Computer
Algebra System
LONCAPA works with
the MAXIMA
CAS and the R project systems.
 This allows for problems that check student answers for mathematical properties rather than simply for agreement with a systemprovided answer. For example, the problem depicted on this page has infinitely many correct answers.
 Answer can be checked for exact algebraic equivalence, for example, sqrt(2) is different from 1.41421356..., which a numerical calculation would not reliably reveal.
 MAXIMA can also be used to generate problems, for example, generate algebraic expressions with certain properties.
 R can be used to randomly generate distributions with desired properties.
Some problem examples can be found on the demo page.
The use of a computer algebra system in recognizing equivalent expressions also makes it possible to match a student's response with an incorrect answer that reveals an underlying misunderstanding. These can then be used to trigger automatic, adaptive hints that give students immediate, tailored feedback to address their misunderstandings. Providing students with multiple tries allows them to reflect on this feedback before attempting the exercises again. This option is an important feature of LONCAPA. 
 Justin Gray, Senior Lecturer, Department of Mathematics, Simon Fraser University, Canada 

Contact Us: loncapa@loncapa.org
Site maintained by Gerd Kortemeyer.
Supported by the National Science Foundation under NSFITR 0085921, NSFCCLIASA 0243126, and NSFCCLI 0717790. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Initial funding for CAPA has been provided by the Alfred. P. Sloan Foundation and the Andrew W. Mellon Foundation.

