Why post (repost?) an article from July 3, 2012? Khan Academy has changed a lot since then. Khan Academy works well for my two younger children.
AFTER EDIT: I'll mention some of the changes that Colin kindly asked for news about. As a lot of Hacker News regulars know, several of the Khan Academy developers regularly visit Hacker News. Some of those developers have interacted specifically with me both on-forum and by private email to ask sincere, action-oriented questions about how Khan Academy mathematics lessons can improve. One suggestion I made a couple years ago was for Khan Academy to arrange its lessons in a "knowledge space" like the competing commerical online program ALEKS,[1] which I like very well for my homeschooled children. Another suggestion I made was to make sure that the online work was more of the nature of "problems" rather than "exercises,"[2] and the Khan Academy developers have come up with some very innovative online mathematics problems to ensure that learners don't merely passively watch videos but actively learn new mathematics.
Simply put, I think Khan Academy is iterating successfully. In many respects, I am in direct competition with Khan Academy as a mathematics instructor who teaches in-person lessons for which fees are billed, but I am happy to let my clients know about the existence of Khan Academy, happy to see my own children use it for a lot of their own mathematics learning, and happy to see schools adopt Khan Academy as they "flip the classroom." I am very much a both-and kind of guy when it comes to mathematics instruction--I like to mix and match a lot of programs--but I think Khan Academy has a useful place in the mix.
Hah. I followed the link from an article that I thought had a little insight, but which might be regarded as blogspam. That was comparatively recent, but, in accordance with the guidelines, I submitted the original.
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I still think it has value, and I hear very similar concerns expressed when the subject in mentioned in my hearing when I'm out and about doing in my school talks. Maybe it has changed, maybe it hasn't changed enough.
Maybe it has - perhaps you should document your experiences for us.
To give the article itself the same MST3K treatment they gave the Kahn videos, a much better demonstration of the difference between mechanical skills and "judging between two equivalent concepts" would focus around shell vs disk integral calculus methods. Trivial to teach the mechanics of either, and the names are very intuitive of what they do, but it takes some experience and discussion to internalize when to use which strategy.
"the study of how to ... pass mathematics exams."
Some .edu folks think its hilarious to use math as a gatekeeper although the grads will never use it on the job... jokes on them if someone hacks that system and bypasses their artificial little gatekeeper.
> Some .edu folks think its hilarious to use math as a gatekeeper although the grads will never use it on the job... jokes on them if someone hacks that system and bypasses their artificial little gatekeeper.
Is it really that entertaining that everyone cavorts around such a useless subject? There's a saying that in a war between kings, the battlefield is the farmers' trampled corn.
If the public school system wasn't a daycare center for parents who need to work but actually focused on educating our kids better, it would have the following structure:
1) Give every family a parental-control iPad if they don't have a computer at home.
2) Deliver the lecture part of each class via an engaging multimedia presentation bought from a marketplace of these things. Instead of a boring teacher or one teacher teaching 20 students, a great presentation would be repeatable by thousands and millions of students, and every year can be improved. It could also be critiqued and fact-checked by reviewers in the market. The market would update them like textbooks.
3) The next day, the school day would start later, so kids could get a good sleep (health and cognitive reasons) and a good breakfast (nutrition reasons), the latter can be delivered in school, for kids to come on time and socialize.
4) After breakfast and homeroom, the Tests would begin. Every day, the tests would be testing for real knolwedge that would be obtained from the previous day's presentations. They would test two levels: minimum adequate comprehension, and solid comprehension. This would replace homework and the method of solution could also be analyzed.
5) Students who did not score high enough to demonstrate minimum comprehension for that day would be quickly identified by their test scores. They would be scheduled for smaller REMEDIAL classes later that day for that subject. That means the main time they spend with a teacher would be more individualized and tailored to where they are struggling as actually determined by their attempts on the tests.
6) For a student who scores well on all or most tests, the day would be quite pleasant and free of remedial classes. They could do any number of things - and if they have to remain in the school, fine - there will be plenty of entertainment and socializing there. That is their reward for learning and comprehending the previous day, proportional to how many subjects they were able to do.
7) Right after the Tests, all students would still have to take classes which aren't only comprehension focused such as Gym and Debate etc. But there are very few of those.
8) The students would themselves choose how to schedule their time to study for the next day. It could be a study session with friends or a private study session. No one would force them to sit through a lecture.
Benefits:
1) Insane amounts of homework from multiple classes are replaced by Tests which are already scored in terms of difficulty, cognitive load, and how much time they take. So the school is fully aware of how much load they are putting on the students. Currently there is homework creep.
2) Instead of struggling privately and spending money on private tutors many low-income families can't afford, the students would get individual attention after their performance was analyzed in a Test setting. Home would be reserved for a lot more passive learning, mimicking the real world.
3) The kids would have freedom and responsibility to set aside their own time to learn, and incentive to learn that they do not have when told to sit down and shut up for 5 hours a day. It would also lower incidents of diagnosis of ADHD, especially in restless younger boys in grades where psychological development and aptitude feedback is crucial to get right.
4) Lectures are boring and too variable in quality. An uncommonly great teacher may only be able to reach 20 students while the rest get mediocre or bad lectures. There is no reason to keep things this way when technology can replace lectures with professionally produced multimedia at home. Animations and stories teaching algebra and calculus for example.
5) If you go to the bathroom or zone out during a lecture, you are faced with big dilemmas, having to copy notes from classmates. Here you just rewind. A kid can even pause the lecture for 2 hours and go play basketball or watch another one, finishing this one when they want. Truancy would be greatly red...
I think #6 is too vague. Specify that the time is for working on personally-defined long-term projects. Investigating a question, experimenting with toolsets and devices like car engines or old computers, constructing and practicing for performances like theater or poetry, etc.
I also think an effort should be made to bring in volunteer teachers from the professional community, but that's a harder task.
You obviously have thought about this and care about the subject deeply. But you haven't challenged the assumptions behind the system. It's not that the system is broken, it's that the system can't handle the rate of change that individuals have to cope with today.
The basic assumptions behind teaching in developed economies are still that of the industrial revolution. The system is good at producing graduates with basic literacy, simple math skills, will accept instructions with little or no question and sit or stand still for long periods of time doing the same thing over and over. It's not designed to do much more than that.
The industrial nature of the system even borrowed from Henry Ford's assembly line. Students pass from one stage to another, and are exposed to a subject which they learn, are then tested on and then never see that material again or understand how it fits into the bigger picture.
The only thing testing does is generate crude metrics. Tests don't actually measure anything other than the student has been able to pass that test. Sadly, when you are dealing with a very high student to teacher ratio, you have no choice but to rely on testing. There is no way around that. The higher the student to teacher ratio, the lower the ability of an educational system will have to actually educate or be able to determine if a student as been educated.
Khan Academy doesn't address these issues, and Gates or whoever is saying it will, will be disappointed. But it is an interesting experiment that may contribute to something that does.
School systems should definitively make use of spaced repitition. It’s like a slap in science’s face not making use of the insight that people forget at an exponentially decreasing rate (which is known as the Ebbinghaus curve [1] since 1885 (!)).
The only attempt I know of that goes into that direction is BrainRush [2], a startup by one of the developers of the Pong game.
Principals and teachers usually care very deeply for educating the next generation, and are equally as often stifled or limited in how they can achieve their goals by a political system in which they're demonized from the right (economic and political) and micromanaged from all sides (c.f. NCLB).
To your specific points:
1) Budget concerns make this prohibitively expensive for the majority of school districts. School districts frequently devolve the expense of providing classroom items on to teachers, or parents. Without an increase in funding, this item is a non-starter. Unfortunately, thanks mainly to conservatives (whether they call themselves "Republicans" or "Democrats") in our government, providing extra funding is unlikely.
2) There are a wide variety of online schools (actual, "accredited" schools run by various public school districts or private companies contracting with state Departments of Education) already. Having some experience in this area (indirectly), I'm not convinced it's a good idea or approach for students who aren't already highly capable and motivated.
3) The start time problem may be solvable. However budget issues arise here, too. Starting later means shifting times for running lights and A/C, possibly during peak usage in some areas of the country, and that has to be accounted for. So all the budgetary problems that conservatives impose would apply for this as well. Throwing in school-provided nutritional breakfasts would just exacerbate the issue.
4) Testing in general is an inadequate, poor, and generally poorly implemented way to measure knowledge. The very bright will either be bored to tears (and receive poor marks) or "game" the test with good test taking skills. Everybody else will just have increased stress with little benefit.
5) Again, budget issues would make this a huge problem to implement. Thank conservatives running our government for that.
6) No comments; I'm neutral on this.
7) See: budget concerns. Gym/P.E., debate, home economics, shop, art, music, etc. are all under retrenchment because conservatives in our government refuse to provide the resources to make these things happen.
8) See my comments from (2); this is great in theory but simply put the majority of students are either not capable of or unwilling to utilize such freedom successfully.
Charter schools are little better than vehicles for the enrichment of private individuals at the expense of the public treasury. They're thinly veiled means for a transfer of tax dollars to connected and wealthy individuals, and they're a non-starter, as far as I'm concerned. They don't belong in a serious discussion about reform of our education system.
Private schools aren't a solution for the majority (the vast, overwhelming majority) of the public, who can't afford tuition. Even if they were, there is scant evidence that private schools provide better education than public schools when compounding factors (e.g. selecting for economic or other privileged status) are taken into account. It's easy to have high graduation and college/Ivy League acceptance rates when one selectively refuses to admit the most disadvantaged students.
I'm in the middle of designing an online course and I've discovered that the technique of live drawing while speaking used in Khan Academy is really quite hard to do well. I certainly don't have the natural ability to do this (perhaps I need a lot more practice) and it's given me a good appreciation for the work that Khan must have put into it.
My technique is to prepare slides with a script and then record myself presenting them. It's not nearly as nice, but at least I can do it.
The format used on Coursera[1] is pretty nice, in my opinion. It's a combination of slides, video/voice, and drawing/annotation, which seems to work to good effect.
The general criticism focused on here is "mechanical processes". At first I misread this as a focus on literally mechanical machines that did something. But now I understand it as demonstration of performing an algorithm used to solve a particular pattern of problem. And the core of the criticism is that knowing the algorithm doesn't mean you understand the algorithm, and could modify it to solve related problems.
However, that criticism doesn't have much power for me, based on how I understand I learn. I like to learn from two ends; one, from above, with an overview of the space, so I know where the next bit fits in. And from below, with concrete examples - yes, mechanical examples - of the individual steps. I infer the deeper structure of what's being taught as more and more variants of the mechanical process are shown.
I generally like what Khan Academy is doing, but it is definitely not a complete replacement for the classroom.
What you are seeing is a blowback against the traditional classroom. Our school systems are so poorly run, that a guy with no teaching experience can create something insanely popular in the education industry.
Why didn't a classroom teacher do what he did? Because our system does not reward teacher innovation and trying new things.
Our system rewards obedience and conservatism.
Our teachers (like our students) are taught to conform and do what the admins want. Those that don't are punished, sometimes directly, but most often indirectly.
Poor salaries and bad working conditions mean the best and brightest do not become classroom teachers. Or, talented people who are classroom teachers bolt as soon as something better comes along.
There are some high quality people who teach, but they are browbeaten so often that it turns the young, dynamic person into a cynical and slightly depressed professional.
I don't have all the answers, but I do know it isn't more of the traditional classroom.
I think its important to not lump all american schools togethor. I went to a public school in a relatively affluent suburb and i feel that i got a really good education. Now I can say with confidence that my experience is way different than one from LA or New York or Texas.
"Why didn't a classroom teacher do what he did? Because our system does not reward teacher innovation and trying new things."
Because most people don't give a shit? Why doesn't every STEM graduate have the same ambitions as Elon Musk? The reality is that most people are too chicken shit to have their own interests and to pursue them in a serious way. You think throwing money at things solves problems?
I don't know any evidence, that teaching the "mechanistics" of math should lower the chance of understanding it.
Quite often "root learning versus understanding" is the difference between being able to show and demonstrate you know your stuff ("root learning") and not being able to show or demonstrate it, but you think you kinda know it ("understanding").
You and onlookers may enjoy reading the article, "Basic Skills versus Conceptual Understanding: A Bogus Dichotomy
in Mathematics Education"[1] (1999) by Hung-hsi Wu, for a discussion of what leads to deep understanding of mathematics. Another classic article on the topic is Richard Askey's review[2] of Liping Ma's book Knowing and Teaching Elementary Mathematics, a very good read indeed.
> I don't know any evidence, that teaching the "mechanistics" of math should lower the chance of understanding it.
Perhaps I missed something or misread it, but that wasn't my takeaway. Rather, it seemed he was expressing that mechanics doesn't, on its own, directly lead to understanding (measurable by ability to apply the tools to novel, to the student, problems/situations). Given that he also endorsed Khan Academy in this same article it seems he has no problem with it developing mechanical understanding as a complement to the understanding needed by practitioners (scientists, mathematicians, engineers, etc.).
'I don't know any evidence, that teaching the "mechanistics" of math should lower the chance of understanding it.' I think that's a bit of a straw man.
The challenge is that simply getting the right answer, especially in terms of arithmetic (one small piece of math), can mask how well a student understands the underlying concepts and whether s/he can flexibly apply the concepts.
Here's a great video on that topic:
https://www.youtube.com/watch?v=_ofQ_WnQiZ4
And here's a great video that shows what a participatory classroom with a great teacher can achieve:
Even if the student can solve optimization or related rates problems just like the ones in the book and in the lecture — but doesn’t know how to start if the optimization or related rates problem does not match their template — then the student hasn’t really learned calculus. At that point, those “applied” problems are just more mechanical processes. We may say the student has learned about calculus, but when it comes to the uses of the subject that really matter — applying calculus concepts to ambiguous and/or complex problems, choosing the best of equivalent methods or results, creating models to solve novel problems — this student’s calculus knowledge is not of much use.
The implication is that most institutions suffer from this disadvantage, and saying "Ivy League" is a shorthand for that proposition, since it is assumed (correctly or not) that Ivy League universities are at least as good as most other educational institutions.
And better to say that! This article seems to confirm that Khan Academy is teaching to university standards. The problem is, that almost all institutions teach the mechanics -- or at least, almost all teachers. If this particular professor teaches to the novel application level, wonderful. But a significant percentage of his peers do not.
what I've seen of khan academy is pretty cursory as far as the math goes (about enough to get through an introductory course, usually), and that seems intentional. There are definitely a few gaping holes in the curriculum, such as no wronskian in diff eqs. And nobody really learns a mathematical concept until they've been confronted with something significant they couldn't do with it immediately, yet conquered it.
Teaching advanced math, on the other hand, is really hard to do when you're interacting with a person because there are so many pitfalls and if you hit even a single one you can't usually continue until you've tracked it down. Khan Academy has material on all sorts of non-math stuff, like economics and other sciences, and they seem to be gearing the math stuff more towards a younger audience, not an older one, which is probably more important anyways to be honest. smart move, mr.Khan, smart move.
I think they're doing a great job grouping and ordering their videos according to common standards. I find myself jumping around trying to figure out what I need to learn less often.
I agree that KA is not a perfect substitute, but one thing I will say is that there is a huge difference in the intrinsic motivation behind someone that wants to watch a series of KA videos vs. someone that is told they must take a class.
As we know, classrooms are not perfect either. But if we could get classroom education and KA education to both be better (after all, some university courses are shown on vidcast and sections are replaced by digital discussion forums), then I do think KA could be a very viable alternative for the traditional classroom. Instead of telling a student s/he needs to learn calculus, you wait until they recognize the need for it in their daily lives and take the class.
Honestly if you don't need it, it really might not be helpful. I can't say I've used any skills from many classes (calculus, accounting, earth science, etc.) other than being able to recount obscure but interesting facts. For those that say well my inherent problem-solving skills have been influenced by the logic of these classes, well they really haven't (and I had great teachers). Everything I learned about framing and solving a problem I learned from real world work experience as a consultant (why schools didn't find a way to teach this to me is a different argument). And in case it sounds like it, yes I do believe I'm more in the "unschooling" movement.
36 comments
[ 3.4 ms ] story [ 82.6 ms ] threadAFTER EDIT: I'll mention some of the changes that Colin kindly asked for news about. As a lot of Hacker News regulars know, several of the Khan Academy developers regularly visit Hacker News. Some of those developers have interacted specifically with me both on-forum and by private email to ask sincere, action-oriented questions about how Khan Academy mathematics lessons can improve. One suggestion I made a couple years ago was for Khan Academy to arrange its lessons in a "knowledge space" like the competing commerical online program ALEKS,[1] which I like very well for my homeschooled children. Another suggestion I made was to make sure that the online work was more of the nature of "problems" rather than "exercises,"[2] and the Khan Academy developers have come up with some very innovative online mathematics problems to ensure that learners don't merely passively watch videos but actively learn new mathematics.
Simply put, I think Khan Academy is iterating successfully. In many respects, I am in direct competition with Khan Academy as a mathematics instructor who teaches in-person lessons for which fees are billed, but I am happy to let my clients know about the existence of Khan Academy, happy to see my own children use it for a lot of their own mathematics learning, and happy to see schools adopt Khan Academy as they "flip the classroom." I am very much a both-and kind of guy when it comes to mathematics instruction--I like to mix and match a lot of programs--but I think Khan Academy has a useful place in the mix.
[1] http://www.aleks.com/
[2] http://www.epsiloncamp.org/ProblemsversusExercises.php
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I still think it has value, and I hear very similar concerns expressed when the subject in mentioned in my hearing when I'm out and about doing in my school talks. Maybe it has changed, maybe it hasn't changed enough.
Maybe it has - perhaps you should document your experiences for us.
"the study of how to ... pass mathematics exams."
Some .edu folks think its hilarious to use math as a gatekeeper although the grads will never use it on the job... jokes on them if someone hacks that system and bypasses their artificial little gatekeeper.
Is it really that entertaining that everyone cavorts around such a useless subject? There's a saying that in a war between kings, the battlefield is the farmers' trampled corn.
1) Give every family a parental-control iPad if they don't have a computer at home.
2) Deliver the lecture part of each class via an engaging multimedia presentation bought from a marketplace of these things. Instead of a boring teacher or one teacher teaching 20 students, a great presentation would be repeatable by thousands and millions of students, and every year can be improved. It could also be critiqued and fact-checked by reviewers in the market. The market would update them like textbooks.
3) The next day, the school day would start later, so kids could get a good sleep (health and cognitive reasons) and a good breakfast (nutrition reasons), the latter can be delivered in school, for kids to come on time and socialize.
4) After breakfast and homeroom, the Tests would begin. Every day, the tests would be testing for real knolwedge that would be obtained from the previous day's presentations. They would test two levels: minimum adequate comprehension, and solid comprehension. This would replace homework and the method of solution could also be analyzed.
5) Students who did not score high enough to demonstrate minimum comprehension for that day would be quickly identified by their test scores. They would be scheduled for smaller REMEDIAL classes later that day for that subject. That means the main time they spend with a teacher would be more individualized and tailored to where they are struggling as actually determined by their attempts on the tests.
6) For a student who scores well on all or most tests, the day would be quite pleasant and free of remedial classes. They could do any number of things - and if they have to remain in the school, fine - there will be plenty of entertainment and socializing there. That is their reward for learning and comprehending the previous day, proportional to how many subjects they were able to do.
7) Right after the Tests, all students would still have to take classes which aren't only comprehension focused such as Gym and Debate etc. But there are very few of those.
8) The students would themselves choose how to schedule their time to study for the next day. It could be a study session with friends or a private study session. No one would force them to sit through a lecture.
Benefits:
1) Insane amounts of homework from multiple classes are replaced by Tests which are already scored in terms of difficulty, cognitive load, and how much time they take. So the school is fully aware of how much load they are putting on the students. Currently there is homework creep.
2) Instead of struggling privately and spending money on private tutors many low-income families can't afford, the students would get individual attention after their performance was analyzed in a Test setting. Home would be reserved for a lot more passive learning, mimicking the real world.
3) The kids would have freedom and responsibility to set aside their own time to learn, and incentive to learn that they do not have when told to sit down and shut up for 5 hours a day. It would also lower incidents of diagnosis of ADHD, especially in restless younger boys in grades where psychological development and aptitude feedback is crucial to get right.
4) Lectures are boring and too variable in quality. An uncommonly great teacher may only be able to reach 20 students while the rest get mediocre or bad lectures. There is no reason to keep things this way when technology can replace lectures with professionally produced multimedia at home. Animations and stories teaching algebra and calculus for example.
5) If you go to the bathroom or zone out during a lecture, you are faced with big dilemmas, having to copy notes from classmates. Here you just rewind. A kid can even pause the lecture for 2 hours and go play basketball or watch another one, finishing this one when they want. Truancy would be greatly red...
I also think an effort should be made to bring in volunteer teachers from the professional community, but that's a harder task.
http://en.wikipedia.org/wiki/Flip_teaching
The basic assumptions behind teaching in developed economies are still that of the industrial revolution. The system is good at producing graduates with basic literacy, simple math skills, will accept instructions with little or no question and sit or stand still for long periods of time doing the same thing over and over. It's not designed to do much more than that.
The industrial nature of the system even borrowed from Henry Ford's assembly line. Students pass from one stage to another, and are exposed to a subject which they learn, are then tested on and then never see that material again or understand how it fits into the bigger picture.
The only thing testing does is generate crude metrics. Tests don't actually measure anything other than the student has been able to pass that test. Sadly, when you are dealing with a very high student to teacher ratio, you have no choice but to rely on testing. There is no way around that. The higher the student to teacher ratio, the lower the ability of an educational system will have to actually educate or be able to determine if a student as been educated.
Khan Academy doesn't address these issues, and Gates or whoever is saying it will, will be disappointed. But it is an interesting experiment that may contribute to something that does.
The only attempt I know of that goes into that direction is BrainRush [2], a startup by one of the developers of the Pong game.
[1] https://en.wikipedia.org/wiki/Forgetting_curve
[2] http://www.brainrush.com/
To your specific points:
1) Budget concerns make this prohibitively expensive for the majority of school districts. School districts frequently devolve the expense of providing classroom items on to teachers, or parents. Without an increase in funding, this item is a non-starter. Unfortunately, thanks mainly to conservatives (whether they call themselves "Republicans" or "Democrats") in our government, providing extra funding is unlikely.
2) There are a wide variety of online schools (actual, "accredited" schools run by various public school districts or private companies contracting with state Departments of Education) already. Having some experience in this area (indirectly), I'm not convinced it's a good idea or approach for students who aren't already highly capable and motivated.
3) The start time problem may be solvable. However budget issues arise here, too. Starting later means shifting times for running lights and A/C, possibly during peak usage in some areas of the country, and that has to be accounted for. So all the budgetary problems that conservatives impose would apply for this as well. Throwing in school-provided nutritional breakfasts would just exacerbate the issue.
4) Testing in general is an inadequate, poor, and generally poorly implemented way to measure knowledge. The very bright will either be bored to tears (and receive poor marks) or "game" the test with good test taking skills. Everybody else will just have increased stress with little benefit.
5) Again, budget issues would make this a huge problem to implement. Thank conservatives running our government for that.
6) No comments; I'm neutral on this.
7) See: budget concerns. Gym/P.E., debate, home economics, shop, art, music, etc. are all under retrenchment because conservatives in our government refuse to provide the resources to make these things happen.
8) See my comments from (2); this is great in theory but simply put the majority of students are either not capable of or unwilling to utilize such freedom successfully.
Charter schools are little better than vehicles for the enrichment of private individuals at the expense of the public treasury. They're thinly veiled means for a transfer of tax dollars to connected and wealthy individuals, and they're a non-starter, as far as I'm concerned. They don't belong in a serious discussion about reform of our education system.
Private schools aren't a solution for the majority (the vast, overwhelming majority) of the public, who can't afford tuition. Even if they were, there is scant evidence that private schools provide better education than public schools when compounding factors (e.g. selecting for economic or other privileged status) are taken into account. It's easy to have high graduation and college/Ivy League acceptance rates when one selectively refuses to admit the most disadvantaged students.
My technique is to prepare slides with a script and then record myself presenting them. It's not nearly as nice, but at least I can do it.
[1] https://www.youtube.com/watch?v=UvMgtcgq34k
However, that criticism doesn't have much power for me, based on how I understand I learn. I like to learn from two ends; one, from above, with an overview of the space, so I know where the next bit fits in. And from below, with concrete examples - yes, mechanical examples - of the individual steps. I infer the deeper structure of what's being taught as more and more variants of the mechanical process are shown.
What you are seeing is a blowback against the traditional classroom. Our school systems are so poorly run, that a guy with no teaching experience can create something insanely popular in the education industry.
Why didn't a classroom teacher do what he did? Because our system does not reward teacher innovation and trying new things.
Our system rewards obedience and conservatism.
Our teachers (like our students) are taught to conform and do what the admins want. Those that don't are punished, sometimes directly, but most often indirectly.
Poor salaries and bad working conditions mean the best and brightest do not become classroom teachers. Or, talented people who are classroom teachers bolt as soon as something better comes along.
There are some high quality people who teach, but they are browbeaten so often that it turns the young, dynamic person into a cynical and slightly depressed professional.
I don't have all the answers, but I do know it isn't more of the traditional classroom.
Because most people don't give a shit? Why doesn't every STEM graduate have the same ambitions as Elon Musk? The reality is that most people are too chicken shit to have their own interests and to pursue them in a serious way. You think throwing money at things solves problems?
A reward could just as well be encouragement rather than being looked down on or be perceived as arrogant.
Quite often "root learning versus understanding" is the difference between being able to show and demonstrate you know your stuff ("root learning") and not being able to show or demonstrate it, but you think you kinda know it ("understanding").
[1] http://math.berkeley.edu/~wu/wu1999.pdf
[2] http://www.aft.org/pdfs/americaneducator/fall1999/amed1.pdf
Perhaps I missed something or misread it, but that wasn't my takeaway. Rather, it seemed he was expressing that mechanics doesn't, on its own, directly lead to understanding (measurable by ability to apply the tools to novel, to the student, problems/situations). Given that he also endorsed Khan Academy in this same article it seems he has no problem with it developing mechanical understanding as a complement to the understanding needed by practitioners (scientists, mathematicians, engineers, etc.).
The challenge is that simply getting the right answer, especially in terms of arithmetic (one small piece of math), can mask how well a student understands the underlying concepts and whether s/he can flexibly apply the concepts.
Here's a great video on that topic:
And here's a great video that shows what a participatory classroom with a great teacher can achieve:If this is the standard, then we can also say
The trouble with Ivy League Universities
Frankly, Sal Khan is better than all of my previous math teachers combined. (sorry guys and gals, but it's probably Alabama's fault anyway).
Teaching advanced math, on the other hand, is really hard to do when you're interacting with a person because there are so many pitfalls and if you hit even a single one you can't usually continue until you've tracked it down. Khan Academy has material on all sorts of non-math stuff, like economics and other sciences, and they seem to be gearing the math stuff more towards a younger audience, not an older one, which is probably more important anyways to be honest. smart move, mr.Khan, smart move.
As we know, classrooms are not perfect either. But if we could get classroom education and KA education to both be better (after all, some university courses are shown on vidcast and sections are replaced by digital discussion forums), then I do think KA could be a very viable alternative for the traditional classroom. Instead of telling a student s/he needs to learn calculus, you wait until they recognize the need for it in their daily lives and take the class.
Honestly if you don't need it, it really might not be helpful. I can't say I've used any skills from many classes (calculus, accounting, earth science, etc.) other than being able to recount obscure but interesting facts. For those that say well my inherent problem-solving skills have been influenced by the logic of these classes, well they really haven't (and I had great teachers). Everything I learned about framing and solving a problem I learned from real world work experience as a consultant (why schools didn't find a way to teach this to me is a different argument). And in case it sounds like it, yes I do believe I'm more in the "unschooling" movement.