Working algebraically and developing algebraic sense as the first priority– can CAS and interactive geometry help?
Noel Baker Centre for School Mathematics
In most introductory algebra classrooms priority is given to the learning and practising of algorithms like adding like terms, expanding brackets and so on.
This paper will argue that the learning and practicing of algorithms should not be the first priority of the introductory algebra classroom. It will offer an alternative approach that aims to develop a person’s ability to work algebraically and to develop algebraic sense. This is done through engaging students in a sequence of delightful, but simple problems. The problems are best understood by the development of a simple mathematical model, a process from which grows the need for algebraic ideas, relations and operations.
The approach does not downplay the importance of learning and practicing algorithms, but provides a foundation that provides a clear need for doing so and a way of thinking that will have students see algorithms in a different light.
A revolutionary use of a Computer Algebra System (CAS) is employed. It reduces the cognitive demand on the students and allows them to focus on the priorities of the moment as well as allowing access to problems previously not possible. A special interface has been made that makes the use of a CAS no different than using a four function calculator.
Interactive geometry also plays a key role in the approach.
The latest version of this approach was tested in four New Zealand schools during 2005 as part of a Ministry of Education pilot project. The project is investigating the value of CAS and interactive geometry when used from the start of secondary school. The four schools employed the use the special interfaced CAS and interactive geometry on the Casio ClassPad 300.