Using LiveMath as an Interactive Computer Tool for Exploring Algebra and Calculus

Abstract

Many mathematics educators in Singapore secondary schools are aware that The Geometer? Sketchpad, a dynamic geometry software, can be used to explore geometry. But most of them do not know of any computer algebra system (CAS) that can be used to explore algebra and calculus. Traditionally, most mathematicians, scientists and engineers have always used a CAS, such as Maple, to perform symbolic manipulations in order to solve algebraic and calculus problems. However most educators do not see any purpose in their pupils learning a CAS to perform symbolic manipulations, such as factorisation, differentiation and integration, when formal assessments still require them to perform such skills by hand. But with the advance of LiveMath (previously known as Theorist and MathView), an intriguing CAS that provides ? unique user interface that allows one to perform ?atural?algebraic maneuvers even more ?aturally?than one can achieve them on paper?(Kaput, 1992), there is now another way of using a CAS in the teaching and learning of mathematics, i.e., to explore algebraic and calculus concepts. Moreover the capability of LiveMath templates to be interactive even on Web pages opens up an exciting chapter in online mathematics learning. This paper looks at some examples of how educators can use LiveMath as an interactive tool for their pupils to explore algebra and calculus. It also provides some research evidence to suggest that the use of LiveMath for exploring mathematics may enhance pupil learning.