The Learning
of Linear Algebra Concepts: Instrumentation of CAS Calculators
Sepideh Stewart
sepideh@math.auckland.ac.nz
Michael O. J. Thomas
moj.thomas@auckland.ac.nz
Mathematics
Auckland University
New Zealand
Abstract
While a relatively small group of researchers internationally has addressed
some of the problems in the learning of linear algebra, including the use of
technology, there are still many problems for students. Many of them find a
number of aspects of linear algebra difficult to learn and often seem to prefer
to engage in procedural manipulations rather than a study of the underlying
concepts and ideas. At Auckland University CAS calculators have in recent years
been made available to beginning students of linear algebra. This research considered
the reactions of a group of these first year university students to the use
of the computer algebra system (CAS) calculator in their learning of linear
algebra. This was the first time that most of these students had used the CAS,
and so we considered issues associated with their initial instrumentation of
the CAS and their attitudes to using it in their learning. We found that the
cost of the technology is an issue preventing many from obtaining it, and that
those few students who did choose to purchase and use the CAS did not often
use it to improve understanding of conceptual ideas. Generally they only used
the CAS procedurally, usually employing it to check answers or to perform single
step direct calculations to calculate, for example a determinant, or an inverse,
of a matrix. Our research supports the view that instrumentation of CAS calculators
does not occur naturally or spontaneously, even when students desire to integrate
the technology. We infer that it is not enough for lecturers to simply be using
the technology but that its use needs explicit and sustained attention.
