About a Computer Algebra Based Online Mathtest

Thomas Wolf, Brock University, Ontario, Canada
and 
Winfried Neun, ZIB, Freie Universitaet Berlin

In the talk the web based online test http://lie.math.brocku.ca/mathtest is
described that
- allows a teacher to compose a test within minutes, 
- offers in total >150 question types from 12 subjects, 
- varies most of the parameters in questions randomly and thus allows students
  to take a test an unlimited number of times each time with slightly varied
  questions, 
- automatically marks the test, stores the mark in a database and sends an
  email to the student,
- allows the teacher to inspect easily all results of a specific test,
- allows students to inspect all outcomes of any test they took,
- is based on the computer algebra system REDUCE and thus accepts mathematical
  input, i.e., it is not a multiple choice test and 
- that is completely free.

A technical problem with computer algebra based tests is that: on one hand it
should be possible for the input to be, for example, x+y or y+x, i.e., input
should be somewhat simplified and put in some canonical form, but on the other
hand simplification is often the content of the question, so (x^2-y^2)/(x-y)
should not be accepted as answer.  In other words a fine-tuned simplification
is necessary.