Education Depression
Mathematics education is hard, in part because the skills it takes to understand mathematics and to teach mathematics are actually quite different. In addition, once grasped, many mathematical ideas switch in an instant from impossible to easy. It can then be hard to put oneself in the position of someone who does not understand. To be honest in my own teaching I know well the frustration of not being able to see how a student who has all the pieces of understanding cannot yet grasp the whole. I also know as a student and as a teacher the joy of breaking through and having things become clear.
One of the biggest barriers in mathematics is that one often has to unpick a previous understanding in order to go further. This is true both of individual learning and the progress of the subject as a whole. I feel that these issues, combined with the desire to assess and make learning visible have caused some deep issues in the way we teach mathematics. The canonical work on this topic is, of course, Lockhart’s lament. In many ways I hoped that the disruption that technology is bringing to established models of education might change this. I believe that effective mathematical education is of great importance to the future will we live in.
Today, I felt cold fear through my veins as a long building realisation crystallised. There is a serious danger that it is already making things worse. The depression really kicked in as I found myself changing my opinion of Sal Khan dramatically. My old opinion, was that he was of great value in making information of reasonable, and often good, quality available. Though perhaps this could only ever replace part of the role of a teacher. An interaction between Khan and Wired blogger/physics educator Rhett Allen, made me change that. Let me set the scene. A couple of math teachers made a video talking about some of the issues in one of Khan’s videos. To Khan’s credit this lead immediately to changes to the treatment of that topic. Dan Meyer and Justin Reich responded by suggesting a competition to find other issues in Khan’s videos. The spirit was to help, by providing free peer review, improve the quality of material within what has become a standard resource, rather than to criticise Khan’s work.
Rhett Allain’s response was quite simple, and did not seem to even deal with the subtlties of pedagogy. Rather it looked at the use of vectors, and pointed out some, perhaps slightly subtle, factual errors in Khan’s treatment. Perhaps because of Rhett’s profile in Wired this video received a personal rebuttal. In many ways what Khan says there is correct. The way he presents the idea of vector certainly makes things easier for the particular problem he is working on. Yet, I also feel he has completely missed the point of Rhett’s criticism. This is one of the situations where making somethings easier can perhaps introduce issues that will actually make things harder later. On the other hand Rhett and I might be wrong and, in any case Khan has every right to defend himself. In particular I do not want this to become a personal attack. He has personally done amazing work. My fear comes instead from the authority that he has gained from this. You can see it in the comments that people made in response to the “Correction Correction”.
Khan’s magnanimity in responding to what was clearly aimed at discrediting a valuable online tool is admirable.
This highly reeks of the criticisms targeted towards Wikipedia from supporters of the traditional encyclopedia. Well, look what happened to Britannica – their physical editions have been discontinued. Those who cannot embrace change are destined to become obsolete.
FATALITY! Rhett Allain, go to amazon.com and buy a rope and a stool! Sal, you are the best!
These are, of course, comments on the internet and should not be taken too seriously, and there are other defending Allen. I believe they do demonstrate something, however. A more worrying example (to me) came from a previous discussion the Khan Academy and education on the edgryders site. There Alberto Cottica, who is a serious and subtle intellect, with experience around education and communication defended Khan saying:
So my crushing fear on this is that people might not be able to recognise the best mathematics teaching. Thus enabling an even smaller number of “master teachers” to dominate, perhaps including Khan. Even worse it might be that the system cannot even choose the best candidates for the role of “master teacher”. My hope instead is that we can move to a new model, summed up by another edgeryder, James Wallbank in what I would love to make a mantra:
Everyone needs to be taught to learn, and to learn to teach.
The beauty of the Khan approach is the Darwinism inherent in it. Understanding and success in an aspect leads one onwards, and failure in an aspect should lead to second, and third….n approaches to that aspect until understanding is reached. The different approaches would compete and if one approach yielded a higher/faster comprehension rate, it would advance until the leading approach was the first encountered. The other approaches would form a hierarchy of secondary, tertiary…n approaches, since minds differ there will always be minds who do better with an alternative approach, and so they will live on in the hierarchical arrangement of the coursework. This can be done with all subjects, and it is so obvious, it must be in play already, but possibly not automatically – requiring human intervention as failed aspects are found. It should then be automated and Darwinized.
Evolution (though perhaps Lamarkism is a better model for this) is exactly what I hoped to see. The fear I am expressing here is that the Khan Academy may start to act against this. In any school you have some level of development from the different teachers. As one teacher is so dominant in the Khan Academy (I know he is not alone) we could end up with a system which is an even more intense monoculture than the present one.
“The spirit was to help, by providing free peer review, improve the quality of material within what has become a standard resource, rather than to criticise Khan’s work.”
The video was posted as a parody and many, including myself found its tone sarcastic and mocking. Khan had the good grace to address the concerns of the authors without reciprocating their obvious malice toward his site.
I think the biggest problem people had with Professer Allains critique was not that it had no merit (which is of course debatable), but that it was presented in such a snarky and negative light (this criticism extends to his “How I’d do it” follow up video). In short, it was an attempt by Allain to challenge this guy – this guy without a degree in Physics! – who dared try and make the topic as accessible as possible.
Had he not come off in such a negative light, you’d no doubt have less volume from the peanut gallery railing against this “. . .arrogant Professor from the south!”
Is Khan infallible? No. But I think a lot of the call to knock him down a few pegs (whether you voice that desire conciously or otherwise) comes from folks foolishly holding him up as the savior of American education.
FWIW, I used Khan’s videos when I transitioned majors from Sociology to Mathematics and they did exactly what they were meant to do – supplement the material I was learning in class (I had to start at Intermediate Algebra).
To be honest I found Khan’s video in many ways more dismissive. I suspect though that this is because I disagreed with the points more than the actual tone. You are right though that the tone of many of the videos is highly critical and perhaps mocking. I certainly agree that the videos being produced are an attempt to challenge Khan. Yet I think that that challenge has some justification.
The people doing the challenging are generally not (as they are often characterised) the professor who drones on at the front of the class. As an example, Rhett Allain has a blog in Wired and Dan Meyer is simply awesome, just read his blog! The criticism is coming from individual teacher who do know what they are doing. Even though they are working within the establishment, however many are actually the weaker party when it comes to this exchange.
In part this is unfair to Khan, he is just putting the material out. Yet he is not unhappy with the people holding him up “as the savior”, and is working on alternative models of more general education.
A related fear of mine is that, whatever the merits of Khan as education, you cannot argue that it is cheaper. This is attractive to many. In bringing it in to replace what we have we risk loosing the value that it does have as well as the (many) weaknesses.
Separately, congratulations for going all the way back to Intermediate algebra to get into a math major. A serious hill to climb, and true achievement.
Additionally, in response to your fear of a league of “Master Teachers”; Khan’s popularity has not arisen from good PR (although he definitely has this) but from developing a product that has more successfully engaged students than the establish approach to teaching.
Leaving alone the subject matter, educators should pay attention to his methods and delivery. That’s what sets him apart from the rest.
I address, as I can, the valid criticism of tone above.
On this comment, this is exactly why I have fear. Khan grew naturally. Does the internet lead to a few incredibly dominant individuals, we are then slaves to their ideas good and bad.
I certainly agree that teachers should pay attention to methods and delivery. This in no way sets Khan apart. I am sure all the teachers engaged in this debate do as well. There are bad teachers, especially professors, out there. They generally do not care enough to even engage in this debate. Far from criticising Khan’s videos they love to play them, it saves on lesson preparation.
I would also like to point out that I fear the idea of “master teachers” whoever it may be. Even the people, such as Dan Meyer and Paul Lockhart who I look to to inspire and inform my own practice as a teacher.
Indeed, this concept of peers teaching peers is exactly what underpins the Stack Exchange network and http://math.stackexchange.com in particular.
I never would have expressed it in terms of “do away with the role of teacher” but that’s an intriguing way of making that point that we’re all teachers, and the best way to understand a topic is to teach it to others.
There’s always someone with more (and less) Kung Fu than you.
These are the models that I really like (though I do feel for some tasks that face to face is important). Bringing teaching into the community would be amazing. The end result might be something like cookery. Anybody can cook, some are better than others, some work harder at it. There are many who even make a living from it.
I was the author of the Wikipedia quote. The main point against Allain, once again, was his tone. It simply didn’t sound like constructive criticism, and felt like he was trying to criticize MORE than just vectors.
I’m very sure that you have heard of the age-old problem of a professor that knows his/her material, but couldn’t communicate correctly. Ask yourself, does that represent a “master teacher”? Probably not. The reason why Khan Academy videos have been so popular is that Sal is able to communicate clearly despite making mistakes.
Thanks for replying. I am certainly aware of the problem, and in my own ways am trying to face it. Not least in working on my own practice and communication. I say in the post that I hope that the established model is disrupted. I also think that wikipedia is a beautiful example of successful disruption. It spread things from the small number to the many. It is not perfect, and can be a little dismissive of expertise, but I use it as my first reference and as a standard to link to from this blog.
I highlighted your comment as I agree that Khan is creating at the head of similar disruption and that is what depresses me. Unlike wikipedia Khan academy does not lead from the few to the many, but to even fewer. Those of us criticising Khan do accept change, we even have hopes for it!
I’m going to argue this point slightly. Khan’s product is not superior to good teaching, it is superior to the average quality of teaching in many US schools (at least I’m assuming this is true – I don’t really know, I’m just judging based on 3rd party experience), Khan’s access to his teaching is far superior than the access most kids have to high quality teaching. So what is really superior about Khan’s teaching is his delivery method, which means that if we have anything to critique in Khan’s approach, we should look at his pedagogy and the platform, which is exactly what Dan Meyer, John Golden and David Coffey are trying to critique.
And why shouldn’t they be allowed to critique his work? If millions of students are following his work, it should be good, it should be the best it can possibly be, and it certainly isn’t! I am open to critique myself as a teacher, and have been for my entire career. The amount of critique one should experience should be proportional to one’s influence.
Everything you argue I agree with, however Khan’s opportunity for access is exactly the same as every other person on this planet with the ability to use a computer. The fact is he has made the effort to take up this opportunity and it has struck a chord with many hundreds of thousands of students. These are not Khan’s ‘fanboys’ or groupies as the mtt2k people would like to think of them, but people who for one reason or another have been unable to ‘access’ the established education system.
Again, I agree that no-one or organisation should be above critique, however criticizing with open mockery and a tone belittling Khan’s work, reflected very poorly on these so-called education experts.
In response to the fear of the rise of a group globally dominant teachers, I believe this to be unfounded: Khan Academy will not be the be-all to end-all of education sites, just like Wikipedia does not even to pretend to describe every nuance of knowledge. However, those with an thirst for knowledge will exhaust these resources and branch out to satisfy their curiosity and understanding. Just like Wikipedia, KA is an excellent point at which to commence your search for knowledge.
Just remember that Khan came out of nowhere on his own initiative. There’s very little stopping anyone else seeking to improve on his work.
I simply don’t see what the problem is. The Khan Academy is there, and it works. I come from a country famously bad at teaching maths, which means already now, for all its Lockartesque shortcomings, the KA has already beaten any school I have been to hands down. Can we do better? Of course, and we will. Notice I wrote “the Khan Academy”, and not “Dr. Salman Khan”. It does, at times, feel like you are overpersonalizing this matter. The KA is many things: badges and reputation points, peer-to-peer Q&A, the all-important pause button. Some of the most important have nothing to do with anyone’s teaching style: rather, they are a way to rearrange the workflow around learning, routing a lot more of it through the people who actually do the learning. Just let’s all keep our eyes on the ball, and develop what works well.
I have no beef with any of the superstar teachers out there. Bring them all on. My goal is trying to nip in the bud the counterreformation of conservative, scared, ill-informed teachers and parents, who will doubtlessly try to build a regulatory barrier around facetime in the classroom – rightly, because when everyone is a teacher a lot of low- and middle-end teachers will go the way of professional musicians and journalists. This is more of a problem with school than with university, because – as a wise friend of mine likes to say – “school teachers are just too many for them to be much better than the average Joe”.