New opportunities for encouraging higher level mathematical learning by creative use of emerging computer aided assessment

Abstract

This article defines ‘higher level mathematical skills’ and details an important class: that of constructing instances of mathematical objects satisfying certain properties. Comment is made on the frequency of higher level tasks in undergraduate work. We explain how such questions may be assessed in practice without the imposition on staff of an onerous marking load. Included are examples which have been implemented on a free computer aided assessment system. Lastly we report an investigation of students’ reactions to these questions and discuss their design and impact.

Acknowledgements

The author would like to thank Joe Kyle, Grant Keady, John Mason and Anne Watson for valuable discussions and encouragement. Also thanks to the students who tested the questions for their diligence and permission to quote their comments. Introduction of the AIM system described in this project has been funded in part by a grant from the Learning Development Unit at the University of Birmingham, UK. The author gratefully acknowledges Dr Mike Finney, School of Mathematics and Statistics Computer Support Officer, for technical support.

Notes

*^{Maple V} and ^Maple are registered trademarks of Waterloo Maple Software.

^†The working system may be veiwed at http://mat111.bham.ac.uk/ or may be downloaded from http://aim.shef.ac.uk/aimsource/. There is also a JISC mailing list, aim@ jiscmail.ac.uk, for staff and developers. See http://jiscmail.ac.uk/lists/aim.html