The Learning of Linear Algebra Concepts: Instrumentation of CAS Calculators

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.