Algebra on Computers
A couple of interesting updates today from Chris Sangwin at Birmingham University.
Anyone who’s ever done any maths on a computer involving concepts as advanced as fractions will be familiar with the difficulty in inputting or outputting mathematical expressions, hence such notions as Donald Knuth’s TEX and MathML. Although maths should lend itself to computer based assessment (Gödel’s incompleteness theorem notwithstanding, things are generally right or wrong), these input/output issues soon get in the way. Moodle’s splendid TEX filter does much to help with the output side of things, although even this doesn’t have the same WYSIWYG functionality teachers or students today perhaps expect. Chris has co-authored a paper which explores some of the input issues in more detail.
To help with this, Chris and Alex Billingsley have produced DragMath, a rather nice little Java applet which lets you drag and drop a whole host of mathematical symbols around, and then produces code in a format which computer algebra systems like Maxima and Maple, or LATEX or MathML can interpret correctly. Very nice work, and better still, Open Source, with the project over on Sourceforge.
Chris’s STACK project also continues development. STACK is an online assessment tool for mathematics, with a computer algebra system, in this case the open source, and very splendid, Maxima, running in the background. Thus, Chris has an assessment system which understands matematics, and so questions like “Give a fraction equivalent to 1/4″, and “Factorise x2+5x+6″ become things which can be marked automatically without having to type in semi-infinite lists of alternative expressions.
There’s been attempts at getting Moodle and Stack to talk since, I think, Moodle 1.5 in Spring 2005, but whilst I played with this I never managed to get it working. The future of STACK looks like being as a fully integrated Moodle module, together with some support for more intuitive, interactive interfaces such as DragMath above, and the java based open-source interactive geometry tool GeoGebra.