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Excercises, randomly generated and automatically checked

asked 2013-02-01 03:40:23 -0500

MvG gravatar image

I've been authoring excercise questions for students using Maple T.A.. These questions are randomly generated, and answers checked online, which gives immediate feedback to students. Students like this service, but I as an author was severely annoyed by the workflow, and thought that it should be possible to achieve something better using Sage.

Is there any project underway which attempts to use Sage to generate questions and check answers in a web-based setup? If so, how mature is it?

If you want an example question, I'd be particularly interested in a question asking students to find an orthogonal basis for a vector space spanned by a given set of vectors. As that basis isn't uniquely defined, a fixed answer won't work, so the provided answer has to be checked using custom code. As the dimension of that vector space might vary between randomizations, a fixed input form doesn't seem a good idea, so I'd prefer either some JavaScript tool to manually adjust the number of vectors in the HTML page, or some way to enter a set of vectors as a single expression. The latter is the approach I currently take with Maple T.A., but it requires students to not only worry about their computations but also about the syntax for entering the results. And it raises the question of how to restrict the set of possible inputs, as executing arbitrary user-entered Python code would be a road to disaster, unless some reasonable sandbox were available.

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What is an "excercise" ? :-)

Bétréma gravatar imageBétréma ( 2013-02-04 02:06:22 -0500 )edit

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answered 2013-02-01 06:15:50 -0500

kcrisman gravatar image

The canonical answer about open source randomly generated exercises is WeBWorK. There are some WeBWorK problems which use the Sage cell server to generate stuff on the fly, and the infrastructure is all there for a lot of interaction back and forth. But what you are looking for is probably done best through them, using Sage to do certain things for them (such as compute the types of things you're looking for). Certainly nontrivial problems of the type you are describing need some finessing, but I think WW is flexible enough for this.

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And the project is certainly mature, though its GUI is somewhat dated. Volunteers welcome :)

kcrisman gravatar imagekcrisman ( 2013-02-01 06:16:33 -0500 )edit
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... and there is work embedding Sage into webwork problems: https://groups.google.com/forum/?fromgroups=#!topic/sage-edu/0L-YwBaoJTY

benjaminfjones gravatar imagebenjaminfjones ( 2013-02-01 08:05:55 -0500 )edit

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Asked: 2013-02-01 03:40:23 -0500

Seen: 218 times

Last updated: Feb 01 '13