Numbas

Numbas is an open-source system developed by the e-Learning Unit of Newcastle University's School of Maths and Stats.

It creates SCORM-compliant exams which run entirely in the browser.

Background

Our main goals for Numbas were for it to be:

Scalable, reliable and accessible to a broad range of users.
Good at maths.
Good-looking and easy to use.
Used by question authors who aren't experts.
A modern replacement for the old commercial system which won an award at e-assessment Scotland 2010.

It is also:

Implemented entirely in client-side javascript - requires no plugins, no installation on client's machine, no communication with servers.
Can be run on almost anything that has a web browser:
IE8+, Firefox 3, Chrome, Safari, Opera, iPhone, Android, etc.
Interacts with LMSs such as Blackboard and Moodle through SCORM. Very detailed session data are recorded.
Extensive support for questions of a mathematical nature; answers to questions can be mathematical expressions.
Questions can be fully randomised.
Mathematics display is pure $\LaTeX$ , using MathJax.
Rich content such as videos, diagrams, interactive graphs easily added.
Questions are written using simple markup with any text editor.
Easily extensible.

Numbas contains a symbolic algebra system written entirely from scratch in Javascript.
This allows the evaluation of sophisticated expressions as answers to questions.
It also has a sophisticated pattern-matching simplification system, fully under the author's control, to improve presentation.
Expressions are converted into LaTeX and displayed immediately as the student types.
Warnings for invalid input are also displayed instantly.
This system is available for projects other than Numbas.

Numbas exams are distributed on DVDs to all new maths undergraduates at Newcastle University. The exams run on Windows, Mac and Linux with no installation.
If you don't need to record scores, exams can be uploaded to the web and will function fully with no server configuration. Ideal for revision exercises.
Thanks to SCORM 2004, Numbas exams can be uploaded to Blackboard 9.1+ and will automatically save scores to the Grade Center.
Software from Newcastle's OLAF project provides a locked-down environment for invigilated exams.
As scalable as anything can be, because it all runs on the client.

Download and extract Numbas package: contains source files and Python scripts to compile exams.
Write exam: plain text file in a JSON-like format, with Textile/HTML for content markup. Shouldn't be any harder than writing a LaTeX document.
Compile exam: creates directory or zip file containing standalone exam. Ready to run straight-away.
Upload to LMS for session tracking, or run standalone.

jQuery - jquery.com - page manipulation, UI.
Sarissa - sarissa.sf.net - cross-browser XML support
MathJax - mathjax.org - maths display \[ \begin{aligned} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned} \]
JSXGraph - jsxgraph.uni-bayreuth.de - interactive graphs and geometry

Adaptive feedback and marking schemes, controlled by exam author.
More question types.
Make more of the really clever code usable by other projects.
Numbas will be used for every first and second year maths module at Newcastle from 2012.