in multiple ways:

Do you have any videos of your own we can watch, so as to get a better handle on the way you think these things should be made?


Sure thing. I'm not a huge fan of expository video, so I don't have a ton of things. Here I use video to show an algorithm: http://www.sophia.org/partial-quotients-algorithm-tutorial

And here is a Ted-Ed video I worked on that is intended to provoke discussion and thought. http://ed.ted.com/lessons/one-is-one-or-is-it


Pick one example where the content has a flaw and use it to claim that all of his content is therefore "useless". I don't know the author's motives.

You don't know the author's main point either. He did not assert this at any point--he instead commented on the necessity of expert/experienced input in developing these videos, using the decimals content as an example.


FFS, that is not what the article says at all.


The dramatic tone of this article seems disproportionate to its complaint.

I can't help but feel that the author has a grudge against Sal Khan which motivates his writing as much as his disapproval of Khan's teaching strategy.


The problem with the article is about 50% due to its tone ("from hell's heart I stab at thee!!!") and 50% due to its lack of the very obvious, constructive criticism. By that I mean if the guy had simply laid out his case, pointed out that this wasn't a new observation, and then suggested KA set up better feedback mechanisms for responding to this sort of thing his criticism would have been just right.

Based on the criticisms from a year ago, the author seems to have a very strong negative view of what KA is doing, but he doesn't appear to be making videos of his own and putting them on Youtube. Not even to illustrate a correct treatment of the topics which he believes Khan is handling badly. Useless negativity.


Talk about missing the forest for the trees.

This person has a valid point, a relatively minute one that is being made in an overly-dramatic and annoyingly self-important way.

KA is great, far better than anything I was exposed to in traditional education. I'm currently using it to refresh and prepare for pursuit of a late CS degree.


Same for me, but I can see a possible issue with very young users. Re-teaching people who are out of school but never really grasped some math concepts is "easy" compared to providing the whole math curriculum to kids.

For me personally it has been a really great resource. I think the fact that there's no pressure when you're watching them compared to the classroom where you're supposed to understand things very linearly - makes it the best possible resource for learning math for me. I love being able to pause and go Google/Wikipedia around or re-watch the video from the beginning when I get lost. Overall I think it's a great resource, you basically get a private teacher any time you want. If someone doesn't see value in that, I guess they never had trouble in school.


I don't think the Khan Academy videos have ever really aspired to be the most pedagogically nuanced videos anyways. It's not necessarily a huge problem for those who are quick learners and have others around them (at home or school) who will correct the inevitable errors (like the one pointed out by the OP). It may become more of a problem for those who are entirely dependent on Khan Academy (or similar online sources) for all of their education, which is not who it was intended for, and there can't be too many who are in that position.

A number of educators do take issue with Khan, but no one else seems to have put the effort in to supplant him rather than simply criticise.


Hi, Ben from Khan Academy here. I just woke up and don't have time for a full response right now but here are a few quick words.

Most of our math content creation work these days is driven by our push to cover the new Common Core math standards, which have recently been adopted by 45 states. We're following these standards not only because of their recent popularity but because they are among the best standards we've seen, primarily because of their focus on conceptual understanding. In the last few months, we’ve hired many experienced content creators to work with us on covering all of the the Common Core standards accurately. So far, they’ve created thousands of new handwritten questions that focus more on conceptual understanding to complement the machine-generated exercises we already have.


All of these questions are going into new exercises, and we're also updating existing exercises when it makes sense. Our new exercises are much more interesting than our old ones; here's one example of an exercise by one of our content creators who joined us full-time this week:


The blog post discusses a few ways in which our decimals content can be improved, all of which are reasonable. Our recent push to improve our math content hasn't yet touched the decimals exercises but it will soon, and we've made a note to make sure that these specific criticisms are addressed, as well as anything else we find.

Most of our content creators have direct teaching experience and we also have multiple people review each new exercise before it's posted, to make sure that it's correct and that it tries to teach students well. In addition to the teachers' own experience, the Common Core progression documents (written by the authors of the standards) have been invaluable. Here's the progression document for the number system for grades K–5:


You can see that on pages 8 and 12 they specifically discuss area models for understanding place value. We already show place values with area for integers; we'll add it to our decimals content soon.

We're making improvements like these on a daily basis, and we're always interested in finding ways to make this process better.


One last thing I forgot to mention is our videos. With each new exercise, we're making complementary videos that explain the exact concepts the exercise covers, so our videos are also aligned to the Common Core standards and progressions (albeit indirectly). Even so, our greatest efforts have been spent in improving our exercises because the schools that we work with currently are more invested in our exercises than our videos, and we're looking to help them as much as we can.


Another Ben from Khan Academy here!

I'd like to also emphasize how much we lean on our community. Khan Academy's goal is not to be perfect, but to iterate towards perfection — it'd be impossible to do that across such a broad array of content without building up a strong community.

Beneath our videos the community creates Q&A to help address (we hope) misconceptions and follow-ups about each topic (fun example: https://www.khanacademy.org/science/cosmology-and-astronomy/...).

When the original WaPo article was posted, it mentioned a user's question ("So is .02009 greater than .0207?") as evidence of KA failure. But to me, the fact that there were already helpful, patient responses to this question from our community...well, that's a success. We know KA can't magically teach everybody everything, and building a community of support is one of our biggest goals.

Of course, we also use the gems in this community to help us iterate on content.

Sal goes back and reworks videos often, but this is difficult to scale so we recently added the ability for us to make "official clarifications" from our community's content. These are video annotations that clarify important or confusing points for videos we haven't had time to redo yet (see an example at 12:47 in https://www.khanacademy.org/science/chemistry/acids-and-base...).

Overall, Sal has imbued the entire company, starting at the top, with a belief that shipping beats perfection.* We're building tools to move as fast as possible any time we can improve our content — but that won't stop the occasional valid criticism from surfacing. We'll make use of it.

On a transparent/personal note, I take issue w/ many of the assumptions and tone behind this letter...but my shortcomings here won't stop our team from plucking some value out of it.

* https://sites.google.com/a/khanacademy.org/forge/for-develop...


Thanks for the clarification! I think you guys are doing awesome, world-changing work.

I, too, took issue with the letter. It seemed like the author was trying to embarrass Khan Academy, using one issue to imply that you're irresponsible and lazy. I think that his approach is in itself irresponsible and lazy - it would have made more sense for the author to reach out privately to get a better understanding of how your organization operates instead of loudly proclaiming, without merit, that you're squandering trust and resources.

Anyway - just wanted to say that I think most people will find that the article reflects poorly on the author and not on Khan Academy. Keep up the good work!


I know nothing of how Khan Academy works and have no specific opinion on whether the author of this blog was right or wrong to call them out... But, as a general rule, I find it hard to fault people for turning to public shaming quickly as a way to get through to a tech/web company about some problem they have these days. It is, sadly, often the best path to results.

There are amazingly large swaths of the software/web/services industry where customer service and back channel communication to decision makers in the company essentially doesn't exist. Phone numbers don't exist, appropriate email addresses are hard to find and are likely to just robo-response you (and point you to a FAQ that doesn't cover your situation) if you do manage to find them, etc. Maybe there is some obscure mailing list the user could be heard on, except that mailing list is only known by experts on the software or service and good luck finding it if you aren't even aware it might exist. Or maybe there is some specific person they could tweet at, but not being part of that culture they have no idea who that would be.

I mostly blame Google for the sad state of this. Though they are hardly the only offenders, they were pioneers in this area and are certainly one of the largest who still practice it across most of their products and their continued practice of it legitimizes it in the minds of other web companies.

Again, I'm not saying any of this does or doesn't apply to Khan Academy. I'd guess based on the community nature of the product it is not nearly as bad as I've seen elsewhere, but I think the sorry state of customer service across the industry is directly responsible for these sorts of public shaming posts and the people making them aren't being irrational all things considered, the service/software companies as a group are bringing it on themselves.


Thanks for the thorough response here. You wrote, "Our recent push to improve our math content hasn't yet touched the decimals exercises but it will soon." But Mr. Khan posted a video of a new decimal exercise just last week, which is what prompted the post. I get that everything can't be perfect right away. Somebody at KA has been working on decimals instruction in the past year, so it was frustrating to see that this instruction was not substantively changed. I look forward to the more robust content to come.


In this particular case, the exercise is one that we've had since November 2011. This week we made a push to have videos created whenever an exercise doesn't have an accompanying explanation, which is why that video was created specifically for exercise.

Reviewing content of the exercises is a separate and important task which is ongoing – as you point out, the exercise itself has a few problems and we'll be sure to revisit its content in the coming months. Thanks for your useful criticism.

(And sorry for not responding yet directly on your blog or to you on Twitter – it was on my to-do list but as I opened Hacker News this morning, I felt the need to comment here, as response speed is key on a site like this.)


Fair enough. Thanks for the reply. No worries about the forum for the response.


One more thing:

As I was looking through our content, I found we have a new exercise on comparing decimals! It was written just 10 days ago (and hasn't yet been added to the main site):


With questions like 0.3 __ 0.03 and 0.02 __ 0.1, I think you'll find that the exercise touches on exactly the misconceptions that you've seen. In addition, the hints use area models to explain the comparison, just as you suggest in your post.


Minor bug report, hints 3 and 5 (where the values are displayed as hundreths) overlap with the previous hints (where they are shown as combinations of tenths and hundredsths) for me on Firefox/Ubuntu, but look fine on Chromium/Ubuntu.


Thanks, should be fixed if you reload.


Can you tell me specifically what Khan Academy's objective and how it goes about achieving it? What does KA view its role as in education?

Your "about" page says "Khan Academy is an organization on a mission. We're a not-for-profit with the goal of changing education for the better by providing a free world-class education for anyone anywhere." Is providing free learning materials the extent of what you do?

Do you have a model of learning? What interaction do you have with the those who study learning?


Aatash from Khan Academy here. As the mission mentions, in addition to providing free learning materials, we care deeply about making the quality of those materials the best they can be.

We work with a lot of teachers who use Khan Academy in their classrooms year-round, giving us constant feedback on how students are interacting with the videos and exercises, in terms of both what's working well and where the gaps lie.

We have also worked with education researchers, and we're constantly studying various models of learning. And more than anything, we learn from testing and feedback from our users. As mentioned in Ben's comment above, we like to ship. We like to put stuff out there for folks to use (especially when learning is at stake), and take feedback and improve from there.

Khan Academy's role in education is a varied and ever-changing one. More than anything, we want to provide a tool/resource for knowledge and learning that's high quality and accessible. How people choose to use it--whether as standalone learners at home or through integration in a classroom environment* --is really up to them.

* We've put up some great videos/articles on how teachers are using KA now, and what our vision for its use in the classroom is: https://www.khanacademy.org/coach-res/KA-in-the-classroom


I'd also like the hear more about your work with educational researchers. In what way does research on learning effect KA's development? And specifically what learning models are you looking at and how are those learning models influencing the videos and exercises you create?


> We have also worked with education researchers, and we're constantly studying various models of learning.

Can you elaborate? What discoveries have you made? How have you advanced the state of the art?


It is hard to get the details right with math. First there is the basic factual level (not saying anything wrong), then there is a language level (will an 6th grader understand this? an 8th grader? a 10th grader?). Finally, and this is the hardest part, presenting the material in the most pedagogical way.

Posting an open letter is a bit of a sensationalist move, but this way it will be sure to gather enough attention. Perhaps there should be a content-improvement suggestion box for this kind of things. With more teachers starting to use the khan videos and exercises, I am sure bugs will be found, but let's treat them as such.

I've seen lot's of the old Khan videos replaced by newer and improved ones. I wouldn't be surprised if the decimal video gets an update.


> Perhaps there should be a content-improvement suggestion box for this kind of things. With more teachers starting to use the khan videos and exercises, I am sure bugs will be found, but let's treat them as such.

We've been working on something just like this – keep your eyes peeled.


> the most pedagogical way

One issue with education research is that all too often, for each set of articles in reputable journals arguing with copious evidence that students learn best when taught left to right there is another set for right to left. It can be very frustrating to try to teach in the most pedagogical way.


From OP's comment-- "While perhaps “useless” is too strong a claim, I stand by the need for a strong claim here. Khan Academy offers nothing beyond place naming in its decimal videos. That is unacceptable for a primary instructional resource, and I cannot imagine how it could be helpful as a supplementary resource for a student struggling with decimal concepts."

I'm confused. I have never been under the impression that KA was replacing the educational system, but rather, to supplement it and help those that may not understand principles in a different ways, and more broadly, affect some change in an industry that needs it. The tone of the letter kinda sucks, and while its a criticism I can't help but point out that this service is free and has empowered so many-- is the intent to be a one stop shop for everyone to learn? Sure that would be sweet, but come on. All I get from the post is -- 'hey sal, can you create an open dialog to discuss the most effective ways to teach'. What a strange way to do it.


he probably feels threatened


I agree with the sentiment of the letter but why does Sal have to provide the optimal video lecture (code) for every topic (module) for his project (Khan Academy).

As a single person, even with a team of advisers, he will not be able to do this for every topic he covers.

One solution can be that he provides a clear interface to each of his modules and sub modules e.g. this module should cover changing base of logarithms and the student should be able to pass these questions (units tests) in the end.

In this model people can contribute in two ways - either make unit test more comprehensive or make the teaching material (code) better.


Sal does a great job with the higher level mathematics. His videos helped me get an A+ in calculus. He does his best, and he should be applauded for that.


I have no hard facts and figures, just some anecdotal evidence, but this reads like pure politics to me as well.

I have never struggled with mathematics, in fact I pursued it to college, then got infatuated with computer science - but my areas of focus (optimization and algorithm design) tend to overlap - and I find myself reading quite a lot of graduate level texts.

My girlfriend on the other hand has always struggled with mathematics, but wishes to pursue a career in computer science also. I watched her for several weeks struggling and worry about a college entrance exam, reading the obscurely written criteria and trying to read through the suggested resources.

It was only when someone else mentioned Khan Academy that we both went to look at it - I found the content accessible, very well presented (for the most part - a couple of the older videos could have done with an update!) and the accompanied exercises were excellent in reenforcing content - the added gamificaiton really adds to it as well.

My girlfriend passed her exam (> 90%) and was even told she should think about taking the extra level exam later on if she wished to skip a few pre courses.

To see her go from "I have no idea what to do" to "I know I can do this" was a joy - so thank you Khan Academy.


I think the problems many educators have with Sal Khan can be traced back to the media. And, perhaps, what Bill Gates said.

If Khan Academy were just some obscure YouTube channel with instructional videos, the OP wouldn't have wasted his time writing this letter. He would have just moved on and selected another source of instructional videos.

Did you know there are 60+ alternatives to Khan Academy? As well as several easy ways to record your own Khan Academy-style videos? Alternatives abound.

Unfortunately, most aren't aware of these alternatives. The media has, for better or worse, made Khan Academy seem like the de facto choice. And therein lies the real source of the criticism KA has faced, in my opinion.

You know what will be really cool? When someone creates a really good rating, review, and curation service of instructional videos. (I've heard from a few who've said they are working on this already, BTW. So hopefully it's coming soon!)


> In short, these videos and their accompanying exercises are useless.

That's a bit harsh


He's saying they got the topic wrong; that when you teach decimals, the meat of the topic is the rules that apply when you have different numbers of digits after the decimal point. His language is imprecise (the video might be useful for something besides teaching decimal math), but the gist is clear.


One thing that bothers me is that the author suggests that the decimal place value exercise is broken because all of the numbers are represented as the same size.

The "representing numbers" exercise uses the 1-10-100 blocks that the poster alludes to using here, but I think the bigger issue is that in the real world, decimal quantities are not always sized proportionally to the value they represent. Money is a good example of this -- a US $100 bill is the same size as a US $1 bill and students need to be able to recognize the difference without seeing an object that's 100x bigger.


I thanked Sal Khan and even donated to this man, He has made my life easier in college.


I fail to see how Sal Khan is not getting everything exactly right.None of my math teachers ever presented math perfectly,but what they gave was enough to get me to graduate top of my college math class.Do not sweat the small stuff,man.


Presenting material in a way that impresses upon students that 0.35 is bigger than 0.4 is not "small stuff".


The point is that it does not spell doom to the rest of your mathematical career because one fact was wrong back in first grade


Is this decimal thing really a big problem? Don't remember when I learned about decimals, but I feel like the chance of only being exposed to such fundamentals from an online video is very slim. I always thought such resources should be used as a supplement to what is taught in school. When it comes to learning math, limiting your scope to one particular learning material must a bad decision.


Khan academy has an issue tracker. It shows over 16,000 open issues out of a total of about 20,000 issues. Almost 15,000 have a status of "New."

Problems like this one should get tracked and resolved through this system, but the system could be stalled.


It's difficult for us to work through all of the submitted issues because most of them are from students who don't understand the problem or have made a mistake in their work, not real issues with the content. We always keep an eye on the number of issues per exercise, and we're lucky to have volunteers who read through the issues and surface the real issues.


You don't have an insurmountable problem. It might take a week or two for one or two individuals to catch you up on filtering out junk submissions and organizing the rest. But a volunteer, unless they are familiar with your priorities, resources, and the nature of valid issues in your systems, probably can't do it.

But that beats dealing with complaints like this pedagogical complaint on an ad hoc basis. If they could track their issue and see progress being made, they wouldn't be yanking your chain. In fact, in my cursory examination, I didn't see content issues being tracked. You must have a few of those.


I really respect what Sal Khan is doing. I think his methodology for creating videos and exercises great because of how adaptable his process is, and how he gets creators who have real teaching experience to create the content.

That being said, it makes me a little happy inside that the company I work for addresses the specific criticism in the article, although it doesn't go to the lengths that Khan Academy does in terms of video and more interactive exercises:



ColinWright (the submitter of the blog post submitted here) is a mathematician who is evidently quite interested in effective mathematics education. This is far from the first Sunday in the United States when I have logged on to Hacker News to see a lively discussion of mathematics education sparked by one of Colin's posts.

I teach decimal arithmetic to third-, fourth-, and fifth-grade age pupils through my local nonprofit supplementary mathematics education program. My program uses the Prealgebra textbook published by the Art of Problem Solving foundation


and I encourage all the children in my classes not only to use the textbook problems and additional problems I assign in class, but also to view Richard Rusczyk's thought-provoking and FUNNY video lectures that go with the course lessons.


To the specific point of the submitted blog post, the Art of Problem Solving (AoPS) lessons teach decimal numbers with varying numbers of decimal places and how to compare them and how to do arithmetic with them quite thoroughly. Anyone on the whole planet with an Internet video connection can watch the Art of Problem Solving video series for free, and even many fully grown adults with university educations could learn some new mathematics from some of the prealgebra videos (which are designed with child viewers of a young age in mind). I like the Art of Problem Solving videos and books a lot.

The Khan Academy developers, two of whom have already replied in this thread as I type this, are very responsive to the concerns expressed by outside observers on the quality of the lectures and especially on the quality of the online problems served up by the Khan Academy program. I have had specific individual email contact with one of Khan Academy developers after a comment of mine to Hacker News about Khan Academy a couple years ago. They are still iterating to make the Khan Academy program better. My third son is of age to begin eighth grade this autumn and has used many Khan Academy videos and online exercises to learn an impressive amount of mathematics and other science topics. We don't sole-source for ANY subject: we always use other materials for mathematics, and we always use other materials for all core academic subjects. (We are a homeschooling family of four children, one now grown up and working as a hacker for a startup.)

The open letter blog post kindly submitted here by Colin specifically mentions the Rational Number Project


at my alma mater (the University of Minnesota), which consumed a lot of federal educational research funding for a long time. I regret that my university is associated with that project. The amount of PRACTICAL, ACTIONABLE, teacher-friendly lesson content that has come out of the Rational Number Project is tiny. Some of the leading mathematicians who write about mathematics education reform suggest better approaches for revising elementary school lessons on mathematics than that project has thus far suggested. For more background, see



Simply put, there are better examples of best practice in teaching decimal numbers to elementary school pupils in several countries of east Asia or southeast Asia or eastern Europe. We don't have to reinvent the wheel here, we just have to encourage the English-speaking mathematics educators to find the best materials used already in English (for example the AoPS materials and the standard school textbooks used in Singapore


and some mathematics contest-preparation materials) or to translate into English materials from Russia, China, Hungary, or Japan.

Meanwhile, I'm sure Khan Academy will keep iterating to improve, and will continue to be free to use. You can already shop around as a parent. There is no crisis here. But the discussion is interesting, and I thank Colin once again for an interesting weekend post on mathematics education.

P.S. I am on staff at Epsilon Camp


this week, as I have been for the last week, so I've had opportunity to make acquaintance with some impressive young mathematics-liking children learning challenging mathematics. Some young people understand decimal arithmetic at quite an early age and need a way to move on beyond the slow pace of the school standard curriculum.


Hi. OP here.

On the Rational Number Project matter, you'll notice that I didn't recommend the entire body of work, but rather one article relevant to the matter at hand. It's worth a read—totally practical and applicable, and it reinforces Mr. Khan's intuitive sense that decomposing decimal numbers is important.

I do look forward to future iterations of the decimals stuff. The teaching and learning of fractions and decimals is tremendously complicated stuff. Problems in this area are arguably at the root of many, many people's struggles in mathematics, which is why I think getting it right matters so very much.


IMHO, KA aims to solve the education-accessibility-gap and does not aim to academically discover the most ideal explanation (as the open letter writer seems to think).

As one KA person mentioned earlier, they're just following "Common Core math standards".


I just quizzed my daughter entering 5th grade and she understood the concept of decimal comparison, so score one for public education.


It's a good suggestion but his evident premise that "licensed teachers" uniformly do better is either extremely naive or speaks to an agenda on his part.


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