Comment by aik | Hacker News Reader

Comment by aik | Hacker News Reader

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!

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:

http://sagemath.org/

sympy would be another alternative--it's light, it's python, but has a web interface and has a very active community.

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 :)!

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.

Or they just want to test that they can reduce a fraction? This was a common requirement when I was in primary school.

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.

I think they would assume that if they had watched the lectures. I can't recall a single one where the final answer wasn't reduced.

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.

I agree, and in a lot of cases I find that to be a sad truth instead of acceptable.

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!

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