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My thoughts on Wolfram Problem Generator

Luca Belli, Wolfram|Alpha
Posted 12 years ago
Hi everyone,

I would like to briefly present the Wolfram Problem Generator, which I have been working on for the past months. There are two features that I think make it special: the ability to generate unlimited problems and free-form input for answers.



Some problem generators do not make random problems on the fly: in fact, they take problems from a repository (which, even if big, is still finite). By contrast, our system generates a totally new problem just for you. Also, we double-check that we haven't shown it already--in this case, we just show you a new one!

Our free-form input takes full advantage of all the technology created by Wolfram|Alpha. Given a problem to try, you can write your answer in whatever way makes sense to you and we will be able to recognize it each time. For example, for





you can type "2 sqrt(3)", "two times square root of three", "two radical 3" or "2 * 3^(1/2)".

Wolfram Problem Generator was not without its challenges in development. The most challenging aspect of this project was implementing a way to distinguish right answers from incorrect attempts. For example, if your problem is "6 x = 10", Wolfram Problem Generator asks you to simplify your result to "5/3" (or "x = 5/3", or "five thirds", etc.), and not leave the answer as "10/6". Because "10/6" is a mathematically correct answer, we relied on Mathematica's powerful pattern matcher to ensure that the answer really was simplified.

You can try Wolfram Problem Generator if you're a member of Wolfram|Alpha Pro. Right now, we have coverage for six core subjects, with a lot more in the works. Let us know what subjects and what types of problems you'd like to see!

Enjoy!
Luca
POSTED BY: Luca Belli
8 Replies
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I would like to see access to the problem generator be part of owning Mathematica rather than having to pay for it via wolfram alpha.

It would also be nice to be able to have a practice sheet generated that pulls from multiple topics, rather than just a single topic.
POSTED BY: John Parker
Ben Hill
Ben Hill
Posted 10 years ago

I love having this feature but I want to point out some problems. These of course could be user issues. I use Firefox 35.0.1 on Ubuntu 14.10.

Integration by parts is barely working most of the time. It is very difficult to input and answer that Wolfram will either parse correctly or accept. Even if I copy and paste answers from Wolfram itself. Example: Integral (3/4)xcos(5x)

Answer from main Wolfram page: (3/100)(cos(5x)+5xsin(5x))+C

This answer is marked as wrong.

The "Input Interpretation" can be flaky. One time it worsk, next time it shows nothing. This is true of other problem generator pages.

If you check at the solution on the problem generation page. It gives a differently factored answer.
POSTED BY: Ben Hill
Clicking on the link just returns me to the page - should it not take me to a file or something like that ??
POSTED BY: William Stewart
We have fixed the link - thank you for bringing this to our attention. We also added an image you can click on that will take you to the Wolfram Problem Generator.
POSTED BY: EDITORIAL BOARD
The problem generator is a great idea. I have been using it to let my eigth year old soon practicing basic sums and multiplications. I think it would be a great idea to let the user to edit the format of the questions. For instance, the problem generator window would present problems such as multiply 3X4?. However, in some books the questions tend to be more contextual. As an example, my soon is often to solve problems like this:

Draw and complete the multiplication:
1.  Three groups of six bycles.
2. Four bags of six apples,
etc.
In these excercises he must write the operation and give the result. Perhaps, less important, he also draws bycles, apples etc.

The format is rather fixed (number) +groups of+ (number)+( thing). With this format an infinite number of problems may be generated. I mean, let problem  generator to receiving format for questions in addition plug in numbers the way it does.
 
I believe WolframAlpha creates widgets with similar ideas.

Best regards

Jesus
POSTED BY: J Jesus Rico-Melgoza
Dear Jesus, 
Thank you for your feedback! We enjoy hearing how Wolfram Problem Generator is being used, and how we can make it better. 
We are considering your suggestion. We agree - it is certainly important that students practice understanding and solving word problems!

Please stay tuned to see new features in the Wolfram Problem Generator.

Happy holidays,
Luca
POSTED BY: Luca Belli
Eliot Weekes
Eliot Weekes
Posted 10 years ago

This is a fantastic idea.

Just keep working at it, improving it, and keep adding more topics which range all the way to tertiary level. I've been looking for an elegant way to practice integration, series, limits, linear algebra, etc. without repeating text-book questions by rote for a long while. This will help keep things fresh and interesting.

As a tangential suggestion, I recommend extending your billing for Pro subscribers to multiple currencies so we aren't hit with international transaction fees and varying monthly or yearly costs depending on the exchange rate at the time, as well as gradually working on the engine so that we come across those "no step-by-step solution available" occurrences less often. They always make me sad. Otherwise,

Great product!!

Thank you!
POSTED BY: Eliot Weekes
James Wang
James Wang
Posted 4 years ago

It is indeed a great tool of this problem generator - but is it available via api calls?

Thanks
POSTED BY: James Wang
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