Good stuff -- the simplification of the code is exciting for sure and is bound to encourage more to join to create more problems (it has for me!)
One question/problem/concern: Just for fun I tried out the "Linear equations 1" problem section.
So I just got the problem "Solve for x: 9x = 6". Naturally I could answer 2/3 and would expect a happy face, however I decided to answer 6/9, also a true answer, to try the system out. I was received with a sad face (incorrect answer). But, why? The solution is actually true -- it's just missing the artificial target the website has set. The site doesn't explain that it wants the lowest denominator (just "Solve for x"). I would think this to be misleading -- what do you think? How could the proper lesson be enforced here? How and why should students assume 2/3 is right and not 6/9? There's a danger here of students looking for the answer the system wants (extrinsic motivator) rather of what they have found to be right and then denied the satisfaction.
I would expect a happy face with 6/9. It seems to me that the problem should allow multiple answers -- or for the goals of the lesson to be more detailed (and perhaps include an explanation/recommendation after the fact of what the problem is really asking for).
We're very aware of this kind of issue; don't worry. We're currently working on A) displaying information to let a user know what kind of format an answer requires (for the problem in question, we require a reduced fraction written as 'A/B') and B) providing more specific feedback than just 'wrong' or 'right' for cases like this when an answer can be mathematically correct but not accepted for the specific problem. Thanks for pointing this out and reminding us of its importance!
Thanks for the response. B) sounds great -- I'll be very curious to see how it's implemented!
A critique of the common school system is that it encourages simply giving the answers the system seeks, rather than a healthier and more realistic method of encouraging exploration of problems and spaces and perhaps guiding the student along their journey of discovery (and as a result encouraging innovation, creativity, curiosity, etc.). So I definitely would love to see the problems go beyond this!
As an afterthought: I imagine teaching requires these sort of innovative abilities as well. KhanAcademy seems to work fairly well as it is, however there are always more, different and better answers to how learning outcomes can be improved -- they just need to be explored. (Isn't it funny how KhanAcademy is constantly in the spotlight to be the best -- I could imagine the pressure :)!
What would be cool is if you guys integrated Mathematica into Khan Academy. There is that new document format they introduced. For math it would be super useful to have the ability to really play with formulas directly in Khan Academy.
Mathematica may be overkill -- I suspect they'd just need something for basic symbolic manipulation, to reduce answers. In any case, a web-based mathematics system already exists; Sage can be run in a browser, and it integrates a number of useful mathematical features with Python:
For that kind of problems you could accept any answer that reduces to the expected one, after accepting it you could then show its reduction (going from 6/9 -> 2/3) to enforce the lesson.
That way it would only show a sad face if the fraction entered is plain wrong.
I completely agree -- and I could easily understand that someone would assume that's what is being asked, but would a child assume that (never being told that is the goal)? Should they have to assume that? I don't see why -- that seems to only "schoolify" them. Giving students incorrect answers only in order to conform them to the workings of the system is potentially damaging.
If they truly aim to teach math and not, say, engineering, then they should not be teaching students to assume constraints that aren't given in the problem.
It's also usually just a part of the course- like putting units on an answer in physics. You don't have to say so in every problem because you are taught from the start how to make your responses correct. I built a lot of content for a student math problem system and this is what the teacher wanted. 6/9 is an incorrect answer in elementary mathematics.
That may be a bug with that particular problem - you should click the "Report a Problem" link at the bottom of the exercise and copy-and-paste what you just aid here, there. At best the problem isn't being clear that it's looking for a reduced form - at worst we should be trying to exclude other possibly valid answers. Thanks!
We're really proud of the improvements we've made to the framework and how much easier we've made it to add new exercises; if you're interested in contributing, please fork the code at https://github.com/khan/khan-exercises.
We're working as fast as we can to fix any bugs that pop up, so we'd appreciate reporting any issues using the "Report a Problem" link at the bottom of every exercise page.
I'm a 33 year old self-taught software developer, that originally skipped college, who is starting at a local community college this fall with plans to transfer to Illinois for Computer Engineering.
I can't express how much your team and Mr Khan have helped me. In June I spent one to two hours a day watching videos and completing exercises to prepare for my schools placement exam. Starting from the beginning, not only did I refresh my memory but also learned essential concepts that my high school education did not cover. Thanks to your site I placed at the highest level my school will place an incoming freshmen for mathematics.
I'm looking forward to finishing off the last 4 exercises and hope to see more soon. I would be very nervous about both working and going to school full time, during my first year, without Khan Academy helping me get a head start before the semester starts. The high quality lectures and exercises you provide are fantastic for someone like me who may not have the ability to attend office hours and tutoring as much as a conventional student.
Thank you for all that you're doing. It's revolutionary.
Heh yeah, the Mathjax API is rather awful. Tons of separate file requests, configuration is only designed to work in inline script tags, and other ugliness. We've been experimenting with MathQuill - it's way faster and much more lightweight. Unfortunately it doesn't have all the features that we need otherwise we'd switch right away.
I've known about Khan Academy for 6 months to a year. Recently, however, I've started to become MUCH more interested in it. I'm starting to feel a strong pull towards doing things to help people in my local community - specifically through education. I think there's a lot of potential for Khan Academy to play a significant role in that. I haven't started something concrete yet, but wanted to take this opportunity to thank you and everyone else working on Khan Academy for what you're doing. I think it's extremely important and valuable work.
It's great that Khan Academy has a 100x engineer even though some have said they don't need one. This can be a 100-year project and having a solid technical foundation will allow it to become one.
The term "10x" engineer refers to engineers who are 10 times as productive as the average engineer, largely because they create better abstractions, solve metaproblems, and make maintainable code (they generally can't type 10x as fast).
Resig is at least 100x in this department but if you really tally up the impact of JQuery etc. it's probably even more than that. Then there are the (infinity)x guys like Torvalds.
I assume that is referring to Paul Graham's assertion that a good developer isn't just a little better than an average developer, but is instead orders of magnitude better.
If I understand correctly, some templating transforms the <var>s, etc., into JavaScript. Why not write the JS as a regular program? The syntax you have doesn't seem dramatically easier than just ordinary JS and has to be a bit confining.
Is it really that repetitive, or does the code need to be expanded in different ways in different contexts?
Supposing many more problems sets are added, how're they going to manage this proliferation.
My 6yo has been using it for a little while - I've not investigated it deeply but it seems that videos and exercises are quite tightly paired. Having many more exercise [overlapping] sets would make it hard to choose which to do.
It seems the whole system wouldn't work as well with an open access method of submitting exercises, so what's this leading towards?
Aside: I think the scratch pad could be vastly improved. When my 6 yo is doing addition/subtraction trying to write out a number line on the scratchpad is harder for them than doing the sums, it gets in the way. Of course he uses a pieces of paper instead but that seems a bit silly. They could integrate a number line drawing tool, ...
One question/problem/concern: Just for fun I tried out the "Linear equations 1" problem section.
So I just got the problem "Solve for x: 9x = 6". Naturally I could answer 2/3 and would expect a happy face, however I decided to answer 6/9, also a true answer, to try the system out. I was received with a sad face (incorrect answer). But, why? The solution is actually true -- it's just missing the artificial target the website has set. The site doesn't explain that it wants the lowest denominator (just "Solve for x"). I would think this to be misleading -- what do you think? How could the proper lesson be enforced here? How and why should students assume 2/3 is right and not 6/9? There's a danger here of students looking for the answer the system wants (extrinsic motivator) rather of what they have found to be right and then denied the satisfaction.
I would expect a happy face with 6/9. It seems to me that the problem should allow multiple answers -- or for the goals of the lesson to be more detailed (and perhaps include an explanation/recommendation after the fact of what the problem is really asking for).