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Yes, The Khan Academy is the Future of Education

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Re: Yes, The Khan Academy is the Future of Education

#11

Post by solipsist »

psykotic wrote: post #10
solipsist wrote: post #5

I haven't exactly been as amazed by the Khan Academy as everyone else has. After watching a few videos, I decided that we need to focus more on the material that we are teaching - rather than the methods we go about doing it. They will obviously go hand by hand, but in my opinion the material that we are teaching is our biggest weakness and therefore needs the most reform. A video that everyone should take the time t…

That too much emphasis is put on manual computation is obvious. But taking the opposite tack is an overcorrection. Computing and solving by hand is a font of endless insight in mathematics at any level and should not be left to computers. Take an elementary matter such as convergence of infinite series. If you've never hand-computed a truncated power series for e^x term by term and noted its rapid convergence rate fo…

If you were going to major in math, then you may need to go back and learn all the basic calculations in order to build on them. But for anyone else (even scientists), the solution I mentioned above should be enough. Your example of e^x is not closely enough tied to a real world application; therefore it's hard for me to work with it.

Re: Yes, The Khan Academy is the Future of Education

#12

Post by psykotic »

solipsist wrote: post #11
psykotic wrote: post #10

Earlier quoted context omitted.

That too much emphasis is put on manual computation is obvious. But taking the opposite tack is an overcorrection. Computing and solving by hand is a font of endless insight in mathematics at any level and should not be left to computers. Take an elementary matter such as convergence of infinite series. If you've never hand-computed a truncated power series for e^x term by term and noted its rapid convergence rate fo…

If you were going to major in math, then you may need to go back and learn all the basic calculations in order to build on them. But for anyone else (even scientists), the solution I mentioned above should be enough. Your example of e^x is not closely enough tied to a real world application; therefore it's hard for me to work with it.

> If you were going to major in math, then you may need to go back and learn all the basic calculations in order to build on them.

The way it actually happens is that once you start majoring in mathematics, you will rarely see any computations. It's entirely possible to take a linear algebra course for mathematicians without ever row-reducing a non-trivial matrix by hand.

Back to teaching kids. If you take a constructivist approach to learning then computing by hand simply cannot be avoided. You'll never have a student notice on their own that, for example, you can quickly multiply x by 9 by subtracting x from 10x unless they tinker with numbers directly. You come across patterns like that by doing the tedious work the hard way and looking for short-cuts.

Re: Yes, The Khan Academy is the Future of Education

#13

Post by solipsist »

psykotic wrote: post #12
solipsist wrote: post #11

Earlier quoted context omitted.

If you were going to major in math, then you may need to go back and learn all the basic calculations in order to build on them. But for anyone else (even scientists), the solution I mentioned above should be enough. Your example of e^x is not closely enough tied to a real world application; therefore it's hard for me to work with it.

> If you were going to major in math, then you may need to go back and learn all the basic calculations in order to build on them. The way it actually happens is that once you start majoring in mathematics, you will rarely see any computations. It's entirely possible to take a linear algebra course for mathematicians without ever row-reducing a non-trivial matrix by hand. Back to teaching kids. If you take a construc…

> You come across patterns like that by doing the tedious work the hard way and looking for short-cuts.

The thing is that you come across short-cuts like those on the larger and broader concepts as well. Tinkering around with numbers is great, but perhaps tinkering around with concepts is even better.

There would be downsides to the reform. Students may not know that notice 9x = 10x - x as a calculation shortcut, but they then again, they would never have to calculate 9x past a certain value of x. Computers can easily do that - let the students discover that x needs to be multiplied by 9, and then the let the computer do the straightforward math.

Re: Yes, The Khan Academy is the Future of Education

#14

Post by enry_straker »

kkleiner wrote: post #9
mey wrote: post #2

The Khan Academy is A Future of Education. Talented educators (non-traditional and traditional) and technology are going to keep coming together in new and interesting ways. There will be lots of failures, but Khan Academy will not be the only success. The article doesn't mention things like MIT's effort in this field that predate Khan's efforts etc.

The article doesn't mention MIT, but it does mention other efforts such as Mathletics. What makes Khan Academy and Mathletics stand out from MIT is that they are MUCH more than just a collection of videos. Khan and Mathletics increasingly represent entire ecosystems with points systems, competitions, tracking of your performance, and so on. That is why Khan exemplifies the future of education vs simple collections of…

MIT's Open CourseWare project or OCW can hardly be described as a simple collection of videos. Each and every course at MIT has put up all their educational documents including slides, exercises, tests, audio, video, schedules etc for free. Many courses also include video and other multimedia artefacts.

The key differentiator is that these are aimed at under-grad and grad students and are simple conversion of what happens in a course, where the internet is only incidental.

Khan Academy videos are aimed primarily at school students and are much shorter, more focused and completely based on the internet. The tests are geared for online testing, the metrics collected are then displayed online etc.

Re: Yes, The Khan Academy is the Future of Education

#15

Post by psykotic »

solipsist wrote: post #13
psykotic wrote: post #12

Earlier quoted context omitted.

> If you were going to major in math, then you may need to go back and learn all the basic calculations in order to build on them. The way it actually happens is that once you start majoring in mathematics, you will rarely see any computations. It's entirely possible to take a linear algebra course for mathematicians without ever row-reducing a non-trivial matrix by hand. Back to teaching kids. If you take a construc…

> You come across patterns like that by doing the tedious work the hard way and looking for short-cuts. The thing is that you come across short-cuts like those on the larger and broader concepts as well. Tinkering around with numbers is great, but perhaps tinkering around with concepts is even better. There would be downsides to the reform. Students may not know that notice 9x = 10x - x as a calculation shortcut, but…

Maybe we're talking past each other. Could you explain your goals with this curriculum? Are you trying to reduce the teaching of mathematics to a bare minimum so people can get on with what you see as more essential subjects?

My stance is that mathematics is first of all useful in the small for normal people. Everyday arithmetic, basic accounting, that sort of thing. But beyond that we need to teach mathematics for the same reason we teach art, music and literature. For achieving this goal, even if what we aim for is an appreciation of general principles, I was arguing that properly directed hand computation and concrete problem solving plays an important part. Concrete tinkering engages your brain in a complementary way to reflecting on nakedly abstract principles.

Re: Yes, The Khan Academy is the Future of Education

#16

Post by dwc »

As an autodidact interested in exploring more mathematics, of course I learned about Khan Academy. One look and I was impressed, but that didn't last long. Though the videos are well done all around, there's no clear curriculum to follow. Or if there is a curriculum, it's not obvious. Instead, I have a bazillion videos to choose from. Which videos depend on knowledge in other videos, and which ones can be done in parallel? No idea.

Education's past is a series of textbooks (plus supplemental info and exercises), providing a clear path to learning. Khan Academy, such as it now stands, is a video analog of textbook chapters as discrete units all in an unorganized pile. Until more is done in the neglected areas, Khan Academy will remain an extremely valuable resource, but not a curriculum. Even if/when these missing bits are done this will only be the future of delivery of fairly traditional materials.

The real future of education is a computerized personal tutor that provides individual assessment, guidance, alternate explanations where comprehension lacks, encouragement to pursue natural ability and enthusiasm, etc. That's pretty ambitious, but not at all inconceivable. We're close enough to being able to achieve it that we should hold up this ideal goal so we know the right direction as we build the pieces.

Re: Yes, The Khan Academy is the Future of Education

#17

Post by dagw »

solipsist wrote: post #8
vidar wrote: post #6

Earlier quoted context omitted.

Thats a tricky thing to do though, where do you draw the line?

That's a good question. We need to keep in mind that computers are never going to go backwards in innovation. Once a computer is capable of some calculation, students will never need to have to do it by themselves again. However, they will still need to know how to interact with that calculation and understand the variables/relationships in order to set up the calculation. Where do you draw the line? Instead of just…

Once a computer is capable of some calculation, students will never need to have to do it by themselves again

However it is important that they know enough to check if the answer they get is at least reasonable and probably correct. So even if they can't solve the problem exactly they really should know how to show that the answer must be between 1/sqrt(2) and 1, for example, so that they know they made a mistake when the computer tells them the answer is 0.3475.

Re: Yes, The Khan Academy is the Future of Education

#18

Post by declancostello »

dwc wrote: post #16

As an autodidact interested in exploring more mathematics, of course I learned about Khan Academy. One look and I was impressed, but that didn't last long. Though the videos are well done all around, there's no clear curriculum to follow. Or if there is a curriculum, it's not obvious. Instead, I have a bazillion videos to choose from. Which videos depend on knowledge in other videos, and which ones can be done in par…

the video linked above does show the view from the web app part of Khan academy which has a map showing the progression from one topic to the next.

As far as I could see each set of questions allows you to watch associated videos and also links to the prerequisites.

I'll go and investigate :) brb

Re: Yes, The Khan Academy is the Future of Education

#19

Post by wallflower »

dwc wrote: post #16

As an autodidact interested in exploring more mathematics, of course I learned about Khan Academy. One look and I was impressed, but that didn't last long. Though the videos are well done all around, there's no clear curriculum to follow. Or if there is a curriculum, it's not obvious. Instead, I have a bazillion videos to choose from. Which videos depend on knowledge in other videos, and which ones can be done in par…

> The real future of education is a computerized personal tutor

In Neal Stephenson's "The Diamond Age", a plot device (not central), is The Young Lady's Illustrated Primer. It is an adaptive AI tutor. To realize TYLIP, hard AI problems will need to be solved. Yet, it is possible the iPad is a big step towards a simpler Primer.

"TYLIP is...a book that is powered by a computer so advanced it’s almost magical, and it teaches children everything. It does this through a fully interactive story. It teaches you how to read, how to do maths, it teaches you morals, ethics, even self-defence. ‘Diamond Age’ is a very entertaining read, mainly because of the TYLIP."

http://en.wikipedia.org/wiki/The_Diamond_Age

http://mssv.net/2006/05/01/the-young-ladys-illustrated-prime...

Re: Yes, The Khan Academy is the Future of Education

#20

Post by solipsist »

psykotic wrote: post #15
solipsist wrote: post #13

Earlier quoted context omitted.

> You come across patterns like that by doing the tedious work the hard way and looking for short-cuts. The thing is that you come across short-cuts like those on the larger and broader concepts as well. Tinkering around with numbers is great, but perhaps tinkering around with concepts is even better. There would be downsides to the reform. Students may not know that notice 9x = 10x - x as a calculation shortcut, but…

Maybe we're talking past each other. Could you explain your goals with this curriculum? Are you trying to reduce the teaching of mathematics to a bare minimum so people can get on with what you see as more essential subjects? My stance is that mathematics is first of all useful in the small for normal people. Everyday arithmetic, basic accounting, that sort of thing. But beyond that we need to teach mathematics for t…

One of my goals with this curriculum is to make teaching mathematic more efficient. This does not necessarily mean teaching a bare minimum. Rather, students should be taught a great amount more at a younger age. In fact, I think mathematics is probably one of the most essential subjects out there. Unfortunately, the way it is taught now is inefficient and gives it a bad name.

The rudimentary basics are important for everyone, and mostly those who will not pursue math-related careers. However, it is the content that is taught after the basics (middle school and high school curriculum) that could be spent on more advanced areas with less calculation work.

I feel embarrassed expressing all of these ideas with little background to support them. I'm sure you are a lot more knowledgeable on this subject than I am, so thanks for taking the time to acknowledge to my arguments and discuss them with me. ;)

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